On Games and Equilibria with Coherent Lower Expectations

Abstract EN

Different solution concepts for strategic form games have beenintroduced in order to weaken the consistency assumption thatplayers’ beliefs, about their opponents strategic choices, are correct in equilibrium.

The literature has shown that ambiguousbeliefs are an appropriate device to deal with this task.

In thisnote, we introduce an equilibrium concept in which players do notknow the opponents’ strategies in their entirety but only thecoherent lower expectations of some random variables thatdepend on the actual strategies taken by the others.

Thisequilibrium concept generalizes the already existing concept ofequilibrium with partially specified probabilities by extendingthe set of feasible beliefs and allowing for comparativeprobability judgements.

We study the issue of the existence of theequilibrium points in our framework and find sufficientconditions which involve the continuity of coherent lowerexpectations and a Slater-like condition for the systems ofinequalities defining beliefs.