Evolutionary dynamics on infinite strategy spaces

Summary. The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinite strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, linear-quadratic games, the harvest preemption game, and games with mixed strategies. Received: June 25, 1999; revised version: January 31, 2000     

企业竞合行为的演化博弈分析--以我国创意产业为例

近年来,创意产业不仅成为学界关注的热点,也成为政府和企业专注与投资的特点。企业之间竞合行为将直接决定其竞争力,进而影响我国创意产业竞争力与发展方向。本文基于文化创意产业集群内企业间的竞合行为,运用演化博弈的理论方法,建立了核心企业之间的横向对称博弈及核心企业与其相邻下游企业之间的纵向非对称博弈的数理模型,分析了其演变的动态过程。研究结果表明,该系统的演化方向与双方博弈的支付矩阵相关,博弈结果受到合作收益、初始合作成本、独立创新能力、合作成功率、以及双方初始状态等因素的影响,最后给出了相关建议,为整合我国文化产业集群提供了理论依据。     

Correlated equilibrium in evolutionary models with subpopulations

We study a version of the multipopulation replicator dynamics, where each population is comprised of multiple subpopulations. We establish that correlated equilibrium is a natural solution concept in this setting. Specifically, we show that every correlated equilibrium is equivalent to a stationary state in the replicator dynamics of some subpopulation model. We also show that every interior stationary state, Lyapunov stable state, or limit of an interior solution is equivalent to a correlated equilibrium. We provide an example with a Lyapunov stable limit state whose equivalent correlated equilibrium lies outside the convex hull of the set of Nash equilibria. Finally, we prove that if the matching distribution is a product measure, a state satisfying any of the three conditions listed above is equivalent to a Nash equilibrium.     

Globally evolutionarily stable portfolio rules

The paper examines a dynamic model of a financial market with endogenous asset prices determined by short-run equilibrium of supply and demand. Assets pay dividends that are partially consumed and partially reinvested. The traders use fixed-mix investment strategies (portfolio rules), distributing their wealth between assets in fixed proportions. Our main goal is to identify globally evolutionarily stable strategies, allowing an investor to “survive,” i.e., to accumulate in the long run a positive share of market wealth, regardless of the initial state of the market. It is shown that there is a unique portfolio rule with this property—an analogue of the famous Kelly rule of “betting your beliefs.” A game theoretic interpretation of this result is given.     

TH视角下产业螺旋失灵的进化博弈分析

作为创新活动中重要一方的产业螺旋,由于各种原因会表现出"失灵"的现象.本文运用进化博弈论分析工具,分析了产业螺旋失灵产生的原因,并给出了相关的政策建议.     

Noncooperative foundations of stable sets in voting games

This paper investigates optimal play in coordination games in which cognition plays an important role. In our game logically omniscient players would be able to identify a distinct coordination opportunity from other obvious facts. Real players may be unable to make the required inference. Our main experimental results are that in a coordination task with a cognitive component (1) players play differently when playing against themselves rather than against another player, and (2) given the opportunity, players signal cognition by choosing the coordination task over an outside option, a phenomenon which we refer to as cognitive forward induction.     

Stable partitions in a model with group-dependent feasible sets

Summary. In this paper we consider a model of group formation where group of individuals may have different feasible sets. We focus on two polar cases, increasing returns, when the set of feasible alternatives increases if a new member joins the group, and decreasing returns, when a new member has an opposite effect and reduces the number of alternatives available for the enlarged group. We examine two notions, stability and strong stability of group structures, that correspond to Nash and Strong Nash equilibrium of the associated non-cooperative game, and identify the classes of stable and strongly stable environments.Received: 29 June 2003, Revised: 17 February 2004, JEL Classification Numbers: C71, C72, D62, D71.The previos version of this paper has been written while the second author was visiting the Technical University of Dresden. He wishes to thank the Alexander von Humboldt Foundation for its generous support and the Technical University of Dresden for its hospitality. The authors are grateful to an anonymous referee for useful comments.     

Evolution in games with a continuous action space

Allowing for games with a continuous action space, we investigate how evolutionary stability, the existence of a uniform invasion barrier, local superiority and asymptotic stability relate to each other. This is done without restricting the populations of which we want to investigate the stability to monomorphic population states or to strategies with finite support. The authors have benefitted from careful and precise comments by Gerard van der Laan, Jan van Mill, the editor and an anonymous referee. Matthijs van Veelen gratefully acknowledges financial support by the Netherlands’ Organization for Scientific Research (NWO).     

Melioration learning in games with constant and frequency-dependent pay-offs

The paper explores the implications of melioration learning—an empirically significant variant of reinforcement learning—for game theory. We show that in games with invariable pay-offs melioration learning converges to Nash equilibria in a way similar to the replicator dynamics. Since melioration learning is known to deviate from optimizing behavior when an action’s rewards decrease with increasing relative frequency of that action, we also investigate an example of a game with frequency-dependent pay-offs. Interactive melioration learning is then still appropriately described by the replicator dynamics, but it indeed deviates from rational choice behavior in such a game.     

Equilibrium selection in bargaining models

This paper examines evolutionary equilibrium selection in bargaining models. We show that random best-response and continuous best-response learning dynamics give rise to (different) simple sufficient conditions for identifying outcomes as stochastically stable. This allows us to characterize the implications of these dynamics in simple bargaining games.