Refinement of acyclic-and-asymmetric payoff aggregates of pure strategy efficient Nash equilibria in finite noncooperative games by maximultimin and superoptimality

Vadim Romanuke

doi:10.31181/dmame210402178r

Authors

Vadim Romanuke Polish Naval Academy, Gdynia, Poland

DOI:

https://doi.org/10.31181/dmame210402178r

Keywords:

Finite noncooperative games, efficient equilibria, refinement, maximultimin, superoptimality, metaequilibrium, uncertainty partial reduction.

Abstract

A theory of refining pure strategy efficient Nash equilibria in finite noncooperative games under uncertainty is outlined. The theory is based on guaranteeing the corresponding payoffs for the players by using maximultimin, which is an expanded version of maximin. If a product of the players’ maximultimin subsets contains more than one efficient Nash equilibrium, a superoptimality rule is attached wherein minimization is substituted with summation. The superoptimality rule stands like a backup plan, and it is involved if maximultimin fails to produce just a single refined efficient equilibrium (a metaequilibrium). The number of the refinement possible outcomes is 10. There are 3 single-metaequilibrium cases, 3 partial reduction cases, and 4 fail cases. Despite successfulness of refinement drops as the game gets bigger, pessimistic estimation of its part is above 54 % for games with no more than four players.

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