Tuesday, June 06, 2006

Looking at Strippers: A Game Theoretic Approach

Craig Holmes*

A father, his son, and two men who are boyfriends to two of his daughters go out on a stag night. The best man takes them to a strip club at the end of the evening, and while all would not have chosen such a move themselves, they decide to go along with it. The following morning, the wives or girlfriends ask them how there evening turned out, and what they did.

Hence, this is a four player game. The strategy set is {Tell Partner, Don't Tell Partner}. All players move simultaneously. If one of the men admits to going to a strip club, all the women will know because they talk. If no-one mentions it, they will never find out. The men receive a payoff of +5 for getting to see some dancing half-naked women. They are penalised if they tell their partner (who gives them the Third Degree and a withering stare, in that order) by -1 , but if they do not and someone else does, then the penality is -3. Finally, they received a bonus of +1 for each other player who does not mention it when they do, because they feel virtuous and honest.

Solve for Nash equilibria.

It can be seen that Tell Partner is a dominant strategy. Consider player 1's choice. If everyone else does not mention the strip club, then mentioning the strip club brings payoff of +7. Not mentioning the strib club brings a payoff of +5. Alternatively, if one, two or three of the other players have mentioned the strip club, not mentioning it will bring a payoff of +2, while mentioning it will bring a payoff of +6, +5 or +4. Hence, it is always a dominant strategy to play Tell Partner, regardless of what the other three players choose.

This reasoning applies to all four players, so the unique Nash Equilibrium outcome should be {Tell Partner, Tell Partner, Tell Partner, Tell Partner}, with everyone getting a payoff of +4. Note that this is Pareto inefficient: if they had all said nothing, then they could have got +5 each. But such an outcome can not occur because of the incentives to deviate.

What happens when this game is played in real life? It would appear that most players attempt to achieve the better outcome and choose Don't Tell Partner. This could be due to that fact that the payoffs are not common knowledge. For instance, three of the men may receive an additional payoff from sticking together and lying, believing they have got one over the womenfolk. This is commonly referred to in the literature as the Male Solidarity Principle. They also have a prior belief that the fourth individual has the same payoffs, so expect him also to play Don't Tell Partner. Such a hypothesis is possible, but to test it, a repeat of the experiment would be required. The players would have to update their beliefs over the fourth player's payoffs, and may act differently.

There are other extensions. We could consider a two stage game, where the first stage involves deciding not to invite me, I mean, not to invite the fourth player, who they believe tells his girlfriend everything, but these are left for the reader to analyse.

*University College, University of Oxford. I'd like to thank the participants of the experiment, and a girl called Misty, who provided me with a discussion on the role of prior beliefs in the equilibrium solution, and could get her legs right behind her ears.

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