We establish global convergence results for stochastic fictitious play four classes of games: games with an interior ESS, zero sum games, potential and supermodular games. do so by appealing to techniques from approximation theory, which relate the limit behavior a process differential equation defined expected motion process. The key result in our analysis is that relevant defines strongly monotone dynamical system. Our analyses other cases combine Lyapunov function arguments discrete...

A community's culture is defined by the preferences and equilibrium behaviours of its members. Contacts among communities alter individual cultures through two interrelated mechanisms: behavioural adaptations driven pay-offs to coordination, preference changes shaped socialization self-persuasion. This paper explores workings these mechanisms a model cultural integration in which vary continuously. It identifies broad set conditions under cross-cultural contacts promote hybridization. The...

We investigate a class of reinforcement learning dynamics where players adjust their strategies based on actions’ cumulative payoffs over time—specifically, by playing mixed that maximize expected payoff minus regularization term. A widely studied example is exponential learning, process induced an entropic term which leads to evolve according the replicator dynamics. However, in contrast functions used define smooth best responses models stochastic fictitious play, this paper need not be...

Journal Article Evolutionary Implementation and Congestion Pricing Get access William H. Sandholm University of Wisconsin Search for other works by this author on: Oxford Academic Google Scholar The Review Economic Studies, Volume 69, Issue 3, July 2002, Pages 667–689, https://doi.org/10.1111/1467-937X.t01-1-00026 Published: 01 2002 history Received: 04 January 2000 Accepted: December 2001

We introduce a class of evolutionary game dynamics — pairwise comparison under which revising agents choose candidate strategy at random, switching to it with positive probability if and only its payoff is higher than the agent’s current strategy. prove that all such satisfy Nash stationarity: set rest points these always identical equilibria underlying game. also show how one can modify replicator dynamic other imitative ensure stationarity without increasing informational demands placed on...

We consider a model of evolution in games which revising agent observes the actions random number randomly sampled opponents and then chooses best response to distribution sample. provide condition on sample sizes under an iterated p-dominant equilibrium is almost globally asymptotically stable these dynamics. show additional size that supermodular games, state must be equilibrium. Since our selection results are for deterministic dynamics, any selected reached quickly; long waiting times...

We model externality abatement as an implementation problem. A social planner would like to ensure efficient behaviour among a group of agents whose actions are sources externalities. However, the has limited information about agents' preferences, and is unable distinguish individual except through their action choices. prove that if concavity condition on aggregate payoffs satisfied, can guarantee globally stable under wide range adjustment processes by administering variable pricing...

We prove that any deterministic evolutionary dynamic satisfying four mild requirements fails to eliminate strictly dominated strategies in some games. also show existing elimination results for dynamics are not robust small changes the specifications of dynamics. Numerical analysis reveals can persist at nontrivial frequencies even when level domination is small.

We consider stochastic approximation processes with constant step size whose associated deterministic system is an upper semicontinuous differential inclusion. prove that over any finite time span, the sample paths of process are closely approximated by a solution inclusion high probability. then analyze infinite horizon behavior, showing if Markov, its stationary measures must become concentrated on Birkhoff center system. Our results extend those Benaïm for settings in which Lipschitz...

We prove that any regular evolutionarily stable strategy (ESS) is asymptotically under impartial pairwise comparison dynamic, including the Smith dynamic; separable excess payoff BNN and best response dynamic.Combined with existing results for imitative dynamics, our analysis validates use of ESS as a blanket sufficient condition local stability evolutionary game dynamics.