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Observable games are game situations that reach one of possibly many Nashequilibria. Before an instance of the game starts, an external observer doesnot know, a priori, what is the exact profile of actions that will occur; thus,he assigns subjective probabilities to players' actions. However, not allprobabilistic assignments are coherent with a given game. We study the decisionproblem of determining if a given set of probabilistic constraints assigned apriori by the observer to a given game is coherent, which we call the Coherenceof Probabilistic Constraints on Equilibria, or PCE-Coherence. We show severalresults concerning algorithms and complexity for PCE-Coherence when only pureNash equilibria are considered. In this context, we also study the computationof maximal and minimal probabilistic constraints on actions that preservescoherence. Finally, we study these problems when mixed Nash equilibria areallowed.

Coherence of probabilistic constraints on Nash equilibria