Kyle Bagwell (Stanford University)

Who’s on First? Commitment and Observability with Move-order Uncertainty

Abstract: This paper explores a two-player game in which actions are imperfectly observed and players are uncertain about move order. We study two examples, a “commitment” example and a “battle-of-the-sexes” example, where in each example each player has two possible actions and observes the realization of a binary signal before moving. If a given player is the actual second mover, then the distribution of the signal observed by that player is affected by the preceding move of the other player. We study first-mover advantages within a single game by examining how, for each Nash equilibrium, player 1’s payoff changes as she becomes more likely to move first. For pure-strategy Nash equilibria, no first-mover advantage or disadvantage is present. By contrast, for mixed- strategy Nash equilibria, payoffs vary with the probability that player 1 moves first. We find that whether a first-mover advantage exists varies across mixed-strategy equilibria in the commitment example and across parameter regions in the BoS example. We also provide a new perspective on Newcomb’s paradox.