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.     

Subgame Monotonicity in Extensive Form Evolutionary Games

A theory of subgame monotonicity is developed for finite extensive form games to model evolutionary processes that respect the subgame structure of the game. It is shown how these evolutionary processes can be decomposed into their evolution on smaller games and also recombined to simplify the analysis of the original game. When applied to the replicator dynamic, a generalization of the Wright manifold from population genetics is a natural consequence of monotonicity. Subgame monotonicity and the Wright manifold are also shown to arise naturally in imitation models based on the extensive form. Journal of Economic Literature Classification Numbers: C70, C72.     

Mixed equilibria in games of strategic complementarities

Summary. The literature on games of strategic complementarities (GSC) has focused on pure strategies. I introduce mixed strategies and show that, when strategy spaces are one-dimensional, the complementarities framework extends to mixed strategies ordered by first-order stochastic dominance. In particular, the mixed extension of a GSC is a GSC, the full set of equilibria is a complete lattice and the extremal equilibria (smallest and largest) are in pure strategies. The framework does not extend when strategy spaces are multi-dimensional. I also update learning results for GSC using stochastic fictitious play. Received: October 16, 2000; revised version: March 7, 2002 RID="*" ID="*" I am very grateful to Robert Anderson, David Blackwell, Aaron Edlin, Peter De Marzo, Ted O'Donoghue, Matthew Rabin, Ilya Segal, Chris Shannon, Clara Wang and Federico Weinschelbaum for comments and advise.     

Brown–von Neumann–Nash dynamics: The continuous strategy case

Brown and von Neumann introduced a dynamical system that converges to saddle points of zero sum games with finitely many strategies. Nash used the mapping underlying these dynamics to prove existence of equilibria in general games. The resulting Brown–von Neumann–Nash dynamics are a benchmark example for myopic adjustment dynamics that, in contrast to replicator dynamics, allow for innovation, but require less rationality than the best response dynamics. This paper studies the BNN dynamics for games with infinitely many strategies. We establish Nash stationarity for continuous payoff functions. For negative semidefinite games (that include zero sum games), we generalize the results of Brown and von Neumann. In addition, we show that evolutionarily robust Nash equilibria are asymptotically stable. A complete stability analysis for doubly symmetric games is also obtained.     

Does Transparency of Central Banks Produce Multiple Equilibria on Currency Markets?

A recent strand of literature shows that multiple equilibria in models of markets for pegged currencies vanish if there is slightly diverse information among traders; see Morris and Shin (2001). It is known that this approach works only if the common knowledge in the market is not too precise. This has led to the conclusion that central banks should try to avoid making their information common knowledge. We develop a model in which more transparency of the central bank implies better private information, because each trader utilises public information according to her own private information. Thus, transparency makes multiple equilibria less likely.     

Fictitious play in ‘one-against-all’ multi-player games

Summary. A compound game is an (n + 1) player game based on n two-person subgames. In each of these subgames player 0 plays against one of the other players. Player 0 is regulated, so that he must choose the same strategy in all n subgames. We show that every fictitious play process approaches the set of equilibria in compound games for which all subgames are either zero-sum games, potential games, or games. Received: July 18, 1997; revised version: December 4, 1998     

Transient and asymptotic dynamics of reinforcement learning in games

Reinforcement learners tend to repeat actions that led to satisfactory outcomes in the past, and avoid choices that resulted in unsatisfactory experiences. This behavior is one of the most widespread adaptation mechanisms in nature. In this paper we fully characterize the dynamics of one of the best known stochastic models of reinforcement learning [Bush, R., Mosteller, F., 1955. Stochastic Models of Learning. Wiley & Sons, New York] for 2-player 2-strategy games. We also provide some extensions for more general games and for a wider class of learning algorithms. Specifically, it is shown that the transient dynamics of Bush and Mosteller's model can be substantially different from its asymptotic behavior. It is also demonstrated that in general—and in sharp contrast to other reinforcement learning models in the literature—the asymptotic dynamics of Bush and Mosteller's model cannot be approximated using the continuous time limit version of its expected motion.     

An extensive form interpretation of the private core

Summary. The private core of an economy with differential information, (Yannelis (1991)), is the set of all state-wise feasible and private information measurable allocations which cannot be dominated, in terms of ex ante expected utility functions, by state-wise feasible and private information measurable net trades of any coalition. It is coalitionally Bayesian incentive compatible and also takes into account the information superiority of an individual. We provide a noncooperative extensive form interpretation of the private core for three person games. We construct game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. In the spirit of the Nash programme, the private core is thus shown to be supported by the perfect Bayesian equilibrium of a noncooperative game. The discussion contributes not only to the development of ideas but also to the understanding of the dynamics of how coalitionally incentive compatible contracts can be realized. Received: July 21, 2000; revised version: January 16, 2001     

时空相对:经济学及其发展的基本特征

人类社会经济活动是无限发展变化的,而经济学及其发展只能相对有限地适应这种变化。有限的适应性,或者有条件的真理性,突出表现出经济学的相对性。在我们看来,经济学的相对性实际上主要表现为经济学的时空相对性。时空相对是经济学及其发展的基本特征。     

What do uncertainty-averse decision-makers believe?

