Rough games modeled via L-fuzzy ambiguous representations of semilattices

Abstract

Monotonic predicates and L-fuzzy ambiguous representations of continuous semilattices with bottom elements are applied to describe rough normal-form games and rough extensive-form two-player zero-sum games with imperfect information. Payoff predicates are introduced to find best guaranteed gains of the players. These predicates are calculated recursively via backward payoff predicate transformers, which are also studied. It is shown how payoff predicates determine almost optimal strategies. An approximate minimax theorem is also stated.