研究計画書
情報容量制約下の組織内情報共有
グループ別集約と最適線形ガウス公共シグナルの効率比較
研究分野：情報デザイン、組織内の適応と協調、情報容量制約
留学神社 · Drafting a research planResearch plan · Japanese draft and English guide
Research plan
Organizational information sharing under limited information capacity
Efficiency loss from group aggregation relative to an optimal linear Gaussian public signal
Read the complete Japanese research plan first, then use the English guide to understand the topic, literature, methods, and evidence. Consider follow-up questions and changes in assumptions to understand the reasons for the research design, its limits, and the next steps.
留学
神社
Research proposal
Research plan
The main text of this sample is about 12,000 Japanese characters and 14 pages. Its length is a sample supplement: the tool generates the length you set, with a default of 1,200 characters. It uses plain-style Japanese, 10.5 pt Mincho type, and three-line tables. As you read, identify the research question first, then compare the method, preliminary results, and feasibility.
目次
要旨
組織の構成員は、局所的な環境に適応すると同時に、相互に行動を協調させる必要がある。伝達能力が限られた公共情報システムにおいて、どの情報を残すべきかは組織設計の基本的な問題である。本研究は、適応と協調を組み込んだ線形二次の組織モデルにおいて、相互情報量で測った情報容量が等しい二種類の公共シグナルを比較する。一つはすべての状態を利用できる最適線形ガウス公共シグナルであり、もう一つは事前に固定されたグループ別集約値だけから生成できる最適線形ガウス公共シグナルである。集約規則と価値のある情報方向との対応関係に着目し、厳密に損失が生じない条件、情報容量の閾値、および近似的に損失が小さくなる条件を検討する。事前分布の異質性と相関を主な拡張として扱う。方法は、均衡と組織目的の簡約、スペクトル分解、情報容量の最適配分、反例の構成、および数値分析である。二人の構成員からなる基準例と公開された小規模ネットワークを用いた予備計算は、再検証可能な分析の出発点を与える一方、一般的な近似損失の上界はなお証明を要する。研究対象を静学的な意思決定、共通の事前分布、外生的なネットワーク、公共シグナルおよび固定されたグループ分けに限定し、二年間で理論的結果、計算付録および修士論文をまとめることを目指す。
キーワード： 情報デザイン；組織内の協調；情報容量；グループ別集約；線形ガウスシグナル；ネットワーク・ゲーム。
1. 研究背景と問題設定
1.1 組織内の情報の流れと集約制度
コミュニケーション技術の変化によって、組織内の情報摩擦が必ずしも解消されるわけではない。Yang et al.（2022）は、Microsoftの従業員を対象とした研究において、分析対象とした状況では全面的なリモートワークにより協働ネットワークがより静的かつ分断されたものになり、コミュニケーション手段の利用も変化したことを示した。これは情報の流れと組織構造との関係を研究する現実的な動機となるが、その結果を日本企業に直接外挿することはできず、以下のモデルのパラメータを推定する根拠にもならない。
本稿では、組織が構成員に共通の状態を示すダッシュボードを配信する制度的な状況を考える。既存の報告手順やアクセス権限によって、ダッシュボードには各グループの状態の平均値しか利用できない場合がある。同じ伝達能力の下では、この事前の集約によって行動の協調に影響するグループ内の差異が失われる可能性がある。一方、情報容量が小さく、全体的な変動が最も価値の高い情報であれば、単純な集約だけで十分な場合もある。分析すべきなのは、伝達能力を所与としたとき、集約規則が均衡上価値のあるどの情報方向を除外し、その除外がどのような場合に組織目的に影響するかである。
1.2 適応と協調から情報構造の制約へ
Dessein and Santos（2006）は、局所的な環境への適応と専門化された業務の協調とのトレードオフを組織分析の中心に据えた。Tamura（2025）はさらに、公共情報のデザインという観点から、構成員の協調インセンティブと組織目的が一致しない場合の情報の与え方を研究し、ネットワークに関する行列を用いて情報開示の価値を特徴づけた。そのモデルの条件の下では、状態の全体平均が最適な情報開示に含まれる。
この研究の流れに沿って、本稿は情報システムが既定の集約規則によって制約される場合の制度比較に焦点を当てる。状態に関するすべての統計量を自由に選べる場合とは異なり、制約を受ける設計者は、あらかじめ定められたグループ別集約値からしか公共シグナルを生成できない。集約構造の影響と伝達精度の影響を区別するため、二つの制度には同一の相互情報量による情報容量の上限を課す。
2. 先行研究と本研究の位置づけ
2.1 情報の価値と戦略的相互作用
Blackwell（1953）は、情報実験を比較する古典的な枠組みを確立した。単独の意思決定者が追加情報を無視できる最適意思決定問題では、より情報量の多い実験によって最適値が低下することはない。しかし、複数の主体が相互作用する場合には、個々の主体が情報を利用するインセンティブと全体としての評価をさらに区別する必要がある。公共情報の社会的価値を扱ったMorris and Shin（2002）の研究は、この違いを理解するうえで戦略的反応が重要であることを示している。
Kamenica and Gentzkow（2011）のベイズ説得の枠組みは、事前の情報構造の選択、受け手の信念更新、および行動を結びつける。本稿もこれに対応するコミットメントの時系列を採用する。設計者が先にシグナル生成規則を定め、その後に状態とシグナルが実現し、最後に構成員が行動を選択する。比較するのは組織目的の下での均衡結果であり、設計者が構成員の行動を直接決めた結果ではない。
2.2 組織ネットワークと線形二次ガウス分析
Tamura（2025）は、本稿に最も近い組織における公共情報のモデルを提供しており、その拡張は相関のある状態や異質な協調要因も扱っている。Miyashita and Ui（2025）は線形二次ガウス情報デザインとその最適化表現を論じ、Smolin and Yamashita（2026）は滑らかなゲームにおける情報デザインを研究している。これらは、均衡の簡約、情報構造の実現可能性、および最適性の条件を比較するための基礎となる。
本稿では、すべての構成員が同一の公共シグナルを観察し、初期時点で私的観測を持たないと仮定する。情報容量と集約の制約を加えたうえで、制度間の最適値を線形ガウスシグナルのクラス内に限って比較する。異なる条件の下で先行研究が示した最適性の結論をこの制約付き問題に適用するには、前提条件の照合が必要である。
2.3 情報容量と制度上の制約
Sims（2003）は、有限な情報処理能力を経済的意思決定に導入した。Gentzkow and Kamenica（2014）は情報の生成に費用がかかる場合の説得を研究し、Le Treust and Tomala（2019）は有限な通信能力の下での説得を直接分析した。本稿の相互情報量制約とガウス情報に対する情報容量の配分は、これらの研究と既存の情報理論の道具（Cover & Thomas, 2006）に基づくものであり、情報容量制約の導入そのものを本研究の貢献とは位置づけない。
Galperti and Perego（2025）は、情報が最初にどの主体へ届き、そこから他の主体へどのように波及するかに関する制約を検討している。これに対し、本稿では最終的なシグナルを全員に共通の放送とし、設計者が利用できる状態の集約値に制約を課す。両者の制度的制約は異なる段階に作用するため、固定された集約規則がもたらす結果は独立に具体的な分析を要する。
2.4 本研究の位置づけ
本稿は、報告書の構造と組織内の協調課題との適合を効率損失の問題として定式化する。同じ相互情報量の上限の下で、固定された集約部分空間は価値のある情報方向の利用をどのように制約するのか。また、情報容量、スペクトル間隔、および部分空間間のずれによって、厳密または近似的に損失が生じない条件を特徴づけられるのかを問う。
重点を置くのは損失の境界とその経済学的解釈であり、既存の情報容量配分の形式を繰り返すことではない。まず集約部分空間が価値のある方向と厳密に整合する基準例を示し、次に近似的に整合する場合の誤差界の改善を試みる。そのうえで、同質ではない事前分布がこの関係をどう変えるかを分析する。候補となる結果の新規性は、研究の初期段階に、最も近い先行研究の仮定と定理を比較してさらに検証する。
3. 研究目的と研究課題
RQ1：厳密な境界。 集約空間が有効な情報価値行列と整合する場合、情報容量がどの水準まで増えると、保持されない状態方向にも限界的な価値が生じ始めるのか。
RQ2：近似的な境界。 集約空間が近似的にしか整合しない場合、効率損失を、ずれの大きさ、情報容量、および重要なスペクトル間隔によって合わせて評価できるのか。どのような場合に二次の界が得られ、どのような場合により弱い結論が必要となるのか。
RQ3：事前分布の拡張。 事前分布の総分散を固定したとき、状態ごとの分散の不均一性や相関は、価値のある情報方向をどのように変え、全体平均またはグループ平均の性能にどう影響するのか。
研究範囲は、一回限りの意思決定、全員が共有し既知である正定値のガウス事前分布、固定された無向ネットワーク、公共シグナル、外生的に定められた空でないグループ、および線形ガウスシグナルのクラスとする。私的シグナル、動学的学習、ネットワーク形成、および内生的なグループ分けは主たる研究対象に含めず、研究課題を二年間の作業量に見合う範囲に保つ。
