Habit Formation and the Evolution of Social Communication Networks

Stochastic learning theory;game theory;network formation;social communication;replicator dynamics

A Myopic Adjustment Process Leading to Best-Reply Matching

stochastic adjustment process;best reply;mathcing;regret equilibrium

Evolutionary Selection of Behavioral Rules in a Cournot Model: A Local Bifurcation Analysis

Evolutionary game theory;heterogeneous behavioral rules;Cournot competition;nonlinear dynamics;bifurcation theory

Regret Equilibria in Games

We study boundedly rational players in an interactive situation. Each player follows a simple choice procedure in which he reacts optimally against a combination of actions of his opponents drawn at random from the distribution generated by a player's beliefs. By imposing a consistency requirement we obtain an equilibrium notion which we call regret equilibrium. An existence proof is provided and it is shown that the concept survives the iterated elimination of never-best responses. Additional properties are studied and the regret equilibrium concept is compared with other game theoretic solution concepts. The regret equilibrium concept is illustrated by means of interesting examples. It is shown that in the centipede game, players will continue to play with large probability.

Adaptive behavior in economic and social environments

Various economic and social environments feature repeated interaction of decision-makers. Firms compete for market shares continually, politicians enter into debates almost every day, and friends communicate regularly. When decision-makers accumulate experience and collect new information each time interaction takes place, they will adapt their behavior over time. This thesis analyzes dynamical systems that provide insights into the evolution of the decision-makers' behavior. The three main topics are an adjustment process leading to best-reply matching behavior, network formation in communication and coordination problems, and the interaction between behavioral routines in a Cournot model

A myopic adjustment process leading to best-reply matching

We analyze a myopic strategy adjustment process in strategic-form games. It is shown that the steady states of the continuous time limit, which is constructed assuming frequent play and slow adjustment of strategies, are exactly the best-reply matching equilibria, as discussed by Droste, Kosfeld, and Voorneveld (2000. Mimeo, Tilburg University). In a best-reply matching equilibrium every player ‘matches’ the probability of playing a pure strategy to the probability that this pure strategy is a best reply to the pure-strategy profile played by his opponents. We derive stability results for the steady states of the continuous time limit in 2×2 bimatrix games and coordination games. Analyzing the asymptotic behavior of the stochastic adjustment process in discrete time shows convergence to minimal curb sets of the game. Moreover, absorbing states of the process correspond to best-reply matching equilibria of the game