On economic applications of evolutionary game theory

Evolutionary games have considerable unrealized potential for modeling substantive economic issues. They promise richer predictions than orthodox game models but often require more extensive specifications. This paper exposits the specification of evolutionary game models and classifies the possible asymptotic behavior for one and two dimensional models.     

Walras and Darwin: an odd couple?

General equilibrium theory and the evolutionary branches of economics and game theory take rather opposite positions in the spectrum covered by the economic science. However, we reveal and explore analogies between Darwinian dynamics and Walrasian tatonnement processes for pure exchange economies, as well as further analogies implied by these.     

Economic Growth and Decline with Endogenous Property Rights

This article introduces endogenous institutional changeinto a neoclassical growth model. For some parameter values,all Markov perfect equilibria involve a shift from common propertyto private property followed by a shift back to common property.Even in the presence of a linear production technology, thissequence of switches generates growth rates that are increasingat low levels of capital and decreasing at high levels of capital.This result rationalizes the hump-shaped growth path followedby some countries through history, as well as the conditionalconvergence observed in postwar data. For other parameter values,there are also equilibria in which common property prevails forever.This result rationalizes the low-growth traps in which many poorcountries find themselves.     

Mixed-strategy equilibria and strong purification for games with private and public information

This paper shows the existence of mixed-strategy equilibria for games with private and public information under general conditions. Under the additional assumptions of finiteness of action spaces and diffuseness and conditional independence of private information, a strong purification result is obtained for the mixed strategies in such games. As a corollary, the existence of pure-strategy equilibria follows. I am very grateful to Yeneng Sun, Nicholas C. Yannelis and M. Ali Khan for helpful discussions and suggestions. I also wish to thank an anonymous referee whose comments led to many improvements in the paper.     

Economic natural selection in Bertrand and Cournot settings

We study economic natural selection in classical oligopoly settings. When underlying pure strategies consist of a finite number of prices, convex monotonic dynamics always converge under a weak condition to the smallest price in the support of the initial state that exceeds marginal cost. When underlying pure strategies consist of a finite number of quantities, monotonic dynamics always converge under a specific condition to a quantity equal or similar to classical Cournot equilibrium.     

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.     

Collaborative innovation and policy support: the emergence of trilateral networks

ABSTRACT

The present article models the critical factors for a successful and evolutionarily stable National System of Innovation. We simulate a model, against the background of increasingly complex technologies, in a national process of agents’ interactions with social-dilemma characteristics. In particular, the articleinvestigates the emergence of a trilateral collaborative innovation alliance among ‘enterprise’, ‘university’ and ‘government’. We apply a tripartite evolutionary game with a replication process and explore the role and options of the public policy agent to support collaboration on innovation. We find that some policy mix, in particular, a combination of (1) public rewards for cooperation, (2) public punishment for non-cooperation and (3) settings of public cost controls and tax income from innovation, can promote broad and sustainable innovation alliances. For instance, threats of strong punishment, even with low public rewards for cooperation, may promote the formation of a collaborative innovation alliance. We run some sensitivity analyses of the results through parametric variation of two critical factors of the model, knowledge spillover and output elasticity of knowledge input. We find some qualifications for the velocity of the process.     

Equilibrium vengeance

The efficiency-enhancing role of the vengeance motive is illustrated in a simple social dilemma game in extensive form. Incorporating behavioral noise and observational noise in random interactions in large groups leads to seven continuous families of (short run) Perfect Bayesian equilibria (PBE) that involve both vengeful and non-vengeful types. A new long run evolutionary equilibrium concept, Evolutionary Perfect Bayesian Equilibrium (EPBE), shrinks the equilibrium set to two points. In one EPBE, only the non-vengeful type survives and there are no mutual gains. In the other EPBE, both types survive and reap mutual gains.     

Can evolutionary algorithms describe learning processes?

Evolutionary algorithms have attracted more and more the attention of economists in recent years. Repeatedly it is claimed that they are an adequate tool to describe learning processes within a population of individuals. The present paper examines this claim. To this end, a learning model is set up that contains the three elements of variation, elimination, and imitation that are claimed to correspond with the processes of mutation, selection, and replication of biological evolution. Subsequently, this model is compared with a formulation of evolutionary algorithms. The comparison reveals that although both processes have a similar structure there are crucial differences between the two dynamics.     

环境税制下政府与企业环境治理协同行为演化博弈及仿真研究

构建了政府与企业在环境治理中的博弈模型,采用拟生灭过程演化博弈分析了不同的环境税水平下主体博弈的演化均衡状态以及实现协同治理的环境税制条件,并分析了环境治理博弈突变率和主体学习能力对主体博弈演化均衡状态稳定性的影响。结果表明：在环境治理主体博弈的演化过程中,环境税率对政府和企业协同治理的实现存在门槛效应,并且在不同的政府监管力度差异和企业治理力度差异条件下,环境税的门槛效应存在差异性;环境治理主体的学习能力降低和治理系统突变率提高都会显著降低主体间的协同治理状态的稳定性。最后为促进我国政府与企业环境协同治理提出相应的对策建议。     

Evolutionary stability and lexicographic preferences

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. Econ. Theory 57, 278–305) are limit Nash equilibria. Modified evolutionary stability differs from “lexicographic evolutionarily stability” (defined by extending the common characterization of evolutionary stability to lexicographic preferences) in the order in which limits in the payoff space and the space of invasion barriers are taken.     

