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.     

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.     

Repeated implementation and complexity considerations

A game form is commitment-free if single actions of players do not have physical consequences, i.e., affect the continuation game. Such game can be thought to represent inifinite interaction with complete patience. A choice rule can be Nash implemented via a commitment-free mechanism if and only if it coincides with the feasible set of a normal form game. However, when players are complexity averse (in the lexicographic sense), then any Nash implementable choice rule becomes available. I am very grateful to Matt Jackson and a referee for their comments. I also thank Klaus Kultti and Hannu Salonen for useful conversations.     

Determinacy of equilibrium in outcome game forms

We show the generic finiteness of the number of probability distributions on outcomes induced by Nash equilibria for two-person game forms such that either (i) one of the players has no more than two strategies or (ii) both of the players have three strategies, and (iii) for outcome game forms with three players, each with at most two strategies. Finally, we exhibit an example of a game form with three outcomes and three players for which the Nash equilibria of the associated game induce a continuum of payoffs for an open non-empty set of utility profiles.     

Mechanism design for a solution to the tragedy of commons

We consider the problem of the tragedy of commons in cooperative production economies, and propose a mechanism to resolve this tragedy, taking into account that the coordinator cannot perfectly monitor each agent’s labor skill and each agent may have an incentive to overstate as well as understate his own skill. Even in such a situation, the mechanism implements the proportional solution (Roemer in Soc Philos Policy 6:74–92, 1989 and Roemer and Silvestre in J Econ Theory 59:426–444, 1993) in Nash and strong equilibria when it is played as a normal form game. Moreover, the mechanism triply implements the solution in Nash, subgame-perfect, and strong equilibria when it is played as a two-stage extensive form game. We are greatly thankful to Semi Koray, William Thomson, and an anonymous referee of this journal for their concrete and helpful comments on improving the paper. An earlier version of this paper was presented at the annual meeting of the Japanese Economic Association held at Hitotsubashi University in October 2001 and at the Conference on Economic Design held at NYU in July 2002. We are grateful to Takehiko Yamato for his useful comments in the former conference. We are also thankful to Tatsuyoshi Saijo, Kotaro Suzumura, and Yoshikatsu Tatamitani for their kind comments.     

资格后审中激励机制对业主和承包商的博弈影响

随着建筑业的发展,工程中的合同形式也越来越多元化,而不同的合同形式业主和承包商所承担的风险也是不同的,业主为了减少风险更多的在合同中采取激励机制。文本主要站在业主的角度,运用不对称信息博弈理论,探讨了在招投标过程中采用资格后审的情况下,业主采取激励机制所可能承担的风险和损失,并据此提出了几点建议,有助于业主和承包商双方最终达到双赢的局面。     

Equilibria in a class of aggregative location games

Consider a multimarket oligopoly, where firms have a single license that allows them to supply exactly one market out of a given set of markets. How does the restriction to supply only one market influence the existence of equilibria in the game? To answer this question, we study a general class of aggregative location games where a strategy of a player is to choose simultaneously both a location out of a finite set and a non-negative quantity out of a compact interval. The utility of each player is assumed to depend solely on the chosen location, the chosen quantity, and the aggregated quantity of all other players on the chosen location. We show that each game in this class possesses a pure Nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and Location–Symmetry. We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.     

供应链企业间信任问题的博弈分析

在新的市场环境下,信任已成为一个具有很强的理论意义和现实意义的课题;而供应链企业间的信任则是整个供应链存在和发展的基础。本文在运用博弈论的方法对供应链企业间的信任问题进行详细分析的基础上,提出了供应链节点上企业间实现信任的三种机制:法律机制、信誉机制和感情机制及其各自的分析模型。     

从博弈论的角度分析我国税务筹划的现状

税务筹划作为一种节税行为应当符合政府的立法意图。但在现实条件下,由于政府征税与纳税人追求最大利益是相违背的,因此形成了一种博弈关系。纳税人和税务机关之间的博弈存在着混合战略纳什均衡,并且我国目前税务筹划在实践中应用滞后的现状与纳税人和税务机关之间的博弈关系存在着紧密联系。     

