A Scalar Compromise Equilibrium for N-Person Prescriptive Games

H. W. Corley, Surachai Charoensri, Narakorn Engsuwan

Center on Stochastic Modeling, Optimization, & Statistics (COSMOS), The University of Texas at Arlington, Arlington, TX, USA.
IMSE Department, The University of Texas at Arlington, Arlington, TX, USA.
Kasikorn Bank PCL, Bankgok, Thailand.

DOI: 10.4236/ns.2014.613098                

Abstract

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.

Keywords

Game Theory, Equilibria, Scalar Equilibrium, Compromise Equilibrium, Scalar Transformation, Prescriptive Analysis

Conflicts of Interest

The authors declare no conflicts of interest.

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