The Fragility of Commitment

We show that the value of commitment is fragile in many standard games. When the follower faces a small cost to observe the leader's action, equilibrium payoffs are identical to the case where the leader's actions are unobservable. Applications of our result include standard Stackelberg–Cournot and differentiated product Bertrand games, as well as forms of indirect commitment, highlighted in Bulow et al. [Bulow J, Geanakoplos J, Klemperer P (1985) Multimarket oligopoly: Strategic substitutes and strategic complements. J. Political Econom. 93:488–511]. Weakening full rationality in favor of boundedly rational solution concepts such as quantal-response equilibrium restores the value of commitment.

This paper was accepted by Peter Wakker, decision analysis.