4. 研究方法
4.1 分析環境と組織目標
組織には 人の構成員がいる。状態ベクトルは とし、 である。本稿における対称行列の大小比較は、すべて半正定値順序によって解釈し、要素ごとの比較ではない。 は が正定値であることを表す。平均をゼロとするのは中心化のための設定である。基準ケースでは とし、非同質的な事前分布を比較する際には を維持する。これにより、規模の変化を構造の変化と取り違えないようにする。
構成員は初期の私的シグナルを持たない。この仮定により、共通の情報ダッシュボードの効果を切り分けて分析できる一方、従業員がすでに局所的な情報を把握している現実の状況は除外される。公共シグナルが実現した後、各構成員は連続値の行動 を同時に選択する。事前分布、ネットワーク、目的関数およびシグナルの生成規則は全員に既知である。
を対称、非負、自己ループのない個人の誘因ネットワークとし、 をそのラプラシアン行列とする。個人の効用は次のとおりである。
第1項は局所状態への適応不足を、第2項は関係する構成員との行動の不調整を罰する。さらに、対称、非負、自己ループのない組織の協調ネットワーク とそのラプラシアン行列 を設定する。組織の評価関数は次のとおりである。
ここで であり、各組の関係は一度だけ数える。これは組織目標であって、すべての個人効用の和に自動的に等しくなるわけではない。個人の誘因と組織の評価を区別するため、二つの協調重みをそれぞれ と で表す。既存モデルと比較する際には、組ごとの数え方に合わせてパラメータを換算する。計算の基準ケースでは とし、その後のネットワーク間の不一致に関する比較では、一方のネットワークを固定する。
4.2 公共シグナル、集約規則と容量制約
一般的な制度では、設計者は状態全体に基づいて線形ガウス公共シグナルを送ることができる。
制約付きの制度では、まず行フルランクの集約行列 を定め、各行を一つのグループの状態の平均値に対応させる。設計者が利用できるのは のみであり、すなわち として、マルコフ制約 を満たす。集約データは別途無料で公開されるわけではなく、構成員が観察するのは最終的な公共シグナル のみである。したがって、両制度の最終的な一斉送信には、いずれも次の制約が課される。
対数は自然対数とし、容量の単位は nat とする。これは同一の公共放送に対する総予算であり、受信者ごとの予算を足し合わせたものではない。グループ数 と情報容量 は異なる次元の制約である。連続値の数が少ないことは、必ずしも相互情報量が少ないことを意味せず、連続的な状態を正確に開示することも、有限の容量の下で無料には実現できない。
4.3 均衡と組織目標の簡約
とする。個人の一階条件と から、一意の均衡が得られる。
事後平均の共分散行列を と定義すると、条件付き期待値の性質から次を得る。
は負の固有値を持ち得る。情報に価値があるかどうかは、その情報によって生じる均衡行動が組織目標にどう作用するかに依存し、予測誤差がどれほど減少するかだけでは決まらない。式（4）～（6）は、以下で情報制度を比較するための分析の基礎となる。完全な導出は、付属する解説冊子の数学付録Aに示す。
4.4 情報容量の最適配分
状態を と白色化し、有効情報価値行列を次のように定義する。
その固有値を とする。線形ガウスのクラス内では、最適化を対応する情報方向への容量 の配分問題に帰着できる。
式（7）の制約は および である。 は、情報を提供しない場合と比較した組織目標の改善を表し、単位はモデルの目標関数と同じである。負またはゼロの価値を持つ方向には容量を配分する必要がない。正の価値を持つ方向については、KKT条件から次を得る。
で正の価値を持つ方向が存在する場合、水位 は容量の総和によって決まる。 の場合は、すべての配分がゼロである。式（8）には既存のガウス情報理論の道具を用いる（Cover & Thomas, 2006）。
グループ別集約については、白色化した状態空間における正規直交基を次のように定義する。
制約付き問題の有効行列は である。式（7）の固有値を の固有値に置き換えることで、 が得られる。主要な結果変数は次のとおりである。
比較では常に を固定し、利用可能な情報に対する集約制約のみを変える。必要に応じて も報告する。相対的な利得損失 は、 が数値的な許容誤差を明確に上回る場合にのみ報告し、負の水準にある元の厚生を恣意的に百分率で表さない。
4.5 厳密に損失がゼロとなる基準条件
とする。 の活性化された方向がすべて に含まれるなら、その容量の下でグループ別集約制度は一般制度の最適シグナルを実施できるため、効率損失はゼロとなる。特に、、誘因ネットワークが連結で の場合、式（6）は を示し、定数方向の最大固有値1が一意となる。すべての構成員を対象とするどのグループ分けの平均値も、この方向を保持する。
2番目に大きい正の固有値が なら、
の範囲では、一般制度も状態の全体平均の方向にのみ容量を配分すればよく、グループ別集約による損失はない。定数方向以外に正の固有値が存在しない場合、この無損失性はすべての有限な容量まで続き得る。この結論は、ここで置いた同質的な事前分布とモデルの条件に依存し、「平均値が常に最も重要である」という無条件の命題ではない。
さらに、 であれば、集約部分空間とその直交補空間はいずれも に関して不変である。 を の固有値とし、 を直交補空間上の最大固有値と0のうち大きい方とする。直交補空間が空の場合は と定める。保持されない方向が利用され始める臨界容量は により特徴づけられる。 のとき、候補となる表式は次のとおりである。
この不変部分空間の条件の下では、この表式を容量配分から直接検証できる。 の場合、正の価値を持つ未保持の方向はなく、損失ゼロの区間は全容量に及ぶ。固有値の重複、閾値で等号が成立する場合、および空和の場合は、正式な証明において一つずつ扱う必要がある。
4.6 近似的な無損失境界と事前分布の拡張
完全に整合的な集約規則は基準ケースであり、現実の組織についての断定ではない。次の段階では、ゼロでない を中心に分析する。 によって有効な情報方向が集約の境界をまたぐ程度を測るとともに、直交補空間内の価値と容量配分の水位も考慮する。保持されない方向と水位の間に厳密な隔たりがあるとき、不一致の程度に関する二次の効率損失界が存在するかを検討する。また、方向が活性化される閾値付近では、より弱い界しか得られないのか、あるいは追加条件が必要なのかを調べる。
二次の界は、今後検証すべき目標である。分析は二次元モデルと対称的なグループ分けのネットワークから始め、まず反例を調べ、その後に証明を試みる。一般的な命題が成立しない場合には、その成立範囲を特定し、より弱い界を導くか、最小の反例を提示する。
相関のある事前分布を、集約と情報価値の方向との不一致が生じる仕組みを検証するための主要な拡張とする。白色化変換によって価値のある情報方向がどのように回転するか、またその回転を同じ誤差界で説明できるかを分析する。一般的な非ガウスシグナルの最適性については、別途証明しない限り、結論を出さない。
4.7 数値分析の設計
本格的な計算では、まず手計算可能な2～6ノードのモデルを用い、次に30、60、120ノードの合成的なグループ分けのネットワークを用いる。さらに、公開されている小規模ネットワークをトポロジーの実演に用いる。異なるグループ分けを比較する際には容量を固定する。ネットワーク規模を比較する際には、期待次数を揃えるか、相互作用の強さを調整したことを明示する必要がある。より密なネットワークの影響を、構成員数の効果として解釈してはならない。
数値結果は、容量制約、一階条件の残差、実施可能性、一般制度が制約付き制度を弱く上回ること、ならびに 、 などの境界条件を同時に満たす必要がある。容量配分については、解析的なKKT解と独立した制約付き数値最適化を突き合わせる。トポロジーの摂動とパラメータ走査は感度分析であり、現実のデータに基づく標本推論ではない。現実の母集団について標本から推論することはしない。
5. 研究の基盤と実行可能性
5.1 分析の入力と公開ネットワーク
主要な入力は、合成ネットワーク、固定されたグループ分け、正定値の事前共分散行列、パラメータの組合せであり、スクリプトによってすべて生成できる。 はモデルの設定値または感度分析の対象であり、ネットワークの位相構造から推定するものではない。したがって、本研究の主たる分析は、利用許可をまだ得ていない企業内部資料に依存しない。
公開された位相構造を用いる実演には、Zachary（1977）の空手クラブ・ネットワークのNetworkX組込み版を使用する（NetworkX Developers, n.d.）。予備計算では34ノードと78本の無向辺をすべて読み込み、自己ループ、連結性、属性の完全性を確認した。基準設定では各辺に単位重みを割り当て、グループをノード番号0—16と17—33に人為的に固定する。分裂後のクラブ所属を事前の部門として使用しない。このグループ分けは計算の実演に限られ、現実の組織制度を意味しない。
5.2 予備分析
予備計算では、まず2人の構成員が互いに結び付くモデルを用い、、、 と設定する。制約付き制度は2人の状態の平均値のみを利用する。有効価値の固有値は1と0.5であり、臨界的な情報容量は natである。
| 情報容量 （nat） | 一般制度 | グループ別集約制度 | 効率損失 |
|---|---|---|---|
| 0.10 | 0.181269 | 0.181269 | 0.000000 |
| 0.50 | 0.642236 | 0.632121 | 0.010116 |
| 2.00 | 1.308607 | 0.981684 | 0.326923 |
情報容量が小さいときには、一般制度の最適シグナルも平均方向のみを利用するため、グループ別集約による効率損失は生じない。情報容量が増えると、状態の相対的な差異にも価値が生じ始める。本稿の目的関数の正規化の下では、 かつ のとき、均衡における行動は、所与の共通情報の下で組織にとって最適な行動と一致する。したがって、この基準例は情報制約の影響を切り出すものであり、行動インセンティブの対立を示すものではない。
事前分布の総分散を2に保ったまま、 を に変更すると、 の時点で約0.000960の効率損失が生じる。この例は、同質的な事前分布の下で得られる平均方向に関する結論を、異質的な事前分布へそのまま拡張できないことを示す。また、集約によって利用可能な部分空間と価値ある方向とのずれを検討する出発点となる。
