HOA Board/Committee Volunteering

I noticed during the last few weeks that HOA Board/Committee volunteering is a good example of Prisoner's Dilemma in a sequential format. Due to some criminal incidents lately, HOA Board of my community decided to establish a Security Committee and asked for help. I was one of the 6 volunteers to work in this committee. We met few times and decided on actions to take. Recently few members stopped supporting the committee. As a result, I have immediately seen an increase in my responsibilities (worse payoff due to more time/effort spent). So some of the players "cheated" causing a worse payoff for "self" while they received higher payoffs. It was because remaining committee members took care of the duties anyways and "cheaters" enjoyed"better payoff" due to less time spent on the matters. Because we are the owners of the houses and we will be playing this and other games with those players again, they will have a bad reputation and will not potentially be trusted in the future.

I created the following simplified sequential game tree where all the players other than "self" were considered to be a single player (called "them") to simplify the game structure. Two strategic moves for each player are (Contribute or not). There is a single nash-equilibrium of (Not contribute, not contribute):

However, collectively as a community, if we could have recruited more volunteers, everyone would be better off. Total payoff would be largest for the society while individual payoff would be reasonably good (5 for self and 5 for them).

In general, most volunteering situations can be considered to be a "Prisoner's Dilemma" type of game. They can also be modelled as simultaneous games.

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!!