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：将原始的2x2博弈嵌入至2x3博弈，其中一名玩家可使用第三种行动。对于大量支付值而言，原2x2博弈中仅有一个纳什均衡在复制动态下保持稳定。我们证明该纳什均衡是修改后2x3博弈状态空间内部所有初始条件的ω-极限。因此，即便未被实际使用，一方玩家拥有的第三种行动仍能使双方玩家协调至一个纳什均衡——该均衡至少是拥有新行动的一方所偏好的。该方法同时解决了协调失败（当存在支付占优纳什均衡时，玩家选择该均衡）与协调失灵（玩家不使用混合策略）的问题。