34ノードの公開ネットワークにおいて、同じ協調の重み、単位の事前共分散行列、前述の人為的なグループ分けを用いると、 における両制度の改善量はそれぞれ2.225420と1.368396であり、効率損失は0.857024となる。この数値は、特定の位相構造とパラメータの下で得られたモデルの出力にすぎず、クラブや企業の実際の業績を表すものではない。
さらに、6ノードの合成環状ネットワークで100,000回のモンテカルロ標本抽出を行った。解析的に求めた組織目的の値は−4.184373、シミュレーション平均は−4.180914、モンテカルロ標準誤差は0.007400であり、その差は約0.468標準誤差であった。19項目の計算チェックと81組の小規模なパラメータの組合せについても実行・通過を確認した。これらの結果は基準式と実装の整合性を支持するが、一般的な命題にはなお独立した証明が必要である。
5.3 再現の計画と適用範囲
予備分析を再検証できるよう、コード、依存ライブラリのバージョン、乱数シード、ネットワーク処理の記録および出力を保存する。解析解と独立した数値解法によって結果を相互に照合する。現段階で確認したのは理論計算に必要な入力を用意できることであり、現実の組織の選好の識別、企業データの利用許可、制度の因果効果の検証ではない。
6. 研究計画
| 時期 | 主な作業 | 検証可能な成果と判断 |
|---|---|---|
| 第1—3か月 | 最も近接する先行研究の精読、組織モデルの再現、確率論と線形代数の補強 | 文献・仮定・命題の対照表。十分に明確な研究上の新規性があるかを判断する |
| 第4—6か月 | 均衡、厚生、情報容量の最適配分、厳密に整合する場合の証明を完成する | 基準命題と反例。コードの独立した再検証。主モデルを確定する |
| 第7—10か月 | 近似的に整合する場合の効率損失の境界と閾値付近の振る舞いを研究する | 条件付きの厳密な結果を少なくとも一つ得るか、強すぎる予想を明確に覆す最小反例を示す |
| 第11—14か月 | 総分散を保った異質的・相関のある事前分布へ拡張する | 基準結果がいつ成立しなくなるかを示す。同時に新たなシグナルの種類は加えない |
| 第15—18か月 | パラメータと位相構造に関する頑健性分析、公開された小規模ネットワークによる実演を完成する | 再現可能な計算結果の表、限界の説明、完全な計算付録 |
| 第19—21か月 | 論文の初稿をまとめ、報告・討論する | 序論、証明、結果、研究上の貢献の範囲が互いに整合した初稿 |
| 第22—24か月 | 改稿、再検証、口頭試問の準備、資料の保存を行う | 最終論文、コード、入力の定義一覧、版と結果の一覧 |
段階ごとの調整。 第3か月に主要な命題が先行研究によって完全に扱われていると判明した場合は、大規模なシミュレーションへ進む前に貢献を再定義する。第10か月までに一般的な摂動に関する境界を確立できない場合は、二グループの対称ネットワークに対象を絞るか、反例と成立条件を提示する。第14か月に相関のある事前分布への拡張が主たる結果の完成を妨げる場合は、今後の研究課題に移す。その後の拡張は主たる研究問題の完成を妨げない範囲に限る。最低限完成すべき単位は、基準結果の再現、文献との照合を経た明確な研究上の増分、再検証可能な証明または反例、完全な計算付録である。最終的な結論が成立条件や反例という形をとることも認める。
7. 期待される貢献と研究上の限界
本研究は、固定されたグループ別集約規則の効率上の境界を主題とし、証明、反例、計算付録を伴う修士論文を作成することを目指す。期待される貢献は、どの状態の差異を残す価値があるか、いつ単純な集約で十分か、また情報容量と事前分布の構造がその判断をどう変えるかを説明する点にある。一般的な近似的効率損失の境界と、それが既存の結果に対して持つ増分については、理論的な導出と文献の比較を通じてなお確認する必要がある。
結論の適用範囲は、公共シグナル、共通の事前分布、初期時点での私的観察がないこと、外生的ネットワーク、固定されたグループ分け、線形ガウス公共シグナルのクラスといった仮定に制限される。情報容量のパラメータは現実の通信資源と推定に基づいて対応付けられておらず、公開された小規模ネットワークも日本企業を代表しない。したがって、本研究は企業に対して定量的な因果効果に基づく政策提言を直接行うものではない。
中核となる研究計画では個人データを新たに収集せず、匿名化されたノードの個人識別も行わない。公開資料とソフトウェアについては出所とバージョンを記録する。今後、従業員への聞き取り、実際の行動データ、実験を追加する場合には、資料利用の許可、インフォームド・コンセント、倫理審査、および対応する統計的設計を別途検討する。
参考文献
Blackwell, D. (1953). Equivalent comparisons of experiments. The Annals of Mathematical Statistics, 24(2), 265–272. https://doi.org/10.1214/aoms/1177729032
Cover, T. M., & Thomas, J. A. (2006). Elements of information theory (2nd ed.). Wiley-Interscience. https://doi.org/10.1002/047174882X
Dessein, W., & Santos, T. (2006). Adaptive organizations. Journal of Political Economy, 114(5), 956–995. https://doi.org/10.1086/508031
Galperti, S., & Perego, J. (2025). Games with information constraints: Seeds and spillovers. Theoretical Economics, 20(2), 667–711. https://doi.org/10.3982/TE5805
Gentzkow, M., & Kamenica, E. (2014). Costly persuasion. American Economic Review, 104(5), 457–462. https://doi.org/10.1257/aer.104.5.457
Kamenica, E., & Gentzkow, M. (2011). Bayesian persuasion. American Economic Review, 101(6), 2590–2615. https://doi.org/10.1257/aer.101.6.2590
Le Treust, M., & Tomala, T. (2019). Persuasion with limited communication capacity. Journal of Economic Theory, 184, Article 104940. https://doi.org/10.1016/j.jet.2019.104940
Miyashita, M., & Ui, T. (2025). LQG information design (Version 4) [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2312.09479
Morris, S., & Shin, H. S. (2002). Social value of public information. American Economic Review, 92(5), 1521–1534. https://doi.org/10.1257/000282802762024610
NetworkX Developers. (n.d.). karate_club_graph. NetworkX documentation. Retrieved October 6, 2026, from https://networkx.org/documentation/stable/reference/generated/networkx.generators.social.karate_club_graph.html
Sims, C. A. (2003). Implications of rational inattention. Journal of Monetary Economics, 50(3), 665–690. https://doi.org/10.1016/S0304-3932(03)00029-1
Smolin, A., & Yamashita, T. (2026). Information design in smooth games (Version 6) [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2202.10883
Tamura, W. (2025). Information design for adaptive organizations (Version 1) [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2501.12669
Yang, L., Holtz, D., Jaffe, S., Suri, S., Sinha, S., Weston, J., Joyce, C., Shah, N., Sherman, K., Hecht, B., & Teevan, J. (2022). The effects of remote work on collaboration among information workers. Nature Human Behaviour, 6(1), 43–54. https://doi.org/10.1038/s41562-021-01196-4
Zachary, W. W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33(4), 452–473. https://doi.org/10.1086/jar.33.4.3629752
Research map
Research map
In an application discussion, first explain which two regimes the research compares and which conditions the conclusions depend on. Reading in the order of the main argument helps connect the question, method, and limits of the evidence.
