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:我们提供了一个新的方法来在协调博弈中实现期望的结果:将原来的 2x2 博弈嵌入到一个 2x3 博弈中,其中一个玩家可以使用第三个动作。对于大量的收益值,原始 2x2 博弈的纳什均衡中只有一个在复制动力学下稳定。我们证明,这个纳什均衡是修改后的 2x3 博弈的状态空间内所有初始条件的 ω-极限。因此,尽管没有使用第三个动作,其中一个玩家的存在允许双方协调选择一个纳什均衡。至少能够满足拥有新动作权的玩家的偏好。这种方法解决了协调失败(玩家选择占优的纳什均衡,如果存在这样的纳什均衡)和失调协调(玩家不使用混合策略)的问题。