On Maskin monotonicity of solution based social choice rules

Howard (J Econ Theory 56:142–159, 1992) argues that the Nash bargaining solution is not Nash implementable, as it does not satisfy Maskin monotonicity. His arguments can be extended to other bargaining solutions as well. However, by defining a social choice correspondence that is based on the solution rather than on its realizations, one can overcome this shortcoming. We even show that such correspondences satisfy a stronger version of monotonicity that is even sufficient for Nash implementability.     

Integrating the Nash program into mechanism theory

Abstract. The present paper provides a method by which the Nash Program may be embedded into mechanism theory. It is shown that any result stating the support of any solution of a cooperative game in coalitional form by a Nash equilibrium of some suitable game in strategic form can be used to derive the mechanism theoretic Nash-implementation of that solution. Received: 29 June 1999 / Accepted: 3 April 2002     

A mechanism implementing the proportional solution

We consider the problem of a commonly owned technology which transforms a single input into a single output. We are interested in implementing a social choice rule called theproportional solution. We introduce a mechanism which implements the proportional solution in Nash, strong (Nash) and undominated Nash equilibria. In the mechanism each agent announces only two numbers which can be interpreted as the total output and her share of the total input-output combination. This paper was originally titled "Doubly implementing the proportional solution." I would like to thank my advisor William Thomson for his detailed comments and suggestions. I would also like to thank Jeffrey Banks and Sung-Whee Shin for their comments. Two anonymous referees and an editor’s comments improved this paper substantially.     

Recursive Nash bargaining over a productive asset

We propose an equilibrium concept (the recursive Nash bargaining solution) that describes the outcome of repeated negotiations between two rational agents under the assumptions that the state of the economic system under consideration changes according to the actions of the players and that neither party can make binding commitments to future behavior. This equilibrium is dynamically consistent but typically not Pareto-efficient. As an application, we compute the recursive Nash bargaining solution in a model of two heterogeneous agents bargaining over the use of a productive asset with constant gross rate of return and study how the time-preference rates and the elasticities of substitution affect the solution.     

基于修正Nash谈判模型的科技创新合作收益分配研究

科技创新合作收益的分配对合作的可持续发展至关重要,目前还缺乏行之有效的模型和方案。文章利用NASH博弈的思想对两人收益分配问题展开讨论,进而扩展到多人收益分配问题,得出多人收益分配博弈的一个Nash均衡解。为反映各主体在科技创新收益分配中的权重,对收益分配的Nash谈判模型进行调整,从而得出修正的纳什均衡解。由此展开科技创新合作收益分配的方案探讨,为科技创新合作的可持续发展奠定理论基础。     

Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem

This study considers a situation in which agents choose the location of a public facility from a street according to a given mechanism. Agents have single-dipped preferences over a set of feasible locations. We analyze coalitional behavior for any given mechanism for this situation. We identify a necessary and sufficient condition for a mechanism to possess a strong Nash equilibrium by applying the minimax theorem of von Neumann and Morgenstern (1944). We introduce a class of core solutions and show that these solutions are characterized by strong Nash implementability. As a byproduct of these results, we propose a simple mechanism that implements any core solution in strong Nash equilibria.     

Contests with multiple alternative prizes: Public-good/bad prizes and externalities

We study contests in which there are multiple alternative public-good/bad prizes, and the players compete, by expending irreversible effort, over which prize to have awarded to them. Each prize may be a public good for some players and a public bad for the others, and the players expend their effort simultaneously and independently. We first prove the existence of a pure-strategy Nash equilibrium of the game, then establish when the total effort level expended for each prize is unique across the Nash equilibria, and then summarize and highlight other interesting and important properties of the equilibria. Finally, we discuss the effects of heterogeneity of valuations on the players’ equilibrium effort levels and a possible extension of the model.     

On evolutionarily stable behavior in contests

It is argued in this paper that the solution concept of an evolutionary stable strategy (ESS) is an adequate analysis tool for contest theory. Moreover, it is shown that in a contest ESS always differs from Nash equilibrium, the hitherto dominant solution concept in contest theory. Finally, an interpretation of finite population ESS contest behavior in terms of Nash behavior is supplied.Received: 10 February 2002, Accepted: 8 July 2002, JEL Classification: C79, D72, D 74Wolfgang Leininger: I have benefited from the comments and suggestions of Burkhard Hehenkamp and two anonymous referees.     

Sufficient conditions for Nash implementation

Given an objective for a group of three or more agents that satisfies monotonicity and no veto power, Maskin (1977) proposes a two-step procedure for constructing a game that implements the objective in Nash equilibrium. The first step specifies the strategy set of the game and three properties of the game rule that are together sufficient to insure Nash implementation of the objective. The second step is the explicit construction of a game that has these properties. An example is presented here that shows that the constructed game of the second step need not have one of the three properties of the first step, and it does in fact not Nash implement the objective in the example. The problem is attributable to restricted preferences. A solution proposed here is to appropriately expand the domain of definition of the objective. This insures that the constructed game has the properties of the game in Maskin's first step, and it therefore Nash implements the original objective.     

