Log-linear dynamics and local potential

Daijiro Okada (1) , Olivier Tercieux (2, 3)

1 Department of Economics
2 PSE - Paris-Jourdan Sciences Economiques
3 PSE - Paris School of Economics

We show that local potential maximizer (Morris and Ui (2005) [14]), a generalization of potential maximizer, is stochastically stable in the log-linear dynamic if the payoff functions are, or the associated local potential is, supermodular. Thus an equilibrium selection result similar to those on robustness to incomplete information (Morris and Ui (2005) [14]), and on perfect foresight dynamic (Oyama et al. (2008) [18]) holds for the log-linear dynamic. An example shows that stochastic stability of an LP-max is not guaranteed for non-potential games without the supermodularity condition. We investigate sensitivity of the log-linear dynamic to cardinal payoffs and its consequence on the stability of weighted local potential maximizer. In particular, for 2×2 games, we examine a modified log-linear dynamic (relative log-linear dynamic) under which local potential maximizer with positive weights is stochastically stable. The proof of the main result relies on an elementary method for stochastic ordering of Markov chains.

Mots clés: Log-linear dynamic; Relative log-linear dynamic; Stochastic stability; Local potential maximizer; Equilibrium selection; Stochastic order; Comparison of Markov chains

Domaines: Economies et finances

Daijiro Okada, Olivier Tercieux. Log-linear dynamics and local potential. Journal of Economic Theory, 2012, 147 (3), pp.1140-1164. ⟨10.1016/j.jet.2012.01.011⟩. ⟨halshs-00754591⟩