Existence of optimal strategies for the Operation Game on amenable semigroups

Details Existence of optimal strategies for the Operation Game on amenable semigroups Existence of optimal strategies for the Operation Game on amenable semigroups

2011-04-15

arxiv.org/abs/1104.3098v2

Computer Science

Computer Science and Game Theory

14 pages

Scientific paper

We extend the theorem about optimal strategies for the multiplication game on compact groups to the setting of amenable semigroups. This answers the question posed by the second author about the existence of optimal strategies in the case of non-compact groups. We give a formal definition for the operation game to be loaded and we show there exist operation games that are loadable in uncountably many different ways. Finally, we introduce a new class of winning sets for which the value of the game does not depend on the loading. In particular, these are examples of games that admit infinitely many different optimal strategies.

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