Summary. This paper introduces the concept of firm belief, which is proposed as a new epistemic model for a wide class of preferences. In particular, firm beliefs are shown to have the following desirable properties: (i) they are derived from preferences according to a plausible rule of epistemic inference; (ii) they satisfy standard logical properties; and (iii) tractable representations of firm belief are available for all (suitably continuous) biseparable preferences [13, 14], including the Choquet expected utility [30] and maxmin expected utility [16] classes. We also use firm belief to construct a generalization of Nash equilibrium for (two-player) normal form games. Received: December 14, 1999; revised version: February 26, 2001     

The power of ESS: An experimental study

Abstract. Our experimental design mimics a traditional evolutionary game framework where players are matched pairwise to play a symmetric 33 bimatrix game that has two Nash equilibria. One equilibrium is an evolutionary stable state, or ESS; the other is an equilibrium in dominated strategies. Our primary experimental result is the observation that the ESS becomes extremely attractive when subjects have minimal information about the payoff functions, although the dominated equilibrium assures the highest equilibrium payoff. The attractiveness of the ESS is only moderate when players are completely informed about the 33 payoff matrix. Correspondence to: S.K. Berninghaus     

Learning with noiseless information and payoff-relevant signals

Summary. In models of active learning or experimentation, agents modify their actions to affect the distribution of a signal that provides information about future payoffs. A standard result in the experimentation literature is that agents experiment, if at all, to increase information. This finding is a direct consequence of Blackwell's theorem: one experiment is more informative than another if and only if all expected utility maximizers prefer to observe the first. Blackwell's theorem presupposes, however, that the observed signal only conveys information and does not directly affect future payoffs. Often, however, signals are directly payoff relevant, a phenomenon that we call signal dependence. For example, if a firm is uncertain about its demand and uses today's sales as a signal of tomorrow's demand, then that signal may also directly affect tomorrow's profit if the good is durable or if consumers form consumption habits. Datta, Mirman and Schlee [9] and Bertocchi and Spagat [4] show that, if the signal is payoff relevant, experimentation may indeed reduce information. Here we show that, despite the inapplicability of Blackwell's Theorem, agents always experiment to increase information if the information structure is noiseless: given the true value of the unknown parameter, the signal realization is deterministic. We then apply our framework to analyze Lazear's [16] model of retail clearance sales, a model with both signal dependence and noiseless information. Received: February 19, 1999; revised version: August 11, 1999     

Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

中国高技术产业成长的时空演变特征及其空间布局研究

文章对中国高技术产业成长的时空演变特征进行分析和研究，结果表明：从时间序列上看，中国高技术产业呈现高增长率的成长和发展，无论是高技术产业年产值、增加值，还是利润和出口额等经济指标的年平均增长率均达到10％以上；但从地理空间上分析，各地区高技术产业成长、发展水平存在明显的差异性，电子通信设备制造业、电子计算机及办公设备制造业广东占有极显著的优势；医药制造业、医疗设备及仪器仪表制造业二个行业具有明显地区性优势的分别是浙江、广东、上海、河北和江苏、浙江、上海、北京；而航空航天器制造业的地区性优势分布在前期国家投资重点地区陕西、黑龙江、江西、辽宁。分地区高技术产业投入地理集中度指数和高技术产业产出地理集中度指数清楚地反映了我国高技术产业呈现较明显的集群发展态势，集群主要发生在以京津唐、长江三角洲和珠江三角洲三大地区。基于上述分析进一步探讨了中国高技术产业发展的空间布局问题，并提出菱形状态的高技术产业发展空间战略布局。     

我国城乡居民收入区域差异分析与对策

自1978年我国实行改革开放以来,城乡居民收入水平大幅度提高,但收入差距呈不断扩大的态势。以我国东中西部三大区域为分析对象,运用1997—2012年数据进行验证,结果表明:经营性收入差距、转移性收入差距、工资性收入差距等对城乡居民收入差距的影响程度相异,其形成原因有自然属性、政策偏向和制度等。因此,缩小我国城乡居民收入差距应从推进城乡一体化、积极改变政府财政职能、构建城乡居民公平的发展机制、推进农业产业化等方面进一步着手和完善。