  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 an- other 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 of play games contain a large variety of well-studied environments, e.g.,
vaccination games. We discuss the interesting implications of our results for
these environments.
