The British daytime game show “Golden Balls” concludes with a sort-of prisoner’s dilemma played between the two contestants. There is a jackpot, which can vary from very little (about 2 pounds) to a lot (about 100k pounds). The contestants are then asked to simultaneously choose “split” or “steal.” If both choose “split,” they both get one half of the jackpot. In one chooses “steal” and the other chooses “split”, then the player choosing “steal” gets the entire jackpot, the other one nothing. Finally, if both players choose “steal” then both get zero. (Strictly speaking, this is not a prisoner’s dilemma since, conditional on the rival choosing “split,” a player is indifferent between “split” and “steal.”)
Before the players choose their strategies, they get a chance to exchange messages in a short period of unstructured conversation. Typically you will hear players assuring each other that they will split.
Game theory states that if players are rational and if their payoffs corresponds to the monetary payoff then (steal,steal) is the predicted outcome. In practice, we see all sorts of things happen: (steal,steal), as theory would predict; but also (split,steal) (see also this one) and (split,split).
If the theory prediction fails, one is led to ask: What assumptions from the theoretical model fail? One possibility is that players are not rational. More likely, however, is the possibility that each player’s expected payoff is related, but different, from their monetary payoff: other payoff elements include reciprocity for past behavior during the contest, altruism, reputation as a future contestant as well as a public figure, and so on.
On one particular occasion, we observed a (split,split) outcome following a most unusual exchange. We know that some times the most rational thing to do is to create for oneself the reputation of being irrational. This example suggests that one way to reach cooperation is to create an expectation that no cooperation will take place.
For more on this, see this great post by Jeff Ely