In an ultimatum game, player 1 makes an offer of $X from a total of $M to player 2. If player 2 accepts the offer, then player 1 is paid $(M − X) and player 2 receives $X; if player 2 rejects the offer, each gets zero. In the ultimatum game experiments reported in the literature, M is typically not more than $10 (see Forsythe et al., 1994, hereafter FHSS; Hoffman et al., 1994, hereafter HMSS, and the literature cited therein). We report new results for 50 bargaining pairs in which M = $100 and compare them with previous outcomes from 48 pairs with M = $10. The need for an examination of the effect of increased stakes on ultimatum bargaining is suggested by a literature survey of the effect of varying the stakes in a wide variety of decision-making and market experiments over the last 33 years (Smith and Walker, 1993b). Many cases were found in which the predictions of theory were improved when the monetary rewards were increased.There were also cases in which the level of monetary rewards had no effect on the results. Consequently, it is necessary to examine the stakes question on a case-by-case basis. The previously reported effect of instructional changes, which define different institutional contexts, on ultimatum game outcomes, and the effect of stakes reported here, suggest a game formulation that explains changes in the behavior of both players as a result of changes in the instructional treatments. We formulated such a model and indicate how it might be further tested.

I. Theory and Previous Results

Suppose the payoffs and individual rationality of the players are common knowledge.