We prove existence and purification results for strategic environments possessing a product structure that includes … existence of pure-strategy equilibria allowing for infinite-dimensional externalities. Applied to stochastic games, the results … yield existence of stationary Markov perfect equilibria with extremal payoffs, which in turn yields existence of pure …

. The results are used to verify existence of equilibrium in a general model of Bertrand–Edgeworth oligopoly. …

We provide a new class of counter-examples to existence in a simple moral hazard problem in which the first … utility function, such as ln(w), in which utility diverges to negative infinity at a finite wealth level, existence will fail … well, existence holds for all specifications of the agentʼs cost of effort if and only if the agent continues to dislike …