Revealed preferences of individual players in sequential games

This paper studies rational choice behavior of a player in sequential games of perfect and complete information without an assumption that the other players who join the same games are rational. The model of individually rational choice is defined through a decomposition of the behavioral norm assumed in the subgame perfect equilibria, and we propose a set of axioms on collective choice behavior that characterize the individual rationality obtained as such. As the choice of subgame perfect equilibrium paths is a special case where all players involved in the choice environment are each individually rational, the paper offers testable characterizations of both individual rationality and collective rationality in sequential games.     

Hierarchies of beliefs and the belief-invariant Bayesian solution

The belief-invariant Bayesian solution is a notion of correlated equilibrium in games with incomplete information proposed by Forges (1993), and hierarchy of beliefs over conditional beliefs is introduced by Ely and Peski (2006) in their study of interim independent rationalizability. We study the connection between the two concepts. We partially characterize the correlations embedded among type spaces with the same set of hierarchies of beliefs over conditional beliefs with partially correlating devices, which send correlated signals to players in a way that preserves each player’s belief about others’ types. Since the belief-invariant Bayesian solution is also implemented by such correlating devices, we then establish that it is invariant on equivalent type space.     

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.     

Sequential bargaining with common values

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players who jointly own this object. The players are asymmetrically informed about the object’s value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium outcome of this game which is unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and non-deterministically. The better informed player obtains a rent.     

The generalized Stackelberg equilibrium of the all-pay auction with complete information

We characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices. We consider a set of n players who are arbitrarily partitioned into a group of players who choose their efforts ‘early’ and a group of players who choose ‘late’. Only the player with the lowest cost of effort has a positive payoff in any equilibrium. This payoff depends on his own timing vis-a-vis the timing of others. We also show that the choice of timing can be endogenized, in which case the strongest player typically chooses ‘late’, whereas all other players are indifferent with respect to their choice of timing. In the most prominent equilibrium the player with the lowest cost of effort wins the auction at zero aggregate cost. We thank Dan Kovenock and Luis C. Corchón for discussion and helpful comments. The usual caveat applies. Wolfgang Leininger likes to express his gratitude to Wissenschaftszentrum Berlin (WZB) for its generous hospitality and financial support.     

Robust games: theory and application to a Cournot duopoly model

In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231–273, 2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of incomplete information for finite games where players adopt a robust-optimization approach to contend with payoff uncertainty. They are called robust players and seek the maximum guaranteed payoff given the strategy of the others. Consistently with this decision criterion, a set of strategies is an equilibrium, robust-optimization equilibrium, if each player’s strategy is a best response to the other player’s strategies, under the worst-case scenarios. The aim of the paper is twofold. In the first part, we provide robust-optimization equilibrium’s existence result for a quite general class of games and we prove that it exists a suitable value \(\epsilon \) such that robust-optimization equilibria are a subset of \(\epsilon \)-Nash equilibria of the nominal version, i.e., without uncertainty, of the robust game. This provides a theoretical motivation for the robust approach, as it provides new insight and a rational agent motivation for \(\epsilon \)-Nash equilibrium. In the last part, we propose an application of the theory to a classical Cournot duopoly model which shows significant differences between the robust game and its nominal version.     

Analysis of information feedback and selfconfirming equilibrium

Recent research emphasizes the importance of information feedback in situations of recurrent decisions and strategic interaction, showing how it affects the uncertainty that underlies selfconfirming equilibrium (e.g., Battigalli et al., 2015, Fudenberg and Kamada, 2015). Here, we discuss in detail several properties of this key feature of recurrent interaction and derive relationships. This allows us to elucidate different notions of selfconfirming equilibrium, showing how they are related to each other given the properties of information feedback. In particular, we focus on Maxmin selfconfirming equilibrium, which assumes extreme ambiguity aversion, and we compare it with the partially-specified-probabilities (PSP) equilibrium of Lehrer (2012). Assuming that players can implement any randomization, symmetric Maxmin selfconfirming equilibrium exists under either “observable payoffs,” or “separable feedback.” The latter assumption makes this equilibrium concept essentially equivalent to PSP-equilibrium. If observability of payoffs holds as well, then these equilibrium concepts collapse to mixed Nash equilibrium.     

Learning games

This paper presents a model of learning about a game. Players initially have little knowledge about the game. Through playing the same game repeatedly, each player not only learns which action to choose but also constructs a personal view of the game. The model is studied using a hybrid payoff matrix of the prisoner's dilemma and coordination games. Results of computer simulations show that (1) when all the players are slow at learning the game, they have only a partial understanding of the game, but might enjoy higher payoffs than in cases with full or no understanding of the game; (2) when one player is quick in learning the game, that player obtains a higher payoff than the others. However, all can receive lower payoffs than in the case in which all players are slow learners.     

Stopping with congestion and private payoffs

This paper analyses a two-player stopping game with multiarmed bandits in which each player chooses between learning about the quality of her private risky arm and competing for the use of a single shared safe arm. The qualities of the players’ risky arms are independent. A player whose risky arm produces a success no longer competes for the safe arm. We assume that a player observes her opponent’s actions but not his realised payoffs. She is therefore never certain whether her opponent is still competing for the safe arm. When the players’ prior probabilities of success are sufficiently close, there exists no pure strategy equilibrium, and we characterise the unique mixed strategy equilibrium. Otherwise, the unique equilibrium is in pure strategies. The amount of experimentation performed in equilibrium is inefficiently low but, for many priors, higher than if successes are publicly observed.     

