golden

Golden Balls - Split or Steal

Description

"Golden Balls" was a British game show that ran on the ITV network from 2008 to 2009. The show features several stages, the last of which invites the players to play a rather familiar looking game. The worksheet is like the others, and payoffs can be altered by clicking on the spinners. The sheet works by using conditional formatting to highlight the best responses of each player, so Nash equilibria are denoted by two arrows within a strategy profile. A number of other simple games have been built with the same basic format, including Chicken, Prisoner's Delight, Prisoner's Dilemma, Battle of the Sexes and Strategic Trade Policy.

Model Layout

Motivating the Payoff Structure

The final stage of the show involves the players, determining the division of the jackpot. Each player is presented with two "golden balls" (hence the name of the show). One of the balls contains the word "split" the other the word "steal." The players are invited to determine which ball is which. They are then given an opportunity to engage in "cheap talk." If both players choose "split," they share the jackpot. If one choose "steal" while the other chooses "split," the player who chose steal takes the whole jackpot. If both players choose "steal," they both go home empty-handed. To see the game in action (and to find out why we have called the player Sarah and Steven), you can watch the following YouTube video.

Explanation

Although at first glance the setup looks like the prisoner's dilemma, it is actually not quite. The {steal, steal} outcome is a weakly dominant strategy equilibrium, but one of three Nash equilibria in the game. Hence, if a player believes that their rival will steal, they are indifferent between splitting and stealing. Nonetheless, rational players usually will choose a weakly dominant strategy (they are never worse off choosing steal in this game, no matter what the rival chooses. The strategies played in the show have recently been examined in a paper by Van den Assem, Van Dolder and Thaler (2011).