TITLE:
Normative Utility Models for Pareto Scalar Equilibria in n-Person, Semi-Cooperative Games in Strategic Form
AUTHORS:
H. W. Corley
KEYWORDS:
Pareto Equilibrium, Scalar Equilibrium, Semi-Cooperative Games, Utility Transformation, Normative Game Theory, Nash Equilibrium, Berge Equilibrium, Compromise Equilibrium, Greedy Equilibrium, Satisficing Equilibrium, Arbitration
JOURNAL NAME:
Theoretical Economics Letters,
Vol.7 No.6,
September
30,
2017
ABSTRACT: Semi-cooperative games in strategic form are considered in which either a
negotiation among the n players determines their actions or else an arbitrator
specifies them. Methods are presented for selecting such action profiles by
using multiple-objective optimization techniques. In particular, a scalar
equilibrium (SE) is an action profile for the n players that maximize a utility function over the acceptable
joint actions. Thus the selection of “solutions” to the game involves the
selection of an acceptable utility function. In a greedy SE, the goal is to
assign individual actions giving each player the largest payoff jointly
possible. In a compromise SE, the goal is to make individual player payoffs
equitable, while a satisficing SE achieves a target payoff level while
weighting each player for possible additional payoff. These SEs are formally
defined and shown to be Pareto optimal over the acceptable joint actions of the
players. The advantage of these SEs is that they involve only pure strategies
that are easily computed. Examples are given, including some well-known
coordination games, and the worst-case time complexity for obtaining these SEs
is shown to be linear in the number of individual payoffs in the payoff matrix.
Finally, the SEs of this paper are checked against some standard game-theoretic
bargaining axioms.