Commitment and Observability in an Economic Environment

Bagwell (GEB, 1995) argues that commitment in undermined by the slightest amount of imperfect observation. Guth, Ritzberger & Kirchsteiger (GEB, 1998) question this assertion: for any finite leaderfollower game, with arbitrary many players in each role and generic payoffs, they show that there always exists a subgame perfect equilibrium outcome which is accessible. That is, this outcome can be approximated by the outcome of a mixed equilibrium of the game with imperfect observation. This paper embeds leader-follower games in an economic environment, where players must contract with other agents or suppliers in order to take actions, and shows that the sequential equilibrium outcome when commitment is perfectly observed may not be accessible. Accessibility requires either that commitment is not required or that the economic environment satisfies a no-surplus condition. Our result follows from a generalized indifference principle which mixed strategies must satisfy in an economic environment.