A Scalar Compromise Equilibrium for N-Person Prescriptive Games


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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.


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