A Note on Game Theory and Verification

Abstract

We present some basics of game theory, focusing on matrix games. We then present the model of multiplayer stochastic concurrent games (with an underlying graph), which extends standard finite-state models used in verification in a multiplayer and concurrent setting; we explain why the basic theory cannot apply to that general model. We then focus on a very simple setting, and explain and give intuitions for the computation of Nash equilibria. We then give a number of undecidability results, giving limits to the approach. Finally we describe the suspect game construction, which (we believe) captures and explains well Nash equilibria and allow to compute them in many cases.