Abstract
In the ultimatum game with complete information a Sender proposes a division of a given amount of surplus (“pie”), which a Receiver can either accept (payoffs are distributed according to the Sender's proposal) or reject (both players earn nothing). We study another version of the ultimatum game under incomplete informaton in which the pie is drawn randomly from a commonly known distribution, the Sender knows the exact size of the pie, but the Receiver only knows her share of the pie, not the residual share requested by the Sender. The basic results are that (1) as the support of the pie distribution increases in a mean-preserving spread, the Senders make lower offers that the Receivers are less likely to reject, (2) for a given support, Senders tend to offer a lower proportion of the pie to the Receivers as the pie size grows larger, and (3) although knowing only their share of the pie, Receivers estimate its size quite accurately.
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References
Bolton GE (1991) A comparative model of bargaining: Theory and evidence. American Economic Review 81: 1096–1136
Güth W (1993) On ultimatum bargaining experiments — A personal review. Tilburg University, Center for economic research. Report
Güth W, Schmittberger R, Schwarze B (1982) An experimental analysis of ultimatum bargaining. Journal of Economic Behavior and Organization 3: 367–388
Güth W, Tietz R (1990) Ultimatum bargaining behavior: A survey and comparison of experimental results. Journal of Economic Psychology 11: 417–449
Harrison GW, McCabe KA (1992) Expectations and fairness in a simple bargaining experiment. The University of South Carolina, College of Business Administration, Working Paper B-92-10
Harsanyi J (1967–68) Games with incomplete information played by ‘Bayesian’ players. Parts I–III. Management Science 14: 159–182, 320–334, 486–502
Hoffman E, McCabe KA, Shachat K, Smith VL (1994). Preferences, property rights, and anonymity in bargaining games. Games and Economic Behavior 7: 346–380
Kreps D, Wilson R (1982) Sequential equilibria. Econometrica 50: 863–894
Mitzkewitz M, Nagel R (1993) Experimental results on ultimatum games with incomplete information. International Journal of Game Theory 22: 171–198
Prasnikar V, Roth AV (1992) Considerations of fairness and strategy: Experimental data from sequential games. Quarterly Journal of Economics 107: 865–888
Rapoport A, Fuller MA (1995) Bidding strategies in a bilateral monopoly with two-sided incomplete information. Journal of Mathematical Psychology 39: 179–196
Rapoport A (in press) Order of play in strategically equivalent games in extensive form. International Journal of Game Theory
Roth AE (1995) Bargaining experiments. In: Kagel J, Roth AE (Eds) Handbook of Experimental Economics. Princeton Princeton University Press
Selten R (1967) Die strategiemethode zür erforschung des eingeschränkt rationalen verhaltens in rahmen einem oligopolexperiments. In: Sauermann H (Ed) Beiträge zür experimentellen wirtschaftsforschung. Tübingen: JCB Mohr, 136–168
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Rapoport, A., Sundali, J.A. Ultimatums in two-person bargaining with one-sided uncertainty: Offer games. Int J Game Theory 25, 475–494 (1996). https://doi.org/10.1007/BF01803952
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DOI: https://doi.org/10.1007/BF01803952