Are women more cautious than men? Evidence from the game show "Golden Balls"

There is empirical evidence in the finance literature that women are more cautious than men and put their money into secure investment products. The view that women are more cautious than men about risks is also supported by numerous psychologists. In addition, there are studies that suggest that women, in situations of strategic interaction, are more likely than men to choose a “cooperative” strategy. In this paper we look at the questions of whether or not women are more cautious and/or more cooperative than men by collecting and analyzing data from a natural experiment, in which cooperation and cautiousness are mutually exclusive strategies. Specifically, we collect and analyze the behavior of contestants/players in the game of “Golden Balls”, a British game show that, from June 2007 to December 2009, aired over 250 episodes on television. In the final stage of the game, each of the two contestants/players is given a set of two balls, one marked "Split" and the other “Steal". Each player must choose one of the two balls, without knowing the other player’s choice. If both choose “Split”, they each receive half the jackpot.

If one chooses “Steal” and the other chooses “Split”, the player who chooses “Steal” wins the entire jackpot. If both choose “Steal”, neither player wins any money. One can characterize this game as a static, simultaneous move game with three Nash equilibria. The only strategy pair that is not a Nash equilibrium is the cooperative outcome in which both players pick the “Split” ball. However, of the three strategy pairs that are Nash equilibria, only the one in which both players pick “Steal” has neither player playing a weakly dominated strategy. Hence, in this game, a rational player may play either the “Split” or the “Steal” ball. However, if we define a cautious player as a player who does not play a weakly dominated strategy, then a rational and cautious player would always play the “Steal” ball. Paying particular attention to the gender of both players in the final stage of the game (i.e. female vs female, female vs male, and male vs male), and the size of the jackpot, we investigate whether or not women display a higher propensity to be cautious or a higher propensity to be cooperative, even if cooperation is risky.