Coordinating under incomplete information

We show that, in a minimum effort game with incomplete information where player types are independently drawn, there is a largest and smallest Bayesian equilibrium, leading to the set of equilibrium payoffs (as evaluated at the interim stage) having a lattice structure. Furthermore, the range of equilibrium payoffs converges to those of the deterministic complete information version of the game, in the limit as the incomplete information vanishes. This entails that such incomplete information alone cannot explain the equilibrium selection suggested by experimental evidence. We thank Atila Abdulkadiroglu, Hans Carlsson, Ani Guerdjikova and an anonymous referee for helpful comments. Part of this work was done while Asheim was visiting Cornell University, which hospitality is gratefully acknowledged.     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.     

Bounded memory and permanent reputations

A recent result in repeated incomplete information games is that after an arbitrarily long history, any equilibrium of the continuation game must be an equilibrium of the complete information game. This result implies that reputation is a short-run phenomenon. We study a particular class of reputation games and show that bounded memory may lead to permanent reputations. In fact, for a particular range of parameters, a bounded memory player may never be able to learn anything at all.     

What restrictions do Bayesian games impose on the value of information?

In a Bayesian game players play an unknown game. Before the game starts some players may receive a signal regarding the specific game actually played. Typically, information structures that determine different signals, induce different equilibrium payoffs. In two-person zero-sum games the equilibrium payoff measures the value of the particular information structure which induces it. We pose a question as to what restrictions Bayesian games impose on the value of information. We provide answers for two kinds of information structures: symmetric, where both players are equally informed, and one-sided, where only one player is informed.     

基于博弈论的供应链管理分析

运用博弈论的思想,从“囚徒困境”类的完全信息静态博弈、重复博弈、不完全信息动态博弈、信号博弈等角度,对供应链节点企业的合作关系进行分析。     

Game contingent claims in complete and incomplete markets

A game contingent claim is a contract which enables both the buyer and the seller to terminate it before maturity. For complete markets Kifer [Finance and Stochastics 4 (2000) 443–463] shows a connection to a (zero-sum) Dynkin game whose value is the unique no-arbitrage price of the claim. But, for incomplete markets one needs a more general approach. We interpret the contract as a generalized non-zero-sum stopping game. For the complete case this leads to the same results as in Kifer [Finance and Stochastics 4 (2000) 443–463]. For the general case we show the existence of an equilibrium point under the condition that both the seller and the buyer have an exponential utility function. For other utility functions such a point need not exist in the context of incomplete markets.     

Observing each other’s observations in a Bayesian coordination game

We study a Bayesian coordination game where agents receive private information on the game’s payoff structure. In addition, agents receive private signals that inform them of each other’s private information. We show, that once agents possess these different types of information, there exists a coordination game in the evaluation of this information. Even though the precisions of both signal types are exogenous, the precision with which agents forecast each other’s actions in equilibrium turns out to be endogenous. As a consequence, there exist multiple equilibria which differ with regard to the way that agents weight their private information to forecast each other’s actions.     

Markov Perfect equilibria in repeated asynchronous choice games

This paper examines the issue of multiplicity of Markov Perfect equilibria in alternating move repeated games. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is “non-generic” in the larger space of state dependent payoffs. We further obtain that the set of completely mixed Markov Perfect equilibria is generically empty with respect to stage game payoffs.     

On the relationship between robustness to incomplete information and noise-independent selection in global games

This note demonstrates that a symmetric 3×3 supermodular game may fail to have any equilibrium robust to incomplete information. Since the global game solution in symmetric 3×3 supermodular games is known to be independent of the noise structure, this result implies that a noise-independent selection in global games may not be a robust equilibrium. Our proof reveals that the assumption in global games that the noise errors are independent of the state imposes a non-trivial restriction on incomplete information perturbations.     

MACROECONOMIC POLICY EVALUATION AND OPTIMAL CONTROL THEORY: A CRITICAL REVIEW OF SOME RECENT DEVELOPMENTS

Abstract. This survey addresses the recent literature on the application of optimal control theory and game theory to macroeconomic policy evaluation and design. This literature focuses on strategic interactions between governments and private agents engaged in dynamic non-cooperative games and emphasizes such issues as precommitment, credibility and reputation as important and endemic aspects of optimal policy design. A dominant theme is the problem of dynamic inconsistency and the inferiority of an equilibrium in single-stage full-information games without commitment. This may be alleviated in repeated games involving reputation effects and threat strategies designed to coerce rivals into pursuing particular strategies and to sustain a sequential equilibrium. The type and characteristics of a sequential equilibrium also depend importantly upon the information structure conditioning players'beliefs under uncertainty. Included here are separating and pooling equilibria, involving notions of learning, signalling and information revelation. Additional dimensions exist in stochastic systems which introduce other forms of uncertainty. Optimal control and game theory have also been applied to international macroeconomic policy design, with emphasis on the potential costs and benefits of non-cooperative and cooperative behaviour between countries and problems of international policy coordination.     