Understand the research in the order of the main text
- 01
Start with the question
Use the abstract and main text §§1 and 3 to identify the question: Under limited information capacity, does predetermined group aggregation hinder organizational members' adaptation to local states and coordination of their actions?
- Outcome
Explain why the two regimes must use the same capacity.
- 02
Then examine the regimes
Main text §§4.1–4.2 explains what members know, how the designer generates a public signal, and where group aggregation constrains the designer.
- Outcome
Draw the sequence of states, aggregation, signals, and actions.
- 03
Next, examine the solution
Main text §§4.3–4.6 moves from members' equilibrium to organizational value and then discusses capacity allocation. Distinguish the zero-loss benchmark that can already be derived from the approximate loss bound that remains to be proved.
- Outcome
Explain when efficiency loss is zero.
- 04
Finally, examine the limits of the evidence
Main text §§5–7 presents preliminary calculations, the research schedule, and limitations. The two-person example and public-network demonstration help check the model; they do not represent actual effects in firms.
- Outcome
Give one example each of a checked result and an open question.
The two regimes being compared
The general regime can generate an optimal linear Gaussian public signal from the full state. The restricted regime must first average states within predetermined groups and then generate a signal from those averages. Both broadcast the same signal to all members and face the same mutual-information capacity limit. The group averages themselves are not disclosed separately.
The comparison holds the network, coordination weights, prior distribution, and capacity constant, changing only the state information available to the designer. Each regime optimizes organizational value under the members' equilibrium; the difference is aggregation efficiency loss within the model. The number of groups differs from information capacity, and this difference is not a percentage of firm productivity.
| Location in the main text | Purpose of the section | Limit to check while reading |
|---|---|---|
| §1 Background | Dashboard aggregation may remove differences within groups, motivating the question. | Background studies do not prove the effect of such regimes in Japanese firms. |
| §2 Literature | Explain how the organizational public-information model, capacity tools, and predetermined aggregation relate. | Check the assumptions and established propositions in the closest papers. |
| §3 Question | Set out the exact boundary, approximate boundary, and prior-distribution extension in order. | Distinguish research aims from completed results. |
| §4 Method | Define timing, equilibrium, organizational value, capacity, and the restricted subspace. | Check the conditions behind formulas and counterexamples. |
| §§5–7 Foundations, schedule, limits | Present preliminary calculations, milestones, and scope of applicability. | Synthetic and public-network demonstrations cannot be used to estimate real-world causal effects. |
What you should be able to explain after reading
Try explaining without formulas: Who sets the signal rule first? What do members actually observe? Why is the optimal value under the general regime at least as high as under the restricted regime? Why might removing state differences still cause no efficiency loss? If the approximate loss bound fails, how will the research scope narrow?
Why this question
Topic and value
If you cannot explain why the topic matters, a professor cannot assess the research plan's value. Start with your actual learning experience, then compare existing studies and explain the potential academic contribution and practical insight.
Limits of the rationale
From a personal starting point to a research question
The student should truthfully explain which courses, readings, or experiences made them want to keep studying organizational information. Then narrow that interest into a researchable question: At equal information capacity, does predetermined group aggregation remove state differences needed for the optimal public signal? At low capacity, it may also preserve exactly the most important direction.
Existing work studies information design, public signals, and limited capacity in organizations, so this topic cannot claim those tools as innovations. Its potential academic contribution lies in bounds on the efficiency loss caused by fixed aggregation rules. A practical insight is to check whether the aggregation used in reports suits the organization's coordination task. Remote-work research provides background motivation only; this project has neither performance data from Japanese firms nor causal identification.
| Research question | Specific question to answer |
|---|---|
| RQ1 · When is there exactly no loss? | When the aggregation subspace is compatible with effective value directions, at what capacity threshold do omitted directions first acquire marginal value? First prove the benchmark that retains the overall mean direction under a homogeneous prior, then address more general compatible subspaces. |
| RQ2 · How large is the loss under approximate compatibility? | When the aggregation subspace is approximately compatible, can mismatch, capacity level, and spectral gap bound efficiency loss? If a second-order bound holds only under a strict gap, identify counterexamples near the threshold or add the necessary conditions. |
| RQ3 · How do conclusions change when the prior changes? | Keep total prior variance constant while changing the variance or correlation of individual states, and examine how valuable information directions and the aggregation subspace change. The two-person heterogeneous-prior demonstration suggests that the mean need not be lossless at low capacity; a general conclusion remains to be proved. |
- 01
‘Less information is obviously worse. Where is the research?’
The feasible signals under the general regime include those under the restricted regime, so its optimal value is at least as high. The research concerns how long zero loss persists as capacity rises, whether approximate loss can be bounded, and when counterexamples emerge; the closest papers' theorems must also be checked.
- 02
‘Why not simply increase communication capacity?’
Increasing transmission capacity is another policy choice. This project gives the two regimes the same capacity so it can isolate the effect of a fixed aggregation rule.
- 03
‘What if a paper already has a similar result?’
Compare assumptions, where constraints enter, objective functions, and theorem conclusions item by item. If an existing paper has proved the proposed bound, revise the contribution claim and research question.
The limits of academic value and practical insight
The two-person benchmark and calculations for specified parameters provide a reproducible starting point. The general approximate loss bound, behavior near thresholds, and whether these results add to the literature remain to be investigated. If the research yields conclusions with clear conditions, they could inform the design of aggregation rules. Information capacity has not been mapped to real communication resources, and this study does not identify firm preferences or causal effects of regimes.
Sources & fit
Literature and supervisor fit
When contacting a professor, explain exactly which research your question builds on and know which results predecessors have already proved. Read papers for their assumptions, methods, and scope so you can raise questions worth discussing.
How 凪野透's research connects to this topic
凪野透 is the fictional target faculty member in this sample. The example portrays them as studying information design, social networks, and organization theory; supervising microeconomics, game theory, industrial organization, and business economics; accepting theoretical or empirical work; and requiring foundations in microeconomics and econometrics. For a real application, check each point against the target faculty member's published laboratory description. Tamura (2025), ‘Information Design for Adaptive Organizations’ (preprint v1), studies organizational members' local adaptation, coordination incentives, public signals, and network structure, making it the direct academic starting point for this project.
