Time averages, recurrence and transience in the stochastic replicator dynamics

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 transience is given in terms of mixed equilibria and definiteness of the payoff matrix. We also present necessary and sufficient conditions for stochastic stability of pure equilibria.Comment: Published in at http://dx.doi.org/10.1214/08-AAP577 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Irrational behavior in the Brown-von Neumann-Nash dynamics

We present a class of games with a pure strategy being strictly dominated by another pure strategy such that the former survives along most solutions of the Brown-von Neumann-Nash dynamics.Nash map, BNN dynamics, Dominated strategies

Stochastic approximations and differential inclusions II: applications

We apply the theoretical results on "stochastic approximations and differential inclusions" developed in Benaim, Hofbauer and Sorin (2005) to several adaptive processes used in game theory including: classical and generalized approachability, no-regret potential procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine

Welfare Maximization Entices Participation

We consider randomized mechanisms with optional participation. Preferences over lotteries are modeled using skew-symmetric bilinear (SSB) utility functions, a generalization of classic von Neumann-Morgenstern utility functions. We show that every welfare-maximizing mechanism entices participation and that the converse holds under additional assumptions. Two important corollaries of our results are characterizations of an attractive randomized voting rule that satisfies Condorcet-consistency and entices participation. This stands in contrast to a well-known result by Moulin (1988), who proves that no deterministic voting rule can satisfy both properties simultaneously

Classical and Bayesian Linear Data Estimators for Unique Word OFDM

Unique word - orthogonal frequency division multiplexing (UW-OFDM) is a novel OFDM signaling concept, where the guard interval is built of a deterministic sequence - the so-called unique word - instead of the conventional random cyclic prefix. In contrast to previous attempts with deterministic sequences in the guard interval the addressed UW-OFDM signaling approach introduces correlations between the subcarrier symbols, which can be exploited by the receiver in order to improve the bit error ratio performance. In this paper we develop several linear data estimators specifically designed for UW-OFDM, some based on classical and some based on Bayesian estimation theory. Furthermore, we derive complexity optimized versions of these estimators, and we study their individual complex multiplication count in detail. Finally, we evaluate the estimators' performance for the additive white Gaussian noise channel as well as for selected indoor multipath channel scenarios.Comment: Preprint, 13 page

Survival of dominated strategies under evolutionary dynamics

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