A basic model of commitment is to convert a game in strategic form to a “leadership game” with the same payoffs, where one player commits to a strategy to which the second player chooses a best reply. This paper studies such leadership games for the mixed extension of a finite game, where the leader commits to a mixed strategy. The set of leader payoffs is an interval (for generic games a singleton), which is at least as good as the set of that player’s Nash and correlated equilibrium payoffs in the simultaneous game. This no longer holds for leadership games with three or more players
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