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Game Theory Rev."],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:p> In this paper, we provide a novel approach to achieving a desired outcome in a coordination game: the original [Formula: see text] game is embedded in a [Formula: see text] game where one of the players may use a third action. For a large set of payoff values, only one of the Nash equilibria of the original [Formula: see text] game is stable under replicator dynamics. We show that this Nash equilibrium attracts all initial conditions in the interior of the state space for the modified [Formula: see text] game. Thus, the existence of a third action for one of the players, although not used, allows both players to coordinate on one Nash equilibrium. <\/jats:p><jats:p> This Nash equilibrium is the one preferred by, at least, the player with access to the new action. 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