A Formal Study of Boolean Games with Random Formulas as Payoff Functions

Abstract

In this paper, we present a probabilistic analysis of Boolean games. We consider the class of Boolean games where payoff functions are given by random Boolean formulas. This permits to study certain properties of this class in its totality, such as the probability of existence of a winning strategy, including its asymptotic behaviour. With the help of the Coq proof assistant, we develop a Coq library of Boolean games, to provide a formal proof of our results, and a basis for further developments. 2012 ACM Subject Classification Theory of computation → Higher order logic, Theory of computation → Algorithmic game theory, Mathematics of computing → Stochastic processes