Rationality, Irrationality, and Transition Dynamics in Evolutionary Game Theory

进化博弈论中的理性、非理性和过渡动力学

• 批准号: 0617753
• 负责人: William Sandholm
• 金额: $ 20.84万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-15 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0617753&HistoricalAwards=false
• 关键词: Rationality; Irrationality; Transition; Dynamics; Evolutionary

This project consists of four studies in evolutionary game theory, a field that models the behavior of large populations of agents engaged in recurring strategic interactions. The first three studies are set in a unified framework for large population modeling. A population game is defined by a finite set of actions and a payoff function for each; payoffs depend continuously on the distribution of agents' action choices. To avoid the assumption of equilibrium play in this large population context, it is assumed that each agent occasionally receives an opportunity to revise his choice of strategy. At such moments, the agent's selection of a new strategy is described using a revision protocol, which specifies the conditional rates of switches between each pair of strategies. Over moderate time spans, aggregate behavior is well approximated by a deterministic differential equation, the mean dynamic, which is defined by the expected changes in the population's behavior. But analyses of behavior over very long time spans must account explicitly for the randomness inherent in the revision process.Elimination of strictly dominated strategies is the mildest requirement employed in standard game-theoretic analysis. Surprisingly, Study 1 argues that few deterministic evolutionary dynamics eliminate strictly dominated strategies. It is shown that any dynamic satisfying three natural conditions--continuity, positive correlation, and innovation--fails to eliminate strictly dominated strategies in some games. Games are explicitly constructed in which dominated strategies survive, and it is shown why existing positive results are not robust to small changes in choice rules.Study 2 studies logit evolution in n strategy potential games. Unlike in the usual mutation model, probabilities of errant choices in the logit model depend on the corresponding payoff losses. This assumption leads to more realistic but more complex disequilibrium dynamics; it complicates the analysis of transitions between equilibria and, consequently, the analysis of equilibrium selection. Using techniques from large deviations theory, the probabilities of and waiting times before escapes are characterized from the basins of attraction of stable equilibria. This enables a precise characterization of the limiting stationary distribution, and thus of the stochastically stable state. Geometric methods are used to determine the rate of convergence of the evolutionary process to its limit distribution.Study 3 addresses a basic question in evolutionary game theory: whether Nash equilibrium can identified with stationary behavior in large populations of myopic, partially informed, and imperfectly responsive agents. In this study, a class of evolutionary dynamics is constructed, whose rest points are precisely the Nash equilibria of the underlying game. The dynamics are based on continuous revision protocols that only require agents to know the payoffs of their current and prospective strategies. Study 4 applies techniques from evolutionary game theory to investigate the dynamics of residential segregation. In a seminal paper, Schelling (1971) showed how segregation can arise even when agents have only a slight preference for residing with members of their own group. The researchers have recently developed tools for the evolutionary analysis of Bayesian games, and they are used to reformulate and extend Schelling's work, allowing both for endogenous determination of the characteristics of outside neighborhoods and for a wider array of preferences over neighborhood compositions.The proposal concludes with a component that develops technology and instructional materials for research and teaching in game theory: namely, a suite of easy-to-use, open source software for constructing phase diagrams and other graphics related to evolutionary game dynamics.

该项目包括四项进化博弈论的研究，该领域模拟了大量参与经常性战略互动的代理人的行为。 前三项研究是在一个统一的框架内进行大规模人口建模的。 人口博弈由有限的行动集和每个行动的支付函数定义;支付连续地依赖于代理人的行动选择的分布。 为了避免在这个大的人口背景下的均衡发挥的假设，它是假设每个代理偶尔收到一个机会来修改他的策略选择。 在这样的时刻，代理的选择一个新的战略描述使用修订协议，它指定了每对策略之间的切换的条件速率。 在适度的时间跨度内，聚集行为可以通过确定性微分方程（平均动态）很好地近似，该方程由种群行为的预期变化定义。 但是，在很长一段时间内的行为分析必须明确地考虑修正过程中固有的随机性，在标准博弈论分析中，排除严格劣势策略是最温和的要求。 令人惊讶的是，研究1认为，很少有确定性的进化动力学消除严格劣势策略。 它表明，任何动态满足三个自然条件-连续性，正相关，和创新-无法消除严格劣势策略在某些游戏。 明确构建游戏中，占主导地位的战略生存，它表明为什么现有的积极结果是不强大的选择rules.Study 2研究logit进化的小变化在n战略潜在的游戏。 与通常的突变模型不同，logit模型中错误选择的概率取决于相应的收益损失。 这一假设导致更现实但更复杂的非均衡动态;它使均衡之间的转换分析复杂化，从而使均衡选择分析复杂化。 使用大偏差理论的技术，逃逸的概率和等待时间的特点是从盆地的吸引力稳定的平衡。 这使得一个精确的表征的限制平稳分布，从而随机稳定状态。 几何方法被用来确定收敛速度的进化过程中，它的极限distribution.Study 3解决了进化博弈论中的一个基本问题：纳什均衡是否可以确定与大种群的短视，部分知情，不完全响应代理的静态行为。 在这项研究中，一类进化动力学，其休息点正是潜在的游戏的纳什均衡。 动态是基于不断修订的协议，只需要代理人知道他们的当前和未来的策略的回报。研究4应用进化博弈论的技术来研究居住隔离的动态。 谢林（Schelling，1971）在一篇开创性的论文中指出，即使行为人只略微倾向于与自己群体的成员居住在一起，隔离也会出现。 研究人员最近开发了贝叶斯博弈的进化分析工具，它们被用来重新制定和扩展谢林的工作，允许内生确定外部社区的特征，并对社区组成进行更广泛的偏好。该提案的结论是为博弈论的研究和教学开发技术和教学材料：即一套易于使用的开源软件，用于构建相图和其他与进化游戏动力学相关的图形。