Friendship as an Assurance Game

Well, another personal example of game theory! Assume two rational players: self (S) and friend (F). Assume also that these people already know each other and they will make a decision whether to invest into the friendship with the other person or not. Similar to other interpersonal meta games like dating, this game could be simplified into a 2x2 matrix assurance game as follows:

Imagine that both players are simultaneously thinking about the other and deciding whether to invest or not, but not sharing this decision with the other person. This meta-game portion is a simultaneous, partial information, repeated (or one-shot), variable sum game with manipulable rules.

There are two Nash equilibria that can be found using Best-response analysis: (Invest, invest) and (Do not invest, do not invest). The first one has a higher individual and total relative payoffs (say, in terms of happiness) for both players. So, if the two players talk and cooperate, they might achieve higher payoffs using (Invest, Invest). If S invests, but F cheats the agreement by not investing in the friendship, then F does not get any payoffs but S is now worse off than not investing because he spent time and resources. In this case he/she may be punished in future games with S and other players.

Obviously, the actual meta-game is a lot more complex and we cannot be friends with everyone. However, when we choose the right opponent player in the "Friendship" game, we should show the game table and let him/her know that cooperation provides better payoffs for both!!