, Volume 25, Issue 3, pp 289-301

On expectations and the monetary stakes in ultimatum games

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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, Horowitz, Savin and Sefton, 1994, hereafter FHSS; Hoffman, McCabe, Shachat and Smith, 1994, hereafter HMSS, and the literature cited therein). We report new results for 50 bargaining pairs in whichM=$100, and compare them with previous outcomes from 48 pairs withM=$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 formulate such a model and indicate how it might be further tested.

The authors gratefully acknowledge research support from the National Science Foundation for the experimental study of bargaining under Grant SBR #9210052. This paper grew out of discussions following the presentation of our earlier work at the 1992 Amsterdam Workshop in Experimental Economics. We especially thank John Carter and Ron Harstad for numerous helpful comments on an earlier draft of this paper.