Hard bargains and lost opportunities

We examine an Outside Option Game in which player I submits a claim for a share of a cake while player II simultaneously either makes a claim or chooses to opt out. If player II opts out, then she receives an opt-out payment while player I receives nothing. If player II opts in and if the claims total less than the cake, then each player receives his or her claim plus half of the surplus. If the claims total more than the cake, both players receive zero. Tension arises in this game between player I's desire to seek as large a share of the cake as possible and the necessity of providing player II with a sufficiently large payoff to ensure that she will opt in. Economic theories that stress efficiency predict that player II will opt in. We argue that trial-and-error learning processes can teach the competitive skills needed to secure large shares of the cake more effectively than the cooperative skills needed to ensure that the cake is available to be divided. As a result, outcomes will arise in which player II opts out, especially when the payment from doing so is attractive. We conduct experiments in which player IIs commonly opt in when their opt-out payment is small, but frequently opt out for larger opt-out payments.