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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