A reader of the blog sent me the following clip, which absolutely made my day. It's a perfect example of breaking the rules. The clip shows the finale of a UK game show called Golden Balls. During the show the players accumulate money in a jackpot and then in the final round they are presented with a Prisoner's Dilemma. Each must secretly choose either "Steal" or "Split". If both choose Split they split the jackpot. If one chooses Split and the other chooses Steal then he takes the whole jackpot. If both choose Steal, they get nothing. Before they decide they get 30 seconds to talk about what they're going to do.
Let's break down what happened.
First, let's review the incentive problem that a Prisoner's Dilemma creates. Imagine that you're one of the players and you know the other person is going to choose Split. You can then either choose Steal (and get the whole thing) or Split (and get half). You're better off choosing Steal. Now imagine you know he's going to choose Steal. You get nothing either way. Thus, Steal can be better than Split but Split can never be better than Steal. In game theory terms, Steal dominates Split.
Given this, the normal play is to spend thirty seconds persuading the other person to choose Split, presumably with the promise that you're going to choose it yourself. Each player will pledge to "do the right thing" and then worry that the other one will choose Steal -- and, of course, some of them will choose Steal themselves.
In this case, however, the gentleman on the right broke the rules. He declared that he was going to choose Steal but promised that if the other player chose Split he would split the money with him after the show.
His move is based on two key insights. First, the show doesn't have to be the endpoint of the game. The whole gambit only becomes possible with the recognition that even if the show awards all the money to one player, the players could have a separate agreement to split it.
The second insight is that this particular Prisoner's Dilemma can be broken. A typical Prisoner's Dilemma requires both players to choose the "cooperate" option (in this case, Split) in order to gain the best combined outcome. In Golden Balls, however, it only requires one person choosing Split for the full jackpot to be awarded. This, combined with the ability to offer an after-the-show promise, allowed him to reverse the game theory implication for his opponent.
Imagine you're the player on the left. You believe that the other player is going to choose Steal. That leaves you with two choices -- Steal (and get nothing) or Split (and hope that he's honest and will divide the money with you). Unless you're really angry with the strong-arm tactics or really want to avoid being suckered when he says, "Thanks for choosing Split but I have no intention of sharing the money with you," your best choice is to choose Split. Instead of the Dilemma pushing you towards a "defect" option, it now pushes you to cooperate.
That leaves one small problem. People aren't always rational, especially under pressure. There has to be a non-zero chance that the player on the left will choose Steal either out of anger or confusion or simply because he really doesn't want to be suckered. Our hero solves this problem by choosing Split in the end! If his gambit succeeds then the players split the money (which was his intention anyway) but if it doesn't then the other player might decide that he had good intentions all along and agree to split the money as they'd both said they wanted to do.
In my experience, opportunities to break the rules aren't rare -- they are the rule rather than the exception. The more we can free ourselves of artificial constraints, the more likely we are to find win-win opportunities (or ways to capture value) that would otherwise have gone unnoticed.