This project extends organizational public-information questions by adding predetermined group aggregation and an equal-capacity comparison. When comparing with Tamura (2025), check the network, organizational objective, and pair counting. The two-person benchmark uses the same network and coordination weights to isolate the information constraint; it does not demonstrate a conflict in action incentives. Similar research interests provide grounds for a discussion, but actual admission and supervision arrangements must be confirmed through official channels and with the faculty member for the target year.
| Source | Its role in this research | What it cannot support claiming |
|---|---|---|
| Tamura（2025，v1） | Check organizational adaptation and coordination, public signals, the network matrix, and extensions already in the original paper. | Do not claim that this project first introduces organizational networks or correlated states. |
| Kamenica and Gentzkow (2011); Gentzkow and Kamenica (2014) | Check ex ante signal design, receivers' actions, and information costs. | Do not claim this project invented information design or costly information. |
| Le Treust and Tomala (2019) | Check existing results on persuasion under limited communication capacity. | Do not call the mere addition of a capacity limit a contribution. |
| Miyashita and Ui (2025, v4); Smolin and Yamashita (2026, v6) | Check whether LQG optimization representations and smooth-game results apply under this project's conditions. | Do not apply an optimality theorem without checking its signal class and constraints. |
| Galperti and Perego (2025) | Compare constraints on information arrival and spillovers with the designer's fixed aggregate input; they act at different stages. | Do not assume the two problems are equivalent simply because both impose restrictions. |
Reading from abstract to proposition
- 01
Confirm the scope
First read the target faculty member's laboratory description and the exact version of Tamura (2025). Record the question, participants, timing, objective function, and the pages and sections you actually read.
- Outcome
One page of authentic reading notes.
- 02
Recheck the direct model
Compare Tamura (2025) with this project's network, public signal, organizational objective, and parameter counting, then check which derivations in main text §§4.3–4.5 can be reused.
- Outcome
An itemized comparison of assumptions.
- 03
Search the closest literature
Search papers and citations on public Gaussian information design, aggregation constraints, finite-capacity persuasion, and network grouping; check whether the proposed conclusions have already been proved.
- Outcome
A list of ‘Have the proposed conclusions already been proved?’
- 04
Revise the claims
For each paper, record its version, the portion read, proposition conditions, differences from this project, and points not understood. Use this in month 3 to decide how to state the research contribution.
- Outcome
Keep, narrow, or replace the contribution claim.
What you should be able to answer before making contact
Before making contact, explain in your own words the mechanism in Tamura (2025) or one representative paper by the target faculty member. Then explain at which step the fixed-aggregation restriction enters, what analysis you hope to learn, and which derivation you have not yet mastered. Check whether prior contact is required, course requirements, and actual availability for the application year.
Method choice
Method and alternatives
In an application discussion, explain why an equilibrium model is appropriate for comparing these regimes and what numerical calculations can establish. The method follows the question; using firm data or an experiment would change both the research question and the evidence required.
Why start with a linear–quadratic–Gaussian model
A public signal changes members' assessments of local states, while they must also coordinate with network neighbors, so their action equilibrium must be solved first. A quadratic objective and continuous actions simplify the equilibrium; only after substituting it into the organizational objective can the two signal regimes be compared. The designer chooses a signal rule and cannot directly prescribe members' actions.
A Gaussian prior and linear Gaussian signals allow the mutual-information limit to be expressed as capacity allocation across information directions. Fixed group aggregation further limits the directions available to the designer. This permits analysis of when aggregation is lossless or costly, but conclusions depend on static, public-signal, and linear Gaussian assumptions.
Proofs, calculations, and counterexamples have distinct roles
- 01
Derive equilibrium and value
First check individual first-order conditions, normalization of the organizational objective, and directions with negative value; impose the same capacity limit on both regimes.
- Outcome
Complete derivations of equilibrium and welfare.
- 02
Prove the exact benchmark
Prove zero loss when the aggregation subspace retains active directions, accounting for equal thresholds, repeated eigenvalues, and positive value in an omitted subspace.
- Outcome
A zero-loss proposition with explicit conditions.
- 03
Test the approximate boundary
First seek counterexamples near the threshold in two-dimensional and symmetric group networks. Then investigate whether subspace mismatch, spectral gaps, and capacity level yield a conditional loss bound.
- Outcome
A formal bound or minimal counterexample and its domain of validity.
- 04
Numerical verification
Use hand-solvable models with 2 to 6 nodes, synthetic networks, and small public graphs to check capacity, equilibrium conditions, the zero-capacity boundary, and whether the optimum under the general regime is no lower than under the restricted regime. Cross-check analytical solutions against independent numerical optimization.
- Outcome
Reproducible inputs, code, and a computational appendix.
| Research methods | Questions this method can answer | Why this study does not use it for now |
|---|---|---|
| Causal empirical analysis (e.g., DID) | The effect of a real policy change on measured outcomes. | There is currently no defined shock, comparison structure, performance data, or identification strategy. |
| Behavioral experiment | Whether people act as the model predicts under given information rules. | Recruitment, treatment, ethics, and the sample would need to be designed separately; this cannot directly prove a general bound on optimal loss. |
| Interviews / surveys | How organizations produce and use aggregated reports. | These can help explain institutions, but cannot by themselves derive the optimal signal and the difference in equilibrium value. |
| Machine-learning prediction | Improving out-of-sample prediction for a variable. | Prediction accuracy is not the organizational objective in this problem, which includes coordination externalities. |
How to narrow the study if a strong claim fails
If a general second-order loss bound fails near the capacity threshold, preserve the smallest counterexample and then check whether a conditional bound holds under a strict spectral gap, or narrow the analysis to a symmetric two-group network. In month 3, check the contribution relative to the literature; in month 10, decide the scope of the loss bound. Move extensions to correlated priors to future work in month 14 if they affect completion of the main question. Numerical results will be used to check derivations and find counterexamples.
Model & mechanism
Hypotheses, variables and mechanism
If asked in an interview to change one assumption, you should be able to say which step of the derivation would be affected. First clarify where information comes from and who chooses actions, then use the variable glossary to explain how the model compares the two regimes.
Sequence of information rules, member actions, and evaluation
- 01
Given environment
A commonly known Gaussian prior, two fixed undirected networks, coordination weights, fixed groups, and a capacity limit are given.
- Outcome
Clarify which quantities remain fixed in the comparison.
- 02
Commitment to a rule
The designer commits to a signal-generation rule before the state is realized. The general regime can use the full state; the restricted regime can use only the average state within fixed groups.
- Outcome
Aggregate first, then generate the signal under the restricted regime.
- 03
Broadcast and update
After the state is realized, all members observe the same final public signal and update their beliefs about each state component.
- Outcome
Group averages are not disclosed for free in addition to the signal.
- 04
Member actions
Members simultaneously choose actions based on their common posterior, balancing local adaptation with network coordination.
- Outcome
Members choose their actions; the designer does not command them.
- 05
Ex ante evaluation
Evaluate each regime's optimal improvement against the organization's objective, then calculate the efficiency loss caused by fixed aggregation.
- Outcome
Explain the model units and conditions for the difference.
| Research assumption | How it helps the analysis | What must be revisited if the assumption is relaxed |
|---|---|---|
| Common public signal, no initial private observations | Isolates posterior and action changes caused by a unified dashboard. | Private posteriors and expectations about others' actions would need to be recalculated. |
| Commonly known, positive-definite Gaussian prior | Allows the state to be whitened, capacity to be calculated, and spectral analysis to be used. | Implementation and optimality must be reexamined for different priors, non-Gaussian priors, or singular covariance. |
| Continuous actions, quadratic loss | The first-order conditions are linear and the equilibrium can be solved explicitly. | Discrete or bounded actions require a new solution method. |
| Fixed, symmetric, nonnegative networks | The Laplacian and value matrix can be analyzed using tools for symmetric spectra. | Directed or endogenous networks require the mechanism to be rewritten. |
| Fixed, nonempty groups; linear-Gaussian signals | Represents the reporting restriction as a retained subspace. | Optimal group selection or a broader class of signals is a new design problem. |
| Capacity as an upper bound | Capacity need not be allocated to directions with negative value. | Requiring specified information to be sent would change the comparison. |
Variable glossary
Environment and actions
- State and prior distribution
is the state vector faced by members; is the commonly known, positive-definite prior covariance. The baseline uses an identity covariance; comparisons of heterogeneity keep total variance fixed.
