How Good Is a Strategy in a Game with Nature?

International audienceWe consider games with two antagonistic players — Éloïse (modelling a program) and Abélard (modelling a byzantine environment) — and a third, unpredictable and uncontrollable player, that we call Nature. Motivated by the fact that the usual probabilistic semantics very quickly leads to undecidability when considering either infinite game graphs or imperfect information, we propose two alternative semantics that leads to decidability where the probabilistic one fails: one based on counting and one based on topology

The Evolution of Coordination under Inertia

This paper models the phenomenon of inertia driven by individual strategy switching costs in a stochastic evolutionary context. Kandori, Mailath, and Rob's (1993) model of a finite population of agents repeatedly playing a 2x2 symmetric coordination game is extended to allow for such inertia. Taking noise to the limit, a number of new short- to medium-run equilibria emerge, centred around the mixed-strategy equilibrium. Thus, unusually, an evolutionary model is seen to provide some justification for the controversial concept of mixed-strategy equilibrium. However, Kandori, Mailath, and Rob's long-run selection of the risk-dominant equilibrium continues to hold, both under fixed-rate mutations and under state-dependent mutations driven by stochastic switching costs. The key to this is the satisfaction of Blume's (1999) "skew-symmetry" of the noise process, which is shown to be crucial even under simultaneous strategy revisions. In fact, the presence of the new short-run equilibria can under certain conditions serve to reduce the expected waiting time before the risk-dominant equilibrium is reached - an instance of Ellison's (2000) idea that evolution is more rapid when it can proceed via a series of small "steps" between extremes. This suggests inertia to be a surprisingly efficient phenomenon, and also serves to moderate the force of the Ellison (1993) critique of excessively long transition times in models with vanishing noise.