Non-cooperative bargaining in apex games and the kernel

This paper studies non-cooperative bargaining with random proposers in apex games. Two different protocols are considered: the egalitarian protocol, which selects each player to be the proposer with equal probability, and the proportional protocol, which selects each player with a probability proportional to his number of votes. Expected equilibrium payoffs coincide with the kernel for the grand coalition regardless of the protocol. The equilibrium is in mixed strategies and the indifference conditions can be reinterpreted in the language of the kernel.     

Nash equilibrium when players account for the complexity of their forecasts

Nash equilibrium is often interpreted as a steady state in which each player holds the correct expectations about the other players' behavior and acts rationally. This paper investigates the robustness of this interpretation when there are small costs associated with complicated forecasts. The model consists of a two-person strategic game in which each player chooses a finite machine to implement a strategy in an infinitely repeated 2×2 game with discounting. I analyze the model using a solution concept called Nash Equilibrium with Stable Forecasts (ESF). My main results concern the structure of equilibrium machine pairs. They provide necessary and sufficient conditions on the form of equilibrium strategies and plays. In contrast to the “folk theorem,” these structural properties place severe restrictions on the set of equilibrium paths and payoffs. For example, only sequences of the one-shot Nash equilibrium can be generated by any ESF of the repeated game of chicken.     

Reputation with observed actions

Summary A single long-run player plays a fixed stage game (simultaneous orsequential move) against an infinite sequence of short-run opponents that play only once but can observe all past realized actions. Assuming that the probability distributions over types of long and short-run players have full support, we show that the long-run player can always establish a reputation for theStackelberg strategy and is therefore guaranteed almost his Stackelberg payoff in all Nash equilibria of the repeated game.The financial support of the National Science Foundation, Grant SES 90-7999, and of Consiglio Nazionale delle Ricerche is gratefully acknowledged. I wish to thank David Levine, Wolfgang Pesendorfer and Seminar Participants at UCLA, Universidad Carlos III de Madrid and University of Naples for useful discussions and suggestions.     

Anonymity in nonatomic games

This paper purpose is twofold. First, it offers a critical review of the proofs of existence of pure strategy Nash Equilibria in nonatomic games. In particular, it focuses on the alternative ways of formalizing the critical assumption of anonymity. Second, the paper proves the existence of pure strategy Nash Equilibria by relaxing anonymity and allowing instead for “limited anonymity” (i.e. players’ decisions depend on the average strategy of a finite number of players’ subsets and not on the average strategy of the whole set of players). (JEL: C72, C79)     

Universality of Nash components

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game—a game where all players have two pure strategies and a common utility function with values either zero or one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k.     

The effects of the 2005 Bankruptcy Reform in Brazil

This paper studies the effect of the 2005 Bankruptcy Reform in Brazil. Using firm-level data we found that the increase in the level of creditors' protection reduced the cost of debt and increased the amount borrowed by the firms.     

英美董事个人在破产中所担民事责任及对我国完善《破产法》的启迪

普通法关于董事在公司正常营运时与公司破产时所承担的义务迥然不同。在公司破产情况出现时,公司风险的承担者由股东转为债权人,后者成为公司的剩余索取者而继之为公司的所有者。他山之石,可以攻玉,通过对英美两国董事在破产前及破产时责任的比较分析来探究其经验教训,可以看到我国《公司法》和《破产法》对董事责任预防性不足之处,也可以为我国破产法后期发展和修订提供借鉴。     

On games with identical equilibrium payoffs

Summary. This paper compares the sets of Nash, coalition- proof Nash and strong Nash equilibrium payoffs of normal form games which are closely related. We propose sufficient conditions for equivalent or closely related games to have identical sets of equilibrium payoffs. Received: April 23, 1999; revised version: November 23, 1999     

Stability of the cooperative equilibrium in N-person prisoners' dilemma with sequential moves

Summary. Nishihara [3] showed that N-person prisoners' dilemma has a cooperative Nash equilibrium, if the players decide their actions sequentially in the order determined by Nature under a certain information structure, and if each player's payoffs satisfy a certain inequality. This paper examines the stability of this cooperative equilibrium against two matters: players' slight mistakes and deviations by coalitions. The main results are as follows: (i) if the inequality on each player's payoffs strictly holds, then the cooperative equilibrium is a strictly proper equilibrium; (ii) if N≤3, and if full cooperation is Pareto efficient in N-person prisoners' dilemma, then the cooperative equilibrium is a strong Nash equilibrium; (iii) the cooperative equilibrium is in general a coalition-proof Nash equilibrium. Received: June 23, 1997; revised version: December 2, 1997     