- Actions and networks
is the vector of actions chosen simultaneously by members; denotes the network governing individual coordination incentives, denotes the network used to evaluate the organization. A network link does not automatically represent an empirically estimated economic incentive.
- Coordination weights
and are used for individual objectives and the organization's objective, respectively. When comparing with Tamura (2025), first check how network relationships are paired and counted.
Information and outcomes
- Group input
is the fixed group-average matrix; the designer under the restricted regime can use only . The number of groups and broadcast information capacity are separate things.
- Public signal and capacity
is the final broadcast; is the vector of members' common posterior means. Both regimes are subject to the constraint , and the unit of is nat.
- Value of information directions
After substituting the members' equilibrium into the organization's objective, we obtain the information-value matrix ; combined with the prior covariance, it gives the effective value matrix . This matrix indicates which combinations of states should be disclosed first when capacity is limited.
- Equilibrium and efficiency loss
The action equilibrium can be written as , where is determined by the individual coordination network. The difference between the two regimes' optimal improvements in organizational value is ; it measures the loss from fixed aggregation within the model.
From public signal to efficiency loss
The signal rule determines which state differences can be learned; members update their beliefs accordingly, and network coordination then changes their actions. The value of each information direction can be compared only after actions are incorporated into the organizational objective. If aggregation removes a direction that the optimal plan would not use at the current capacity, the efficiency loss can be zero. As capacity rises or the prior distribution changes, the same aggregation rule may cause a positive loss; that remains a conclusion within the model.
Results & limits
Results, evidence and limits
If asked in an interview, “What results have you obtained so far?”, distinguish computational outputs for specific models, results that can be proved under conditions, and claims that remain to be investigated. These numerical results support comparisons within the specified setup; they cannot be used to describe company performance. The numbers in the table are preliminary calculations self-reported by the sample applicant in §5.2 of the research plan; the tool only organizes calculations you provided and does not generate numbers on its own.
What do the two information regimes compare?
Both regimes use the same upper limit on public broadcast capacity. The general regime can use the full state; the restricted regime can generate a signal only from predetermined group averages. and denote the optimal improvement under each regime relative to the no-information baseline; efficiency loss is defined as , in units of the model objective.
The two-person baseline uses an identity prior, a connected network, and coordination weights of 0.5 for both individuals and the organization. The restricted regime retains only the average state. The effective values of the two information directions are 1 and 0.5; when capacity is below approximately 0.346574 nat, the general regime's optimal signal also uses only the average direction, so aggregation causes no loss in the model. The difference between the two people's states is still removed.
With this parameter set, members' equilibrium actions coincide with the organization's optimal actions under the given common information, allowing the effect of the information constraint to be observed on its own. It does not show conflicts in action incentives or information with negative value; the differences in the table cannot be converted into company performance, monetary amounts, or percentages.
| Information capacity （nat） | General regime | Mean only | Efficiency loss |
|---|---|---|---|
| 0.10 | 0.181269 | 0.181269 | 0.000000 |
| 0.50 | 0.642236 | 0.632121 | 0.010116 |
| 2.00 | 1.308607 | 0.981684 | 0.326923 |
Low-capacity counterexample with a heterogeneous prior
Change the two people's prior variances from 1 each to 1.8 and 0.2, keeping total variance at 2, and set capacity to 0.01 nat; the loss is about 0.000960. The change is in the prior structure, not the sample size or total variance of a shock. This counterexample refutes the claim that mean aggregation is lossless at low capacity under every prior; it does not affect the conditional result under a homogeneous prior.
Even with no cross-coupling between the retained and omitted directions, losslessness is not guaranteed at every capacity. An omitted direction may still have positive value; as capacity rises, the general regime may use it. Assessing the loss also requires checking the value of the omitted direction and the capacity-allocation threshold.
Calculations checked so far and contributions still to be verified
Existing evidence
- Analytical baseline
Under a homogeneous prior and specified network conditions, a zero-loss threshold at low capacity can be derived; the two-person example is for hand calculation and verification.
Status: conditional result within the model
Source: research plan §§4.5, 5.2
- Computational verification
The three-row two-person results, heterogeneous-prior counterexample, and 19 computational checks are verification records self-reported by the sample applicant in §5.2 of the research plan.
Status: run under specific settings; not a general proof
Source: research plan §5.2
- Public graph and simulation
A public graph with 34 nodes and 78 edges is used to illustrate topology; 100,000 Monte Carlo trials refers to the number of artificial random draws.
Status: does not identify company preferences or real-world causal effects
Source: research plan §§5.1–5.3
Research contributions still to be verified
- Closest related work comparison
Record the exact version, assumptions, and propositions for each paper, and check whether existing literature directly implies the candidate result.
Status: the student must read and complete this work; references listed in §2 of the research plan do not certify novelty
Source: research plan §2
- Candidate contribution
When fixed aggregation approximately matches effective value directions, study the relationship between capacity, spectral gaps, and loss bounds.
Status: a general second-order bound remains to be proved; a weaker result may be needed near the threshold
Source: research plan §§4.6, 7
- Work actually completed by the applicant
The applicant should separately record what they personally read, derived, and ran; calculations mentioned in the research plan should be supported by their own notes or code.
Status: statements made to others must be supported by the applicant's own records
Source: research plan §5.3
- 01
Why can't the general regime have a lower optimal value?
It can choose any rule that the restricted regime can implement, so its choice set is larger. This concerns the optimized value of each regime; it does not imply that any particular fixed signal with more information improves the organization's objective.
- 02
Does increasing capacity always improve the organization?
Capacity is an upper bound, so the additional budget can go unused and the optimal value cannot fall. Requiring specific information to be sent would be a different problem.
- 03
Do 19 successful checks mean the research is complete?
The 19 checks support the consistency of these inputs and this implementation. A general proof and the nearest-neighbor literature still need to be checked separately; the applicant also needs to explain which readings, derivations, and runs they personally completed.
Feasibility & preparation
Two-year feasibility and preparation
If a professor asks, “Can this be completed in two years?” or “What preparation do you have now?”, explain what can be completed at each stage and show your own study records. Progress reviews in months 3, 10, and 14 will allow uncertain extensions to be narrowed in time, leaving enough time for the core study.
Milestones and verifiable outputs over 24 months
- 01
Months 1–3: establish a researchable contribution
Read the nearest-neighbor literature closely, reproduce the organizational model, and strengthen probability and linear algebra; compare existing propositions with the conditions of this study one by one.
- Outcome
Comparison table of literature, assumptions, and propositions; decision on whether to redefine the contribution
- 02
Months 4–6: finalize the main model
Complete the derivations for equilibrium, welfare, capacity allocation, and exact compatibility cases; verify the calculations with an independent method.
- Outcome
Baseline propositions, counterexamples, and verification records
- 03
Months 7–10: address the approximate boundary
First look for counterexamples in two dimensions and symmetric group structures, then try to establish conditional loss bounds, with particular attention to activation thresholds.
- Outcome
A formal conditional result, or a smallest counterexample that refutes an overly strong conjecture
- 04
Months 11–14: test prior extensions
With total variance held comparable, check how heterogeneous or correlated priors rotate value directions; do not expand the signal class at the same time.
- Outcome
Conditions under which the baseline fails and the boundaries of extensions
- 05
Months 15–18: robustness and appendix
After clearly defining capacity, grouping, and network density, run parameter scans and demonstrate the model on small public graphs; retain anomalous results.
- Outcome
Reproducible experiment tables, a limitations statement, and a computational appendix
- 06
Months 19–21: draft the paper
Align the introduction, differences from the nearest literature, proofs or counterexamples, and interpretation of results; present the work for discussion.
