Coordination Games with Strategic Delegation of Pivotality

Abstract

We analyze a broad class of binary-action, two-player, coordination games with uncertain payoffs. Players receive private signals about a stochastic payoff that they obtain whenever they both take the action''. The game structure allows a player to exploit the information contained in the other's signal only if he takes the action'', which makes the other player pivotal in determining whether players receive the stochastic payoff. Unlike supermodular and typical global games, best responses feature both strategic complementarities and strategic substitutes. We characterize equilibria in pure monotone strategies, and identify conditions under which (a) players are less likely to take the stochastic-coordination action than is socially optimal, and (b) players are more likely to take the stochastic-coordination action than in the analogous public-signal setting (even though public signals facilitate coordination). Finally, we characterize equilibria when strategies are non-monotone. Applications include technology adoption, investment, trade wars, lobbying, protests and revolutions.