Correlation with Forwarding

關聯性與訊息轉傳

10.6277/TER.202310_51(4).0001

Chun-Ting Chen(陳俊廷)

pre-play communication ； correlated equilibrium ； forwarding ； 賽前溝通 ； 關聯性均衡 ； 轉傳

經濟論文叢刊

51卷4期（2023 / 10 / 01）

429 - 462

英文;繁體中文

In this paper, I consider three-player complete information games augmented with pre-play communication. Players can privately communicate with others, but not through a mediator. I implement correlated equilibria by allowing players to authenticate their messages and forward the authenticated messages during communication. Authenticated messages, such as letters with signatures, cannot be forged but sent or received by players. With authenticated messages, I show that if a game G has an α as a point in the convex hull of Nash equilibrium, then any correlated equilibrium distribution in G, which has rational coefficients and gives each player a strictly higher payoff than what α does, can be implemented via a pre-play communication. The proposed communication protocol does not require perfect public recording, as has been used in Bárány (1992), and does not publicly expose players' private messages at any stage during communication.

我考慮三人完全資訊賽局的賽前溝通。賽前溝通可以讓玩家們在賽局開始前，與其他玩家互相傳遞私有訊息。當玩家可以轉傳訊息並驗證訊息時，我證明關聯性均衡可以被賽前溝通實現。可驗證的訊息，比如簽了名的信件，可以被傳遞但不能被偽造。當訊息可以被驗證時，我證明：如果一個賽局具有在其Nash均衡凸包上的點α，那麼，對於任何一個此賽局的關聯性均衡，若其係數皆為有理數且給予任何玩家嚴格大於在α下的報酬，此關聯性均衡就可以被賽前溝通實現。此文章所提出的賽前溝通過程，不需要可以將訊息完美記錄的物件（Bárány,1992），且在溝通過程中的任何階段，玩家的私有訊息都不會被公開。

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