Stochastic stability in games with multiple populations: Theory and application

在随机稳定性/演化分析中，虽然单种群模型已经发展得很好，但它们不太擅长处理多人和/或非对称博弈。 相比之下，多种群模型可以很容易地适应这些游戏。我们的研究项目旨在发展基于多种群模型的随机稳定性分析，特别是考虑在追求个人利益与社会福利最大化相冲突的社会困境中，合作群体的形成和长期稳定性。适应性博弈模型被应用到一个游戏的群体形成自愿参与者谈判的机构，以强制他们合作。对于一类具有两种类型的群体形成对策，其随机稳定均衡可以用相应的鹰鸽对策的纳什乘积来刻画，鹰鸽对策概括了对策中个体之间的策略互动。

In stochastic stability/evolution analysis, while single-population models have been developed well, they are not very good at dealing with many-person and/or asymmetric games. In contrast, multiple-population models can easily accommodate those games. Our research project aims to develop stochastic stability analysis based on multiple-population models.In particular, we consider the formation and long-run stability of cooperative groups in a social dilemma situation where the pursuit of individual interests conflicts with the maximization of social welfare. The adaptive play model is applied to a game of group formation where voluntary participants negotiate for an institution to enforce them to cooperate. For a class of group formation games with two types, the stochastically stable equilibrium can be characterized in terms of the Nash products of the associated hawk-dove games, which summarize the strategic interaction among the individuals in the game.