Existence of Nash networks in one-way flow models

This paper addresses the existence of Nash equilibria in one-way flow models in a number of different settings. In these models players form costly links with other players and obtain resources from them through the directed path connecting them. We find that heterogeneity in the costs of establishing links plays a crucial role for the existence of Nash networks. The paper also provides conditions for the existence of Nash networks in models where costs and values of links are heterogeneous. We would like to thank an anonymous referee for useful suggestions. We would also like to thank Hans Haller and participants at the AEA Meetings 2007 for helpful comments. Sudipta Sarangi acknowledges the support of NSF grant HSD-0527315 and the hospitality of CREUSET, Jean Monnet University.     

Undecidability of the existence of pure Nash equilibria

Summary. The purpose of this paper is to show that for any positive integer n, there exists no algorithm which decides for each non-cooperative n-person game in strategic form with partially computable payoff functions whether it has a pure Nash equilibrium or not.Received: 20 March 2002, Revised: 23 April 2003, JEL Classification Numbers: C72.The author thanks the Referee and the Associate Editor for offering critical comments on this paper, which is dedicated to his brother Konstantinos Efstathiou Sofronidis.     

基于非合作博弈的期货市场策略分析

本文基于非合作博弈的方法,通过建立非合作博弈模型对期货市场多空双方的行动策略进行分析,分别就完全信息博弈、不完全信息博弈和不完美信息博弈三种不同的博弈环境,讨论了多空双方在不同的市场形势下的行动策略、博弈的均衡及结果。分析结果表明在不同的博弈环境下,无论是均势市场、多头市场还是空头市场,资金和信息对于期货市场多空双方的博弈策略具有至关重要的影响。基于此结论,本文进一步提出,为了获得资金优势和信息优势,建立期货投资基金,形成博弈联盟是一种有效的博弈形式,以此为基础的合作博弈分析方法是分析联盟博弈的有效方法。     

Large games with transformed summary statistics

Summary. The existence of pure-strategy Nash equilibrium is shown for a non-cooperative game with a continuum of small players and a compact action space. The players payoffs depend on their own actions and the mean of the transformed strategy profiles. This covers the case when the payoffs depend on players own actions and finitely many summary statistics.Received: 24 November 2003, Revised: 29 March 2004, JEL Classification Numbers: C7, D4. Correspondence to: Haomiao YuThe authors are grateful to Yeneng Sun for his help and guidance. They also thank Ali Khan, Kali Rath, and an anonymous referee for useful comments.     

电信产业默契合谋的存在性与稳定性分析

合谋是产业组织理论研究的重要问题之一,它易出现于寡头垄断行业中。合谋的出现会降低消费者剩余,对整个社会福利造成损失,因此应当尽量去除。电信产业是一个典型的寡头垄断产业,电信运营商之间具有很强的相互依赖性,易出现合谋,特别是默契合谋。所谓默契合谋是指寡头垄断厂商以一种纯粹“非合作”的方式进行的合作。本文首先应用古诺模型对电信产业默契合谋的存在性进行理论分析,并举出实例予以佐证。在此基础上,从理论上进一步证明了电信产业默契合谋具有不稳定性,指出运营商之间的合谋是一个“囚徒困境”。进而应用冷酷策略,研究了电信产业默契合谋维持的激励条件,并从成本对称性、市场信息透明度、产品差异性、卖方集中度和技术进步程度等方面分析了影响电信产业默契合谋的相关因素。并指出现实中,默契合谋和价格竞争往往是交替出现的。     

Resolving Indeterminacy in Coordination Games: A New Approach Applied to a Pay-as-you-go Pension Scheme

This paper shows that when players ignore what outcome will emerge because of the presence of multiple equilibria, they can coordinate their expectations by forming an initial belief based on the principle of indifference followed by a process of reasoning that updates this belief. Since this procedure describes a natural way to form beliefs under indeterminacy, it is reasonable for every agent to conjecture that all the others form their beliefs according to the same logic. Exactly the fact that agents are aware that they form their beliefs following the same procedure allows them to successfully coordinate their expectations.