A variant of the prisoner’s dilemma:
So this was the payoff matrix they faced:
Stealing is a weakly dominant strategy: regardless of whether Sarah splits or steals, stealing always gives Steve a payoff that’s at least as good as splitting. Orange and red indicate the three Nash equilibria, where neither player has an incentive to unilaterally change his or her action. What’s most interesting however, is the strategy of both stealing. In fact, “both get nothing” isn’t exactly representative of the payoff to the loser. After all, if you were Steve, wouldn’t you feel a little consoled if you managed to thwart her plans? At the same time, wouldn’t you be much more upset if you simply allowed her to get away like that?
Some payoff clearly needs to be added for revenge. Indeed this is an important finding in the ultimatum game, where people offered significantly less than a 50-50 split typically choose to punish the other person by rejecting the entire sum. Not economically rational, since getting a little is better than getting nothing; but this experiment shows the importance of emotions in decision making.
Steve wasn’t rational by any measure, but maybe he did it on the (mistaken?) belief that many wouldn’t be able to walk away with that kind of guilt. In her defense, Sarah can truly claim to be a rational economic agent.