Efficient equilibria in a differential game of capitalism

One considers a differential game of capitalism ‘à la Lancaster’. Feedback Nash equilibria and Pareto optimal solutions are characterized under the assumption that the planning horizon is infinite. It is then shown that, by combining a Pareto optimal solution with the Nash feedback equilibrium strategy pair, which plays the role of a threat, one can obtain an efficient equilibrium which is also subgame perfect in the sense of Selten. This result modifies sensibly the previous interpretation of the inherent inefficiency of capitalism.     

Bargaining solutions with non-standard objectives

I examine the pure-strategy solutions of the sealed-bid bargaining game with incomplete information, when the buyer's and seller's objectives are other than the standard objective, namely maximization of expected profit. The motivation for this exploration lies in three problems of the standard formulation: the necessity of assuming common priors, the existence of uncountably many Nash equilibria, with no means for the players to coordinate on any one of them, and the uncertain relationship between these equilibria and observed behavior in bargaining experiments. Specifically, I consider two alternative objectives: minimization of maximum regret, and maximization of maximum profit. The solution concept here is not Nash equilibrium, but rather -individually rational strategy bundle. For that reason, I shall, where appropriate, use the word “solution” in place of “equilibrium.” Yet we find that the notion of Nash Equilibrium reappears, in a sense to be explained. In the minimax-regret case I find (in contrast to the case of expected profit) a unique solution; this solution reduces, for priors with coincident support, to the linear equilibrium of Chatterjee-Samuelson. In the maximum-profit case there are many solutions; they turn out to be slight generalizations of the one-step equilibria of Leininger-Linhart-Radner.     

Bayesian Nash equilibrium and variational inequalities

This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (1965) and that in a team by Radner (1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph.     

Bargaining with independence of higher or irrelevant claims

This paper studies independence of higher claims and independence of irrelevant claims on the domain of bargaining problems with claims. Independence of higher claims requires that the payoff of an agent does not depend on the higher claim of another agent. Independence of irrelevant claims states that the payoffs should not change when the claims decrease but remain higher than the payoffs. Interestingly, in conjunction with standard axioms from bargaining theory, these properties characterize a new constrained Nash solution, a constrained Kalai–Smorodinsky solution, and a constrained Kalai solution.     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

Buying cooperation in an asymmetric environmental differential game

We consider a two-player asymmetric differential game of pollution control. One player is non-vulnerable to pollution, or unwilling to consider damages when choosing her production policy in a non-cooperative game. We characterize the feedback-Nash equilibrium and the cooperative solution. We establish conditions under which the vulnerable player can buy the cooperation of the non-vulnerable player to control her emissions. We further use the Nash bargaining solution to allocate the total cooperative dividend between the two players and propose a time-consistent decomposition overtime of the total payoff.     

The relationship between mixed strategies and strategic groups

This paper identifies a theoretical basis for the existence of strategic groups. We represent the competitive marketplace by means of a game-theoretic model and motivate the existence of markets wherein the only Nash solution may be in mixed strategies. Given deterministic behavior on the part of the firms, we interpret this solution in terms of a strategic groups equilibrium. The major implication of this analysis is that strategic groups can exist even if there is no inherent asymmetry (in terms of skills) between firms.     

企业社会资本的自愿供给:一个静态博弈模型

本文在相关文献的基础上，重新界定了社会资本的内涵，并采用完全信息静态博弈模型研究了企业网络中社会资本的自愿供给问题。模型分析表明，在企业社会资本的供给决策过程中，纳什均衡解是可以达到的，但它小于帕累托最优解。论文还指出，企业的规模是影响企业社会资本均衡供给水平的重要因素之一。     

中国债券市场开放度的博弈分析

本文从信息是否完全的角度出发,运用博弈论和信息经济学的相关理论,对债券市场信息不对称、境外机构发行人民币债券和境外机构市场准入问题进行了静态和动态博弈分析。求解了不同情况下的纳什均衡,对债券融资中现实问题给予了理论阐述和证明,并分析了境外机构在境内发行人民币债券的各种影响。     

石油企业海外开发策略——反馈纳什均衡解法的应用

微分博弈是博弈论中最复杂而又甚有实用价值的分支。由于经济系统处于时时的动态之中,很多经济行为或状态变量在时间上无法割裂。由于前一刻的最优决策在下一刻可能不再为最优,甚至是最劣的,决策者需要在每时每刻根据环境的转变而制定相应的对策。因此,引入微分博弈研究相关动态经济问题具有更大的实用价值。在研究微分博弈的反馈纳什均衡解法的基础上,联系中国石油企业海外开发的实际情况,通过建立一个石油跨国开采微分博弈模型,分析并得出跨国石油开采的最优策略轨迹,为中国石油企业的跨国经营提供了建设性的策略。     

Bargaining over an uncertain outcome:¶the role of beliefs

We study the Nash bargaining solution of a problem in which two agents bargain over an uncertain outcome. Under the assumptions of risk neutrality and of constant absolute risk aversion, we study the way that the solution varies, ex ante, when we vary the beliefs of one agent. Changing an agent's beliefs in a way that makes them “more distant” from the other agent's beliefs makes the second agent better off. Received: 10 May 2001 / Accepted: 22 August 2001