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- William H. Sandholm
- Economic learning and social evolution
- 2010

We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential… (More)

Noncooperative game theory is one of a handful of fundamental frameworks used for economic modeling. It is therefore troubling that the solution concepts on which the theory’s predictions are based are not as firmly grounded as one might desire. For example, while Nash equilibrium is the starting point for most game theoretic analyses, the conditions on… (More)

- William H. Sandholm
- J. Economic Theory
- 2001

We study potential games with continuous player sets, a class of games characterized by an externality symmetry condition arising naturally in models of network congestion. We offer a simple description of equilibria which are locally stable under a broad class of evolutionary dynamics, and prove that behavior converges to equilibrium from all initial… (More)

- Josef Hofbauer, William H. Sandholm
- J. Economic Theory
- 2009

We study a class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs of strategies to which revising agents are switching are always exceeded by the improvements in the payoffs of strategies which revising agents are abandoning. We prove… (More)

This text offers a systematic, rigorous, and unified presentation of evolutionary game theory, covering the core developments of the theory from its inception in biology in the 1970s through recent advances. Evolutionary...

- Jeffrey C. Ely, William H. Sandholm
- Games and Economic Behavior
- 2005

We introduce best response dynamics for settings where agents' preferences are diverse. Under these dynamics, which are defined on the space of Bayesian strategies, rest points and Bayesian Nash equilibria are identical. We prove the existence and uniqueness of solution trajectories to these dynamics, and provide methods of analyzing the dynamics based on… (More)

- William H. Sandholm
- J. Economic Theory
- 2005

We consider a model of evolution in games in which agents occasionally receive opportunities to switch strategies, choosing between them using a probabilistic rule. Both the rate at which revision opportunities arrive and the probabilities with which each strategy is chosen are functions of current normalized payoffs. We call the aggregate dynamics induced… (More)

- William H. Sandholm
- Games
- 2010

We introduce a class of evolutionary game dynamics — pairwise comparison dynamics — under which revising agents choose a candidate strategy at random, switching to it with positive probability if and only if its payoff is higher than the agent’s current strategy. We prove that all such dynamics satisfy Nash stationarity: the set of rest points of these… (More)

We consider an implementation problem faced by a planner who manages a roadway network. The problem entails both hidden information and hidden actions. We solve the planner's problem by introducing a new class of mechanisms and a new notion of implementation. The mechanisms, called price schemes, attach transfers to the available routes; they do not involve… (More)