Symmetric Coordination Games Coordination games are a class of games that involve players making decisions that influence or depend on the decisions of other players. These games typically have multiple Nash equilibrium, meaning that it is not always obvious what the optimal strategy for any particular player is.
One type of coordination game is the symmetric coordination game. In this type of game, each player has the same set of strategies, and each strategy provides the same reward for each player. The symmetry in the game means that the players can deduce what the other is likely to do and then adjust their own strategies accordingly.
The most famous example of a symmetric coordination game is the prisoners dilemma. In this game, two prisoners are each offered the same deal by the police. They can either betray each other, in which case they will receive a reduced sentence, or they can remain silent, in which case they will receive a full sentence. The players can only choose either the betrayal or the silence strategy, but the outcome is dependent on what both players chose.
If both players choose to remain silent, they will both receive a full sentence. If both players choose to betray each other, they will both receive a reduced sentence. However, if one player betrays the other while the other remains silent, the betrayer will receive a full sentence and the other will receive a reduced sentence.
Given this set-up, the players optimal strategies depend on whether or not their opponent will betray them. If their opponent is likely to remain silent, the player can benefit by betraying them. If their opponent is likely to betray them, the player is better off remaining silent. The classical solution to the prisoners dilemma is that both players should remain silent, because the reward from this strategy is greater than the reward from the alternate strategy, regardless of what their opponent does.
However, in reality, people often behave differently from the optimal strategy in the prisoners dilemma. This is because players may not be able to accurately predict the strategy of their opponent, and/or may feel a desire to punish the other player for what they perceive as an unfair or immoral decision.
Given this tendency to deviate from optimal strategies, researchers have explored how to design symmetric coordination games that lead to better outcomes. Examples include games with multiple Nash equilibria, allowing players to discover the optimal strategy either through trial and error or through communication. In addition, games can be designed with incentives that reward cooperative behavior, encouraging players to cooperate with one another rather than to simply pursue their own self-interest.
Overall, symmetric coordination games are a useful tool for investigating decision-making strategies, as well as for designing games that lead to better social outcomes. By understanding the underlying dynamics of these games, we can design them to favor cooperative behavior, and increase our understanding of how people interact and make decisions in social settings.
