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

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.