基于博弈论的供应链合作伙伴选择研究

以博弈论为基础,针对供应链管理中供应商的选择问题,利用信息博弈的方法,研究通过高能力供应商特有的特点,在不完全信息的情况下甄别出供应商真实的能力。     

例谈探究式教育游戏设计

探究式教育游戏是以游戏为载体,以网络为平台,将知识以游戏任务的形式融入主题游戏并通过交互策略来引导学生探究思维的学习软件。本文以"乐中学"游戏为例阐述了探究式教育游戏的设计流程、基本结构以及应注意的问题。     

Social pressure,uncertainty, and cooperation

We analyse the role of uncertainty in a sequential game where players have to decide whether to contribute to a public project or not. A player's payoff may depend on his belief about the other player's action which allows us to model social pressure. Using the theory of psychological games, we show that the players' propensity to choose an individually costly action such as cooperation in a public project may increase if there is some uncertainty about who has cooperated before. A central agency, e.g. the government, can induce incomplete information by using a randomization policy, thus crowding in private contributions. Received: November 16, 1998 / Accepted: May 31, 1999     

Strategic Interaction between Governments and Investors under Privatization Programs

This article analyses the strategic moves of governments and investors under privatization programs in a game‐theoretic context. In sequential‐move games of both perfect information and incomplete information, the best response of the strategic investors to observing a slow pace of privatization is to have a low participation in economic activity because of concerns over public policy credibility. This is true even if the government chooses to randomize its action to send mixed signals to the investors while adopting a slow pace of privatization for budgetary reasons. However, the outcome is Pareto inferior to a situation of phased but fast implementation of privatization programs and high private‐sector participation under plausible assumptions. Copyright © 2011 John Wiley & Sons, Ltd.     

铁路军事运输保障作战模拟不完全信息动态博弈模型研究

通过分析战时铁路军事运输过程中的博弈问题,提出了基于红蓝对抗的不完全信息动态博弈,并构建了相应的博弈模型,通过模拟实验分析单列车梯队的不完全信息动态博弈过程。     

RECENT ADVANCES IN OLIGOPOLY THEORY FROM A GAME THEORY PERSPECTIVE

Abstract. This paper surveys the contribution that recent developments in game theory have made to the understanding of oligopoly theory. It is argued that conventional models suffer from the problem that there are a number of solution concepts offered with little guidance as to which should be selected, and this is related to the static nature of the models employed. One important development in game theory has been the analysis of repeated games, and when applied to oligopoly theory this suggests that outcomes may be more cooperative than conventional theory suggests. Related to this is the requirement that firms employ credible threats to punish cheating from cooperative outcomes, and the paper examines the extent to which imperfect information may restrict the scope of firms to employ such punishments. One way in which firms may seek to make threats credible is through strategic investments, for example in production capacity, and the paper explores how competition over price or output is integrated with competition over instruments for strategic investment.     

The testable implications of zero-sum games

We study collective choices from the revealed preference theory viewpoint. For every product set of individual actions, joint choices are called Nash-rationalizable if there exists a preference relation for each player such that the selected joint actions are Nash equilibria of the corresponding game. We characterize Nash-rationalizable joint choice behavior by zero-sum games, or games of conflicting interests. If the joint choice behavior forms a product subset, the behavior is called interchangeable. We prove that interchangeability is the only additional empirical condition which distinguishes zero-sum games from general non-cooperative games.     

我国民族游戏开发探讨

文章对游戏产业的飞速发展、游戏开发人才的需求和培养以及政府对游戏产业的政策等方面作了较详细的分析,针对上述分析,提出了采用先进的Mstudio移动游戏开发网络系统进行游戏开发和培训,并对Mstudio系统的基本结构、功能、工作流程和特点作了较系统的阐述。     

Endogenous mechanisms and Nash equilibrium in competitive contracting games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.