Marriages and Approaches to Games

John Nash developed equilibrium solutions to cooperative games and non-cooperative games. In a cooperative game, negotiators can enforce a binding agreement. In this case, the negotiators can come to a binding agreement that maximizes the joint welfare of the negotiators. In a non-cooperative game, a binding agreement is either not possible to negotiate or enforce. In this case, each person acts in their own self-interests.

Is a couple more likely to divorce if one of them tends to play games cooperatively and the other tends to play them non-cooperatively? I can think of a couple reasons why they might.

1. Strong relationships are built on mutual trust. If we model a marriage as a repeated prisoners' dilemma, then the two people will be best-off jointly if they cooperate with one another each time the game is played. But there is an incentive to deviate from the cooperative solution at each stage. The person who plays games cooperatively, once he/she has observed the others person's playing of a "marriage game", loses trust in the partner and the marriage can dissolve.

2. The person who plays games non-cooperatively would have little trust of the other person, thinking that the other person plays games non-cooperatively when, in fact, the other person plays games cooperatively. The non-cooperative person could be a person who is very jealous or suspicious of the other person when that person goes out or when a person of the opposite sex speaks with him/her. This also can put strains on the marriage.