Randomized strategy equilibrium in the action commitment game with costs of leading

摘要

We investigate a two-player action commitment game where one simultaneous-move and two sequential-move pure strategy equilibria exist when the cost of leading is zero, while the simultaneous-move outcome is not an equilibrium when the leading cost is small positive. We show that this discontinuity disappears if we consider randomized strategy equilibria. We investigate a price competition model and show that randomized strategy equilibria exist and any of them converges to the Bertrand equilibrium when the leading cost converges to zero.