Leadership Games With Convex Strategy Sets

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A basic model of commitment is to convert a two-player game in strategic form to a "Leadership game" with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. The authors apply them to mixed extensions of finite games, which they analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader's payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. They also consider leadership games with three or more players, where most conclusions no longer hold.