- Outcome
A paper draft ready for peer scrutiny
- 07
Months 22–24: verify and archive
Revise the paper and bring the code, input dictionary, proof versions, and final figures into alignment.
- Outcome
Paper, reproducibility materials, and defense-preparation checklist
| Milestone | Trigger | Adjustment | Minimum result to retain |
|---|---|---|---|
| Month 3 | A candidate proposition is fully covered by the nearest-neighbor literature | Redefine the contribution first; stop treating large-scale simulation as proof of novelty | An accurate account of the literature gap and a researchable smaller question |
| Month 10 | Unable to establish a general approximate loss bound | Narrow to a symmetric two-group network, adopt weaker conditions, or formally present a counterexample | Conditions, proof, or counterexample that can be checked |
| Month 14 | Heterogeneous or correlated priors slow the main line of work | Move them to future work so they do not delay the main result | Reproduction of the baseline, a clear contribution, and a computational appendix |
What evidence of ability should the applicant present?
All of the following must be verified by the applicant against their actual study records
- Microeconomics and game theory
Can independently write the best responses for two players, the simultaneous-move equilibrium, and the basis for its uniqueness; if not, review first-order conditions and concavity first.
Status: Awaiting verification through the applicant’s own handwritten derivation
- Probability and conditional expectation
Can explain priors, common posteriors, and the law of total variance; if weak, start by practicing updates with one-dimensional Gaussian signals.
Status: Awaiting verification with example problems
- Linear algebra and optimization
Can explain the Laplacian, eigen-directions, positive definiteness, and capacity allocation with a 2×2 example; then move on to general KKT conditions.
Status: Awaiting verification through an independent calculation
- Code and reproducibility
Keep the actual inputs and logs from runs performed by the applicant, the results after changing parameters, and explanations; screenshots alone are insufficient for verification.
Status: Fill in only from actual runs
- Literature and language
At least one closely related paper that has actually been read, with its version, sections read, mechanism, and points not understood recorded; also prepare the necessary Japanese and English reading skills and exam fundamentals.
Status: Awaiting verification through reading notes
Model feasibility and the scope of the applicant’s preparation
Core theoretical research can proceed using synthetic networks, fixed groups, and specified parameters; prior access to internal company data is unnecessary. The public 34-node graph is only a topology demonstration. If the topic changes to the causal effect of an actual policy, data authorization and the identification design will need to be established anew.
The two-year main line should include at least a baseline replication, a clearly stated contribution checked against the literature, a verifiable proof or counterexample, and a computational appendix. The school and research lab decide whether the results meet degree requirements. Before applying, also check language, materials, and exam deadlines for the target selection process, and understand the content submitted in the applicant’s own name.
Explain & repair
Explaining your research to a professor
A professor may ask you to briefly introduce your topic, then ask follow-up questions about its significance, methods, and results. Expand your explanation in response so they understand why you compare these two information systems. Practicing at different lengths can help you judge whether you understand the research rather than simply remember a script.
20-second, 60-second, and three-minute explanations of the same research
Practice at your own speaking pace and check that the facts are consistent across all versions
- About 20 seconds
Under the same information-capacity constraint, this research compares a public signal that uses the full state with one based only on fixed group means. It examines when aggregation causes no efficiency loss and when it omits valuable differences.
- About 60 seconds
Organization members must adapt to their own environments while coordinating with one another. A uniform report may discard valuable differences in state, so this research holds information capacity fixed and changes only the inputs available to the signal. The method is to first solve for members’ equilibrium and then compare organizational objectives. The two-player baseline shows that the mean may suffice with homogeneous priors and low capacity; losses arise when capacity increases or priors change. A general approximate-loss bound remains to be proved, and the current numerical results do not represent firm performance.
- About three minutes
An organization must enable its members to adapt to the states they each face while keeping their actions coordinated. This research compares two public signals: one can use the full state, while the other can use only the means of groups fixed in advance; both systems have the same upper limit on information capacity. This distinction matters in practice because a uniform report is easy to communicate but may discard differences that are valuable for coordination before the information is sent. Existing research discusses organizational information design and capacity constraints, so I need to check whether the loss bound resulting from a fixed aggregation rule constitutes a new result. In the model, the designer commits to a signal rule in advance, and members act on their individual incentives after observing the public signal; the organizational objective is calculated from those equilibrium actions, so the actions the designer wants cannot simply be treated as the outcome. The two-player homogeneous-prior baseline gives a zero-loss threshold at low capacity, with losses arising at higher capacity; changing the prior variance can produce losses even at low capacity. These are derivations and calculations under specific conditions. The general approximate-loss bound and its difference from the closest literature still need to be checked. The work plan is to first replicate and compare the literature, then try to prove the result or find a counterexample. The core theoretical component does not require company data; the public network is used only for a computational demonstration. If the general bound does not hold, the scope will be narrowed to provable conditions or a clear counterexample.
本研究計画では、同じ情報容量の下で、全ての状態を利用できる公共シグナルと、あらかじめ決められたグループの平均値だけに基づく公共シグナルを比較します。組織の構成員が行動を調整する際、集約によってどの差異が失われ、どの条件では損失が生じないのかを明らかにしたいと考えています。理論モデルと数値計算を用いますが、一般的な近似損失の評価は、今後検証すべき研究課題です。
The wording above is for practice and does not represent the applicant’s prior achievements
| Situation | Japanese example | Action to take |
|---|---|---|
| Did not hear clearly | 申し訳ありません。最後の部分をもう一度お聞かせいただけますか。 | Ask the other person to repeat only the part that was unclear |
| Question has two possible interpretations | ご質問は、モデル内の最適性と、現実への適用可能性のどちらについてでしょうか。 | First confirm whether the discussion concerns the model’s conclusion or its real-world generalizability |
| Not familiar with the paper mentioned | その論文については、現時点では十分に理解できていません。 | Note the exact reference and later check its version and proposition |
| Realize you stated a condition incorrectly | 先ほどの説明を訂正します。この結論には、情報開示の前には私的情報を持たないという条件が必要です。 | State the original error, the necessary condition, and the scope of its effect |
| Presented a calculation as a proof | これは特定の設定での数値結果であり、一般的な証明ではありません。 | Identify which results still need proof |
- 01
How should you answer if a professor interrupts your explanation and asks about one point?
Answer only the point they asked about: give your judgment first, then explain your reasoning and conditions.
- 02
How should you explain why you use a theoretical model if a professor asks?
Public information changes members’ beliefs and actions, and coordination among their actions also affects the organizational objective, so the equilibrium must be specified first. Linear, quadratic, and Gaussian assumptions provide a verifiable baseline and also limit the scope of the conclusions.
- 03
How can you ask for time to think in Japanese when you cannot answer yet?
You can say, “条件を整理してからお答えしてもよろしいでしょうか。” Then state what you already know and distinguish whether the point to check concerns a fact, a formula, or a paper.
Contact & application
Contact, meetings and application checks
When contacting a professor, raise a research question they can answer; if there is a preliminary interview, turn their feedback into specific revisions. Check application procedures separately against the target year and selection category: a similar research direction does not substitute for formal admission or materials requirements.
Prepare a specific research question before contacting a professor
Write the research question in one sentence, then prepare a related paper you have actually read and a point you have not resolved. The message should state your real identity, study status, target year and program, the extent of your paper reading, and one specific question you would like to ask. Write the message yourself based on your actual circumstances, and attach materials only as permitted by the school or recipient.
You could ask whether the economic interpretation of fixed group means is clear, or whether a candidate bound follows directly from prior research. If discussing an empirical direction, ask the professor to clarify the research question and data requirements.
- 01
Suppose a professor says in an interview, “The scope is too broad.” What should you ask first?
Ask whether the main question, prior extension, or general loss bound is too broad; explain that you plan to retain a main line with two players or a clearly specified group structure, and defer the prior extension.
After the meeting, separately record explicit decisions, suggestions, and points to confirm; do not describe a scope discussion as an agreed thesis topic.
- 02
Suppose a professor says in an interview, “This is too mathematical” or “It is not realistic enough.” What should you do?
