We provide a novel approach to achieving a desired outcome in a coordination game: the original 2x2 game is embedded in a 2x3 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 2x2 game is stable under replicator dynamics. We show that this Nash equilibrium is the {\omega}-limit of all initial conditions in the interior of the state space for the modified 2x3 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. This Nash equilibrium is the one preferred by, at least, the player with access to the new action. This approach deals with both coordination failure (players choose the payoff-dominant Nash equilibrium, if such a Nash equilibrium exists) and miscoordination (players do not use mixed strategies).

翻译：我们提出了一种在协调博弈中实现期望结果的新方法：原2×2博弈被嵌入一个2×3博弈中，其中一方玩家可使用第三个行动。对于一大类支付值，原2×2博弈中仅有一个纳什均衡在复制动态下是稳定的。我们证明，该纳什均衡是修正后2×3博弈状态空间内部所有初始条件的ω-极限。因此，一方玩家存在第三个行动（尽管未被使用）使得双方玩家能够协调于一个纳什均衡。这一纳什均衡至少是拥有新行动的玩家所偏好的。该方法同时解决了协调失败（若存在支付占优纳什均衡，玩家选择该均衡）与失调（玩家不使用混合策略）问题。