Commitment and Observability in an Economic Environment

Bagwell (1995) argues that commitment in undermined by the slightest imperfectness in observation. Guth, Ritzberger & Kirchsteiger (1998) question this assertion: for any finite leader-follower game, with arbitrary many players in each role and generic payoffs, they show that there always exists a subgame perfect equilibrium outcome that is accessible, i.e. it can be approximated by the outcome of a mixed equilibrium of the game with imperfect observation. We show that accessibility fails in a class of games played in economic environments, where the payoffs to commitment actions depend upon prices set by other agents, prices being chosen from a continuum. Accessibility requires either that commitment is not required or that the price setting agents have no monopoly power. Our result follows from a generalized indifference principle which mixed strategies must satisfy in such economic environments.