Skip to main content
Log in

Comparative accuracy of value solutions in non-sidepayment games with empty core

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

This article reports a test of the predictive accuracy of solution concepts in cooperative non-sidepayment n-person games with empty core. Six solutions were tested. Three of these were value solutions (i.e., λ-transfer value, λ-transfer nucleolus, and λ-transfer disruption value) and three were equilibrium solutions (deterrence set, stable set, and imputation set). The test was based on a laboratory experiment utilizing 5-person, 2-choice normal form games with empty core; other related data sets were also analyzed. Goodness-of-fit results based on discrepancy scores show that the three value solutions are about equally accurate in predicting outcomes, and that all three are substantially more accurate than the other solutions tested.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aumann, R. J.: 1961, ‘The Core of a Cooperative Game Without Sidepayments’, Transactions of the American Mathematical Society 98, 539–552.

    Google Scholar 

  • Aumann, R. J.: 1985, ‘An Axiomatization of the Non-Transferable Utility Value’, Econometrica 53, 599–612.

    Google Scholar 

  • Aumann, R. J., and Peleg, B.: 1960, ‘von Neumann-Morgenstern Solutions to Cooperative Games Without Side Payments’, Bulletin of the American Mathematical Society 66, 173–179.

    Google Scholar 

  • Bonacich, P.: 1979, ‘A Single Measure for Point and Interval Predictions of Coalition Theories’, Behavioral Science 24, 85–93.

    Google Scholar 

  • Champsaur, P.: 1975, ‘Cooperation versus Competition’, Journal of Economic Theory 11, 394–417.

    Google Scholar 

  • Charnes, A., Rousseau, J., and Seiford, L.: 1978, ‘Complements, Mollifiers and the Propensity to Disrupt’, International Journal of Game Theory 7, 37–50.

    Google Scholar 

  • Gillies, D. B.: 1959, ‘Solutions to General Non-Zero-Sum Games’, Annals of Mathematics Studies 40, 47–85.

    Google Scholar 

  • Kirk, R. E.: 1982, Experimental Design, 2nd edition. Brooks/Cole, Belmont, CA.

    Google Scholar 

  • Kohlberg, E.: 1971, ‘On the Nucleolus of a Characteristic Function Game’, SIAM Journal of Applied Mathematics 20, 62–66.

    Google Scholar 

  • Komorita, S. S.: 1978, ‘Evaluating Coalition Theories: Some Indices’, Journal of Conflict Resolution 22, 691–706.

    Google Scholar 

  • Laffond, G., and Moulin, H.: 1977, ‘Stability by Punishment in Normal Form Games’, Technical report, Institut National de la Statistique et des Etudes Economiques, Paris.

    Google Scholar 

  • Laffond, G., and Moulin, H.: 1981, ‘Stability by Threats and Counterthreats in Normal Form Games’, in J. P. Aubin, A. Bensoussan, and I. Ekeland (eds.), Mathematical Technics of Optimization, Control and Decision, Birkhauser, Boston, MA.

    Google Scholar 

  • Maschler, M., Peleg, B., and Shapley, L. S.: 1979, ‘Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts’, Mathematics of Operations Research 4, 303–338.

    Google Scholar 

  • Michener, H. A., Choi, Y. C., and Dettman, D. C.: 1986, ‘Stability by Deterrence in Cooperative Non-Sidepayment n-Person Games’, Journal of Economic Behavior and Organization 7, 375–402.

    Google Scholar 

  • Michener, H. A., Dettman, D. C., and Choi, Y. C.: 1984, The Beta-Core Solution in Cooperative Non-Sidepayment n-Person Games’, in E. J. Lawler (ed.), Advances in Group Processes, vol. 1, JAI Press, Greenwich, CT.

    Google Scholar 

  • Michener, H. A., Potter, K., Depies, C. G., and Macheel, G. B.: 1984, ‘A Test of the Core Solution in Finite Strategy Non-Sidepayment Games’, International Journal of Mathematical Social Sciences 8, 141–168.

    Google Scholar 

  • Michener, H. A., Potter, K., Macheel, G. B., and Depies, C. G.: 1984, ‘A Test of the von Neumann-Morgenstern Stable Set Solution in Cooperative Non-Sidepayment n-Person Games’, Behavioral Science 29, 13–27.

    Google Scholar 

  • Michener, H. A., Potter, K., and Sakurai, M. M.: 1983, ‘On the Predictive Efficiency of the Core Solution in Side-Payment Games’, Theory and Decision 15, 11–28.

    Google Scholar 

  • Michener, H. A., Salzer, M. S., and Reimer, M. S.: 1987, ‘The Lambda-Transfer Value and Lambda-Transfer Nucleolus in Constant-Sum Non-Sidepayment Games’, Technical report, Department of Sociology, University of Wisconsin-Madison.

  • Michener, H. A., Salzer, M. S., and Richardson, G. D.: 1989, ‘Extensions of Value Solutions in Constant-Sum Non-Sidepayment Games’, Journal of Conflict Resolution, in press.

  • Peleg, B.: 1985, ‘An Axiomatization of the Core of Cooperative Games Without Side Payments’, Journal of Mathematical Economics 14, 203–214.

    Google Scholar 

  • Rapoport, A. and Kahan J. P.: 1976, ‘When Three Is Not Always Two Against One: Coalitions in Experimental Three-Person Cooperative Games’, Journal of Experimental Social Psychology 12, 253–273.

    Google Scholar 

  • Schmeidler, D.: 1969, The Nucleolus of a Characteristic Function Game’, SIAM Journal of Applied Mathematics 17, 1163–1170.

    Google Scholar 

  • Shapley, L. S.: 1953, ‘A Value for n-Person Games’, in A. W. Kuhn and A. W. Tucker (eds.), Contributions to the Theory of Games, Vol. II, Princeton University Press, Princeton, NJ.

    Google Scholar 

  • Shapley, L. S.: 1969, ‘Utility Comparison and the Theory of Games’, in G. Th. Guilbaud (ed.), La Decision, Editions du Centre National de la Recherche Scientifique, Paris.

    Google Scholar 

  • Shapley, L. S., and Shubik, M.: 1969, ‘Pure Competition, Coalition Power, and Fair Division’, International Economic Review 3, 337–362.

    Google Scholar 

  • von Neumann, J., and Morgenstern, O.: 1944, The Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ (third edition, 1953).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Michener, H.A., Salzer, M.S. Comparative accuracy of value solutions in non-sidepayment games with empty core. Theor Decis 26, 205–233 (1989). https://doi.org/10.1007/BF00134106

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00134106

Keywords

Navigation