Coherence of probabilistic constraints on Nash equilibria
Abstract
Observable games are game situations that reach one of possibly many Nash equilibria. Before an instance of the game starts, an external observer does not know, a priori, what is the exact profile of actions that will occur; thus, he assigns subjective probabilities to players' actions. However, not all probabilistic assignments are coherent with a given game. We study the decision problem of determining if a given set of probabilistic constraints assigned a priori by the observer to a given game is coherent, which we call the Coherence of Probabilistic Constraints on Equilibria, or PCECoherence. We show several results concerning algorithms and complexity for PCECoherence when only pure Nash equilibria are considered. In this context, we also study the computation of maximal and minimal probabilistic constraints on actions that preserves coherence. Finally, we study these problems when mixed Nash equilibria are allowed.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.00746
 Bibcode:
 2022arXiv220100746P
 Keywords:

 Computer Science  Computer Science and Game Theory
 EPrint:
 Preprint