信息不对称下供应链上下游企业质量守约博弈分析

讨论了在信息不对称情况下,供应链上、下游企业交接货品时质量守约的博弈问题,给出了购买者/供应者非合作博弈的纳什均衡解和多次重复博弈模型。通过模型分析,提出了双方增加质量守约的有效途径。     

建筑工程项目无标底招标行为的经济博弈分析

运用博弈方法对建筑工程项目无标底招标行为展开模型化研究,剖析各投标人的出价策略以及招标人的期望收益,演绎其博弈特性和博弈均衡.在实证中提出建筑工程项目无标底招标行为博弈所需满足的条件,设计可操作的建筑工程项目无标底招标博弈机制,规范建筑行业经营及行政管理部门提供决策支持.     

Implementing the nash extension bargaining solution for non-convex problems

Conley and Wilkie (1993) introduced an axiomatization at the Nash extension bargaining solution defined on a domain of comprehensive but not necessarily convex problems. In this paper we present a non-cooperative game which implements the Nash extension solution in subgame perfect equilibria in the limit as the discount rate applied between rounds of play vanishes.     

A game theoretic approach to optimize multi-stakeholder utilities for land acquisition negotiations with informality

To combat the critical stresses of rising urbanization, the government acquires land from private owners using the power of eminent domain. This land assembly causes negative externalities such as increasing social tension and injustice that may impose a long-term threat to stability and sustainable development. Therefore, there is a need to make the land acquisition process more transparent and just. Considering the unique Indian context where informality has a strong presence, we propose an approach based on game theory that models the bargain through a three-stage Nash equilibrium game. Four agents – the government, the private developer, the landowner, and the free rider – are considered. We provide conditional solutions for the generalizable Case and proceed to model different stakeholder behavior patterns through two utility functional forms – linear and exponential. In the linear case, we find that the free rider obtains half of the revenue of the project, whereas the landowner gains between one-fourth and one-half of the revenue. Thus, we highlight the undeniably crucial role free riders play in land acquisition negotiations. However, closed form solutions cannot be obtained for the exponential form, due to which we use simulations to demonstrate a solution procedure. We conclude by stating that the proposed model can be useful in formulating future land policies in a sustainable and inclusive manner, with optimal utility derivations for all concerned stakeholders. Our model can also be extended to other spatial contexts where informality features heavily in the land market, especially in the Global South.     

Nash-implementation of competitive equilibria via a bounded mechanism

We deal with the problem of providing incentives for the implementation of competitive outcomes in a pure-exchange economy with finitely many households. We construct a feasible price-quantity mechanism, which fully implements Walras equilibria via Nash equilibria in fairly general environments. Traders’ preferences need neither to be ordered nor continuous. In addition, the mechanism is such that no pure strategy is weakly dominated, hence is bounded (in the sense of Jackson 1992). In particular it makes no use of any integer game.     

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.     

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 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.     

集合竞价问题研究

20世纪中期以来,随着纳什均衡理论的提出和发展,博弈论(game theory)逐渐成为一门新兴的科学,它涉及了经济学、管理学、计算机科学、社会学等各个领域,对社会的发展起了极大的推动作用。本文侧重在博弈论中一些具体问题的优化算法的实现与比较,以及其在高性能平台下的并行度和改进情况的分析和研究。     

会计准则制定导向的博弈论分析

本文运用博弈论的分析方法,对在不同的会计准则制定导向和会计监管下,企业管理当局和企业投资者之间的效用进行了分析。分析的结果表明:在规则导向会计准则和严格会计监管之下的纳什均衡点是社会效用最高的一种情况。最后,本文结合我国的现实情况分析了我国在制定会计准则的过程中要注意的问题。