The microfoundations of macroeconomics: an evolutionary perspective

We consider the microfoundations controversy from the perspectiveof economic evolution. Although the analogy between biologyand economics has been noted before, it has rarely focused onclarifying the micro–macro distinction in economic theoryand modelling. The micro–macro debate is more developedin biology than in economics owing to a greater degree of specialisationand a greater degree of interaction between various sub-disciplines.The task for economists is to distinguish between insights directlyrelevant for economic theory and ones that hinge on unique featuresof biological systems. We argue that both micro and macro processesdrive economic change and that macroeconomic change cannot beexplained by microlevel optimising alone. We show that debatesin biology about group selection and punctuated equilibria arerelevant to understanding economic evolution. The oppositionof reductionism and holism is of little use and, in its place,a hierarchical approach is proposed. This allows for both upwardand downward causation and interaction between levels.     

Correlated equilibria, incomplete information and coalitional deviations

This paper proposes new concepts of strong and coalition-proof correlated equilibria where agents form coalitions at the interim stage and share information about their recommendations in a credible way. When players deviate at the interim stage, coalition-proof correlated equilibria may fail to exist for two-player games. However, coalition-proof correlated equilibria always exist in dominance-solvable games and in games with positive externalities and binary actions.     

Stochastic evolutionary stability in extensive form games of perfect information

Nöldeke and Samuelson [Games Econ. Behav. 5 (1993) 425] investigate a stochastic evolutionary model for extensive form games and show that even for games of perfect information with a unique subgame perfect equilibrium, non-subgame perfect equilibrium-strategies may well survive in the long run even when mutation rates tend to zero. In a different model of evolution in the agent normal form of these games Hart [Games Econ. Behav. 41 (2002) 227] shows that under suitable limit-taking, where small mutation rates are accompanied by large population sizes in a particular way, the unique prediction is again the subgame perfect equilibrium. This paper provides a proof of a similar result for the model of Nöldeke and Samuelson.     

Anticipating Nelson and Winter: Jack Downie's theory of evolutionary economic change

An Evolutionary Theory of Economic Change , by Richard Nelson and Sidney Winter continues to have great influence on evolutionary economic thought. While their modeling techniques and the breadth of their vision for evolutionary theorising must be seen as seminal and effective innovation in economic theory, they were not the first inventors of such a theory. Close examination reveals that much of the economic theory was anticipated by Jack Downie whose book, The Competitive Process, was published in 1958. The extent of anticipation is remarkable, with not merely the two elements of population ecology, selection and mutation, but the way in which they are theorised to work being replicated by Nelson and Winter.     

Stochastic evolution with slow learning

Summary. This paper studies the extent to which diffusion approximations provide a reliable guide to equilibrium selection results in finite games. It is shown that they do for a class of finite games with weak learning provided that limits are taken in a certain order. The paper also shows that making mutation rates small does not in general select a unique equilibrium but making selection strong does. Received: January 19, 2000; revised version: September 25, 2000     

On the Co-existence of Conventions

Recent stochastic evolutionary models have shown that the most likely outcome when the probability of a mutation is sufficiently small is coordination on the risk-dominant strategy rather than on the payoff-dominant one. This paper looks at the consequences of player movement between locations when there are constraints which limit the number of agents who can reside at each location. If the constraints are tight then the risk-dominance result continues to hold. However, we show that when sufficient movement is possible, the most likely outcome involves a mixed state in which agents at different locations coordinate on different strategies. In the asymmetric case, it is the location with the tighter constraint that coordinates on the payoff-dominant strategy. Journal of Economic Literature Classification Numbers: C72, C73, D83.     

Cooperation through imitation

This paper characterizes long-run outcomes for broad classes of symmetric games, when players select actions on the basis of average historical performance. Received wisdom suggests that when agent's interests are partially opposed, behavior is excessively competitive: “keeping up with the Jones' ” lowers everyones' welfare. Here, we study the long-run consequences of imitative behavior when agents have sufficiently long memories and evaluate past actions in terms of (weighted) average payoff. Imitation robustly leads to cooperative outcomes (with highest symmetric payoffs) in the long run. Furthermore, lengthening memory reinforces this effect. This provides a rationale, for example, for collusive cartel-like behavior without collusive intent.     

Rapid evolution under inertia

This paper demonstrates that inertia driven by switching costs leads to more rapid evolution in a class of games that includes m×m pure coordination games. Under the best-response dynamic and a fixed rate of mutation, the expected waiting time to reach long-run equilibrium is of lower order in the presence of switching costs, due to the creation of new absorbing states that allow Ellison's [Ellison, G., 2000. Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution. Rev. Econ. Stud. 67, 17–45] “step-by-step” evolution to occur.     

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.