蜈蚣博弈新视角——预期心理的应用

考虑到在蜈蚣博弈中运用逆推归纳法具有不稳定性以及混合策略的存在,无论是理性人假设发生偏离和理性人假设不发生偏离的情况下,逆推归纳法解蜈蚣博弈都具有不合理性。采用预期心理的方法可以预测蜈蚣博弈结果最有可能出现的结果。通过第三方的实验数据检验,蜈蚣博弈结果会以70 %的概率出现在预期心理预测的阶段。     

Delay,multiplicity, and non-existence of equilibrium in unanimity bargaining games

We consider a class of perfect information bargaining games with unanimity acceptance rule. The proposer and the order of responding players are determined by the state that evolves stochastically over time. The probability distribution of the state in the next period is determined jointly by the current state and the identity of the player who rejected the current proposal. This protocol encompasses a vast number of special cases studied in the literature. We show that subgame perfect equilibria in pure stationary strategies need not exist. When such equilibria do exist, they may exhibit delay. Limit equilibria as the players become infinitely patient need not be unique.     

审计风险成因--基于信息经济学的分析

文章从信息经济学的角度,通过对自然存在的不确定性以及股东和审计人员、管理层与审计人员之间的信息不对称等对审计风险的影响的分析表明,建立和完善审计风险的管理体制,完善审计市场结构、公司与事务所的治理结构,引入必要的激励和约束机制,可以减少交易各方的信息不对称,从而改善审计业务市场的交易效率和效益,降低社会性的审计风险水平。     

Uncertainty,the Lemon Problem,Asymmetric Information and Countertrade

Abstract

A review of the International Trade literature suggests that uncertainty caused by the lack of perfect information and/or asymmetric information provides a motivation for countertrade (Hennart, 1990; Mirus & Yeung, 1986; Yavas & Vardiabasis, 1988). After presenting the most prevalent forms and examples of countertrade, this study shows how uncertainty can lead to some of the most common forms of countertrade; counterpurchase, buyback and offset. The paper compares and contrasts two strategies facing the management team of a profit-maximizing firm. The standard neoclassical mathematical model developed and presented shows that countertrade strategy may be superior to standard money-mediated trade strategy when there is uncertainty. Therefore, countertrade (particularly, buyback, counterpurchase and offset) may be a rational response to conditions that restrict standard trade. As such, countertrade can supplement standard money-mediated trade and contribute to the growth of international business.     

Communication equilibria with partially verifiable types

This paper studies the set of equilibria that can be achieved by adding general communication systems to Bayesian games in which some information can be certified or, equivalently, in which players’ types are partially verifiable. Certifiability of information is formalized by a set of available reports for each player that varies with the true state of the world. Given these state-dependent sets of reports, we characterize canonical equilibria for which generalized versions of the revelation principle are valid. Communication equilibria and associated canonical representations are obtained as special cases when no information can be certified.     

The foundation of stability in extensive games with perfect information

This paper studies the decision-theoretic foundation for the notion of stability in the dynamic context of strategic interaction. We formulate and show that common knowledge of rationality implies a “stable” pattern of behavior in extensive games with perfect information. In the “generic” case, our approach is consistent with Aumann’s [Aumann, R.J., 1995. Backward induction and common knowledge of rationality. Games and Economic Behavior 8, 6–19] result that common knowledge of rationality leads to the backward induction outcome.     

信息产业化环境下数字图书馆著作权合理使用的立法完善

文章结合当前信息产业化环境下著作权保护中的合理使用制度,以及数字图书馆具有的特点,分析我国《信息网络传播权保护条例》第7条关于数字图书馆对著作权合理使用制度的立法不足,并提出完善该方面制度的立法建议。     

Learning and decision costs in one-person games

This paper reports the results of a two-part data analysis of learning in a repeated costly decision experiment. In the first part we test payoff dominance under the hypothesis of expected payoff maximization. We utilize a dynamic probability distribution over decisions for each player, characterizing what each player has learned about the payoff function by the moments from these distributions. In the second part, we test the hypothesis of expected payoff maximization for players in each treatment group. Expected payoff maximization is supported but payoff dominance is not. Copyright © 1999 John Wiley & Sons, Ltd.     

基于管理层视角的不确定性会计信息披露分析

现有的和潜在的投资者、债权人等需要不确定性的信息,来减少他们决策的不确定性,从而增加期望收益。但是,对于管理层来说,信息的披露有可能带来负面影响。因此,管理层在选择信息披露时会在信息披露带来的收益与产生的成本之间作出权衡,从而选择信息披露的程度。本文主要从管理层的角度,分析了管理层不会完全披露信息的原因,并运用成本恒定模型分析管理层信息披露程度。     

Solving the incomplete markets model with aggregate uncertainty by backward induction

This paper describes a method to solve models with a continuum of agents, incomplete markets and aggregate uncertainty. I use backward induction on a finite grid of points in the aggregate state space. The aggregate state includes a small number of statistics (moments) of the cross-sectional distribution of capital. For any given set of moments, agents use a specific cross-sectional distribution, called “proxy distribution”, to compute the equilibrium. Information from the steady state distribution as well as from simulations can be used to chose a suitable proxy distribution.