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The main obstacle for the evolution of cooperation is that natural selection favors defection in most settings. In the repeated prisoner's dilemma, two individuals interact several times, and, in each round, they have a choice between cooperation and defection. We analyze the evolutionary dynamics of three simple strategies for the repeated prisoner's(More)
This note characterizes the impact of adding rare stochastic mutations to an " imitation dynamic, " meaning a process with the properties that any state where all agents use the same strategy is absorbing, and all other states are transient. The work of Freidlin and Wentzell [10] and its extensions implies that the resulting system will spend almost all of(More)
We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for tran-sience is given in terms of(More)
We derive strong uniform approximations for the eigenvalues in general Laguerre and Hermite β-ensembles by showing that the maximal discrepancy between the suitably scaled eigenvalues and roots of orthogonal poly-nomials converges almost surely to zero when the dimension converges to infinity. We also provide estimates of the rate of convergence. In the(More)
In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash equilibria correspond to stable fixed points that are always evolutionarily stable. However, in finite populations(More)
We analyze a class of imitation dynamics with mutations for games with any …nite number of actions, and give conditions for the selection of a unique equilibrium as the mutation rate becomes small and the population becomes large. Our results cover the multiple-action extensions of the aspiration-and-imitation process of Binmore and Samuelson [3] and the(More)
this paper D-optimal designs for the weighted polynomial regres-Ž 2. yn sion model of degree p with efficiency function 1 q x are presented. Interest in these designs stems from the fact that they are equivalent to locally D-optimal designs for inverse quadratic polynomial models. For the unrestricted design space ‫ޒ‬ and p-n, the D-optimal designs put(More)
Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of(More)