Return to who designs, who acts, and which differences in state could change the organizational objective; acknowledge that public signals and no initial private observations are strong assumptions, then ask whether the application setting should be reconsidered.
The economic explanation or research question may need to change; simply deleting a few formulas is not an adequate response.
- 03
Suppose a professor suggests, “Switch to empirical work” or “Read this paper first.” What should you do?
First clarify the specific issue the suggestion addresses; record the paper’s version and the proposition to read. If switching to empirical work, reassess data authorization, identification, and the two-year workload.
Check first, then write a revised version; do not promise on the spot that every direction can be completed.
Check the official application requirements for the target selection process
Record the version of the requirements, the date obtained, and evidence of completion for each item
- Applicant status and selection
Enrollment year, program, selection category, academic qualifications, and whether a preliminary eligibility review is required.
Status: Check for each application round; keep the master’s and non-degree research student routes separate
- Application and exam dates
Record separate dates for online applications, payment, materials due by the specified deadline, and exams, including the exact time, time zone, and proof.
Status: Do not assume that payment means all procedures are complete
- Language and materials
Score type, validity period, and score-reporting method; forms, length, format, authorship rules, and restrictions on changing materials.
Status: Check the rules for that application round
- Research and supervision
Supervisor list, webpage updates, and fit with the research fields and methods required by the program.
Status: Do not omit required content just because the sample has no separate heading for it
- Date requirements were checked
The administrative information cited on this page was checked on October 6, 2026; no corresponding new requirements for the 2027 academic year had been verified at that time.
Status: Recheck dates for the new application round; do not carry last year’s dates forward by one year
Interview preparation and formal application procedures
If invited to an interview, first confirm the time, format, language, and required materials. Bring a one-page research question, notes on a paper you have actually read, evidence of your own preparation, and a question on which you want feedback; before the meeting ends, restate your understanding of the proposed revisions and ask the professor to confirm it.
Based on the information checked through October 6, 2026, the announced date for the 2027 general first-round recruitment has passed, while older-year information remains visible in other sections. The requirements for that round call for an online application, payment, and submission of materials within the stated period, and include restrictions on changing materials and on who may author application essays. Check other rounds separately against their official requirements; direct procedural questions to the admissions office. A sample text must not be passed off as an application essay independently written by the applicant simply by changing the name or pronouns.
Questions & revision
Follow-up questions and revisions
Interview questions may change the capacity, priors, or information held by members. You can use that feedback to revise the research plan only if you can say which conclusion needs recalculating and what you misstated. Handling of submitted materials must still follow the formal rules for that application round.
- 01
If the grouping rule preserves every state, will aggregation still cause an efficiency loss?
See the explanation and limits of the answer
The grouping rule no longer removes any state direction, so the two regimes can use the same inputs and have the same optimum; the efficiency loss is zero. This follows because their feasible signal sets are identical.
- 02
If information capacity is zero, can either regime improve the organizational objective?
See the explanation and limits of the answer
The signal cannot carry information about the state, so neither regime improves on the no-information baseline. This conclusion applies only when capacity is zero.
- 03
In the two-person unit-prior baseline, what happens if the individual coordination weight is 0.5 and the organizational weight changes to 2?
See the explanation and limits of the answer
The value of the mean direction remains 1, while the value of the difference direction becomes −0.25. The optimal design does not allocate capacity to a direction with negative value, so under this setting it uses only the mean and has no loss at any finite capacity. This is a model calculation and cannot be used to describe real organizations.
- 04
If both coordination weights are changed to zero, does the zero-loss result at low capacity still hold?
See the explanation and limits of the answer
No. Under a unit prior, both directions are equally valuable; the general regime allocates capacity to both directions, while the mean-only regime can use only one. In this case (capacity greater than zero). The connected-coordination condition in the original benchmark cannot be omitted.
- 05
How should you correct someone who calls 100,000 Monte Carlo draws “an experiment with 100,000 people”?
See the explanation and limits of the answer
100,000 is the number of artificial random draws, not the number of participants. The simulation is used to check the analytical calculation and signal implementation; the applicant should also state accurately whether they have run these calculations themselves.
- 06
Can theoretical research continue if the public-network demonstration is removed?
See the explanation and limits of the answer
Yes. The small public graph is a computational demonstration, not a prerequisite for the theoretical proof; the list of outputs and oral explanation should also remove references to that demonstration.
| Change or feedback | What needs to be checked again | What to change in the plan |
|---|---|---|
| Members already have private information | Beliefs, expectations about others’ actions, equilibrium, and welfare | The original public-posterior equilibrium equation cannot be reused directly |
| Heterogeneous or correlated priors | Value directions after whitening, the aggregation subspace, and capacity allocation | The zero-loss result for the mean at low capacity needs to be reverified |
| Switching from theory to firm-level empirical work | Research question, data authorization, variables, and identification design | Withdraw the claim that firm data are unnecessary for the new topic |
| Closest related papers cover the candidate contribution | Exact versions, assumptions, propositions, and differences from this project | Update the abstract, research question, schedule, and oral explanation of the contribution together |
Oral-exam correction practice
Turn an overgeneralized claim into a conclusion with stated conditions
Hypothetical claim: “Group means are always lossless at low capacity.” It could be revised to: Under the current network and parameter conditions with two people and a unit prior, the optimal signal below a specified threshold uses only the mean direction, so aggregation to the mean is lossless in this benchmark; a low-capacity counterexample already exists for heterogeneous priors.
Hypothetical claim: “Numerical checks have proved a general second-order loss bound.” It could be revised to: Calculations for specific parameters support checks of the implementation; the general second-order bound remains to be proved, and the closest related literature and behavior near the threshold also need to be checked.
How to preserve versions and continue the research before and after submission
- 01
Before submission: check that everything uses the same version
If you find an error in a number or code, check the original output, tables, abstract, and oral figures together; if you change a model assumption, update the timing, equilibrium, welfare, and workload together. Keep the reason for each revision and a record of work you completed yourself.
- Outcome
The main text, figures, attachments, and oral outline from the same version
- 02
After submission: preserve the submitted draft and new findings
Keep the submitted version and later notes; when speaking, distinguish “the setup at submission” from “a problem found later.” Check the formal procedure for that application round to see whether supplemental materials or replacements are permitted; do not replace anything without authorization.
- Outcome
The submitted version, issue log, and official responses on how to handle them
- 03
After the interview: record questions and omissions
Note the original question, your original answer, omitted conditions, and sources to check; do not infer your admission chances from facial expressions, interview length, or polite wording.
- Outcome
Checklist for the next study and revision
- 04
After admission or changing application route: confirm again
After admission, check the formal notice and turn the plan into first-month tasks for reading, replication, and comparing contributions. If not admitted or changing supervisors, review academic fit, preparation, language, and procedures separately; do not invent a reason or merely swap in another supervisor’s name.
- Outcome
A new version suited to actual supervision and formal procedures
Sources & reading
Sources and reading
When a professor asks where a conclusion comes from, you need to find the original text and explain which part you understood. The links below can help you check the literature; see the requirements for the target year in the official application guidelines.
How to look it up again
Where to find the content
- Research plan
The abstract summarizes the research plan; §§1–2 explain the background and literature; §§3–5 explain the model, methods, and preliminary results; §§6–7 explain the schedule and limitations.
- The student’s own records
Reading, derivations, and calculations already included in the sample must be recorded separately from work actually completed by the applicant.
Scope of evidence
- Preliminary calculations
Numerical results in the sample are for demonstration only and should be recalculated independently before use.
Scope: finite examples cannot prove a general theorem, and they cannot be presented as research experience already completed by you.
- Research still to be completed
The general approximate-loss bound and candidate academic contribution still require proof, counterexample checks, and review of the closest related literature.
- Application rules
Check official documents for the target year, program, and selection round.
Scope: The formal version should be in Japanese or English; English is used for instructional explanation. Confirm the specific length, format, authorship rules, and restrictions on changing materials with the target program.
Links to papers and official information
First record the exact version and the extent of your actual reading, then compare the research question, assumptions, and conclusions. The following are links to papers and official pages; 凪野透 is a fictional example faculty member and has no corresponding researcher page.