The paper by Paul Milgrom and John Roberts examines supermodular games, a class of noncooperative games with strategic complementarities. These games include models of oligopoly, macroeconomic coordination, arms races, bank runs, technology adoption, and others. The paper shows that for these games, the sets of pure strategy Nash equilibria, correlated equilibria, and rationalizable strategies have identical bounds. Additionally, for dynamic adaptive choice models, players' choices eventually fall within the same bounds. These bounds vary monotonically with exogenous parameters. Supermodular games are characterized by strategic complementarities, where the marginal returns to increasing one's strategy rise with increases in competitors' strategies. The paper discusses various applications of supermodular games, including macroeconomic models, oligopoly theory, technology adoption, and bank runs. It also explores Bayesian games and shows that supermodularity can hold even with uncertainty and private information. The paper presents Theorem 5, which establishes that the set of serially undominated strategy profiles has a maximum and minimum element, both of which are Nash equilibria. It shows that all major equilibrium concepts predict the same bounds on joint behavior in supermodular games. The paper also considers adaptive dynamics, showing that the bounds on eventual behavior under these processes coincide with those predicted by other solution concepts. The paper provides several examples of supermodular games, including a Diamond-type search model, a Bertrand model, an arms race model, an oil drilling model, and a team coordination model. It also discusses comparative statics and welfare theorems, showing that the largest equilibrium is Pareto-best and the smallest is Pareto-worst under certain conditions. The paper concludes with a comprehensive theory of adaptive dynamics applicable to supermodular games.The paper by Paul Milgrom and John Roberts examines supermodular games, a class of noncooperative games with strategic complementarities. These games include models of oligopoly, macroeconomic coordination, arms races, bank runs, technology adoption, and others. The paper shows that for these games, the sets of pure strategy Nash equilibria, correlated equilibria, and rationalizable strategies have identical bounds. Additionally, for dynamic adaptive choice models, players' choices eventually fall within the same bounds. These bounds vary monotonically with exogenous parameters. Supermodular games are characterized by strategic complementarities, where the marginal returns to increasing one's strategy rise with increases in competitors' strategies. The paper discusses various applications of supermodular games, including macroeconomic models, oligopoly theory, technology adoption, and bank runs. It also explores Bayesian games and shows that supermodularity can hold even with uncertainty and private information. The paper presents Theorem 5, which establishes that the set of serially undominated strategy profiles has a maximum and minimum element, both of which are Nash equilibria. It shows that all major equilibrium concepts predict the same bounds on joint behavior in supermodular games. The paper also considers adaptive dynamics, showing that the bounds on eventual behavior under these processes coincide with those predicted by other solution concepts. The paper provides several examples of supermodular games, including a Diamond-type search model, a Bertrand model, an arms race model, an oil drilling model, and a team coordination model. It also discusses comparative statics and welfare theorems, showing that the largest equilibrium is Pareto-best and the smallest is Pareto-worst under certain conditions. The paper concludes with a comprehensive theory of adaptive dynamics applicable to supermodular games.