Split or Steal? Game Theory in Action

In the third round of the British game show "Golden Balls," two contestants face off with a pot of winnings between them. They are each given two golden balls with the word "split" or "steal" written inside each (giving them each two options for the behavior regarding the money). The rules are simple: if they both choose split, the pot of winnings is split equally between them. If either chooses steal while the other chooses split, the "stealer" receives all of the winnings. If they both choose steal, neither receives any money. This situation is structured very similarly to the classic "Prisoner's Dilemma," which we studied in class, but with one key difference: in the classic example, if one player defects, the other player is better off defecting as well (rather than cooperating)—and therefore the dominant strategy for both players is to defect, so there is a single Nash equilibrium of defect/defect. However, in the Golden Balls situation, if one player steals, the other player gains nothing by stealing also; no matter what he does, he receives nothing. Thus, there is the weakly dominant strategy of stealing, and the three Nash equilibria are the configurations where at least one person steals. In other words, both players have an incentive to steal, but no incentive to split the pot.

In this clip from the show, something pretty remarkable happens. One of the players convinces the other that "no matter what," he is going to choose to steal. He asks his partner to choose to split the pot, giving the "stealer" all the winnings, and then trust him that after the show he will give him half his winnings. Through this tactic, he essentially narrows the options facing his opponent to just two: either split, and hope that his opponent is kind enough to give him money after the show, or steal, and they both get nothing. Although there is nothing binding here (so the strict payoff matrix would not change), through the introduction of psychological manipulation and new incentives one opponent induces the other to choose to "split," as the lesser of two evils. As you will see, this strategy works: the man on the left chooses to split, knowing that this is his only chance of getting any money at all, and his opponent does an about-face and chooses to split as well, so they both split the money. His strategy all along was to find a way to force his opponent to choose to split not out of altruism and fair-mindedness (as is usually necessary, and usually fails), but because of the economic incentives at play.

The purpose of this long post, which I hope was worth the read, is that game theory oftentimes works on the premise that the two sides cannot communicate—or, at the very least, they cannot change the incentives of the payoff matrix, so it's difficult to escape the inexorable pull of the dominant strategy and subsequently end up in a Nash equilibrium. This show illustrates that actors in the game can at times use communication, persuasion, and personal trust to influence the incentives in the payoff matrix and reach the "unstable" strategy of cooperating together. I'm not sure what implications this might have for the field of economics, if any, but it's at least interesting to contemplate.