Ultimatum Bargaining for a Shrinking Cake — An Experimental Analysis —

Abstract

In an ultimatum bargaining game two players have to divide a given positive amount c of money. First player 1 demands how much of the ‘cake’ c he desires for himself. Then player 2 can either accept or reject this proposal which shows that player 2 faces an ultimatum. If 2 accepts player l’s proposal, player 1 gets what he demanded and player 2 the residual amount. In case of rejection by player 2 we follow the experimental procedure of Binmore, Snaked, and Sutton, i.e., there is another round of ultimatum bargaining with exchanged roles about a “cake” c’ with c’ < c. If also the second round of ultimatum bargaining ends with a rejection, the game ends with 0-payoffs. Our study differs mainly in two aspects from the original experiment of Binmore et al. The monetary payoffs are higher and the game theoretic solution is more extreme. To explore experience each subject was engaged in two subsequent games. One main result is that contrary to Binmore et al. the game theoretic solution has nearly no predictive power. Whereas in one round-games the major consideration is to protect an unfair agreement by sufficiently high cost for choosing conflict, limited rationality will require to analyse the more complex two round-games in a completely different way, e.g. by considering the amounts c and c’ as resources of that player who has the right to propose.