Pay or play

We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and another with a payoff dependent on others' selected actions. This is, arguably, the simplest setting that models selection among certain and uncertain outcomes in a multi-agent system. We study the properties of equilibria in such games from both a game-theoretic perspective and a computational perspective. Our main positive result establishes the existence of a semi-strong equilibrium in every such game. We show that although simple, pay or play games contain well-studied environments, e.g., vaccination games. We discuss the interesting implications of our results for these environments.