Share This Article:

A Scalar Compromise Equilibrium for N-Person Prescriptive Games

Abstract Full-Text HTML Download Download as PDF (Size:2560KB) PP. 1103-1107
DOI: 10.4236/ns.2014.613098    2,340 Downloads   2,715 Views   Citations


A scalar equilibrium (SE) is defined for n-person prescriptive games in normal form. When a decision criterion (notion of rationality) is either agreed upon by the players or prescribed by an external arbiter, the resulting decision process is modeled by a suitable scalar transformation (utility function). Each n-tuple of von Neumann-Morgenstern utilities is transformed into a nonnegative scalar value between 0 and 1. Any n-tuple yielding a largest scalar value determines an SE, which is always a pure strategy profile. SEs can be computed much faster than Nash equilibria, for example; and the decision criterion need not be based on the players’ selfishness. To illustrate the SE, we define a compromise equilibrium, establish its Pareto optimality, and present examples comparing it to other solution concepts.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Corley, H. , Charoensri, S. and Engsuwan, N. (2014) A Scalar Compromise Equilibrium for N-Person Prescriptive Games. Natural Science, 6, 1103-1107. doi: 10.4236/ns.2014.613098.


[1] Aumann, R. (1985) What Is Game Theory Trying to Accomplish? In: Arrow, K. and Honkapohja, S., Eds., Frontiers of Economics, Basil Blackwell, Oxford, 5-46.
[2] Maschler, M., Solan, E. and Zamir, S. (2013) Game Theory. Cambridge University Press, Cambridge.
[3] Myerson, R. (1991) Game Theory: Analysis of Conflict. Harvard University Press, Cambridge.
[4] Nash, J. (1950) Equilibrium Points in N-Person Games. Proceedings of the National Academy of Sciences, 36, 48-49.
[5] Nash, J. (1951) Non-Cooperative Games. The Annals of Mathematics, 54, 286-295.
[6] Poundstone, W. (2011) Prisoner’s Dilemma. Random House, New York.
[7] Beckenkamp, M. (2006) A Game-Theoretic Taxonomy of Social Dilemmas. Central European Journal of Operations Research, 14, 337-353.
[8] Rubinstein, A. (1991) Comments on the Interpretation of Game Theory. Econometrica, 59, 909-924.
[9] Daskalakis, C., Goldberg, P. and Papadimitriou, C. (2009) The Complexity of Computing a Nash Equilibrium. SIAM Journal on Computing, 39, 195-209.
[10] Barbera, S., Hammond, P. and Seidl, C. (1999) Handbook of Utility Theory: Volume 1 Principles. Springer, New York.
[11] Barbera, S., Hammond, P. and Seidl, C. (2004) Handbook of Utility Theory: Volume 2 Extensions. Springer, New York.
[12] Rabin, M. (1993) Incorporating Fairness into Game Theory and Economics. The American Economic Review, 83, 1281-1302.
[13] Korth, C. (2009) Fairness in Bargaining and Markets. Springer-Verlag, New York.
[14] Ehrgott, M. (2005) Multicriteria Optimization. Springer-Verlag, New York.
[15] Harsanyi, J. and Selten, R. (1988) A General Theory of Equilibrium Selection in Games. MIT Press, Cambridge.
[16] Cooper, R. (1998) Coordination Games. Cambridge University Press, Cambridge.

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.