Randomized Strategy Equilibrium and Simultaneous-Move Outcome in the Action Commitment Game with a Small Cost of Leading

We introduce a small cost of leading (small gain from waiting) in the two-player action commitment game formulated by Hamilton and Slutsky (1990). We investigate a quantity competition model with linear demand and constant marginal costs. We find that there exists a unique randomized strategy equilibrium as long as the leading cost is positive and not too large. The randomized strategy equilibrium converges to the simultaneous-move equilibrium (Cournot equilibrium) as the cost of leading approaches zero. We also investigate a price competition model in differential product markets. We show that there exist randomized strategy equilibria, and any of them converge to the simultaneous-move equilibrium (Bertrand equilibrium). ∗Institute of Social Science, University of Tokyo †Department of Economics, University of California, Berkeley ‡Corresponding author: Akira Ogawa, College of Liberal Arts, International Christian University, 3-102, Osawa, Mitaka-shi, Tokyo 181-8585, Japan. Phone: (81)-422-33-3169. Fax: (81)-422-34-6982. E-mail: [email protected]