Strategies with Parallel Causes

Abstract

We imagine a team Player engaging a team Opponent in a distributed game. Such games and their strategies have been formalised within event structures. However there are limitations in founding strategies on traditional event structures. Sometimes a probabilistic distributed strategy relies on benign races where, intuitively, several members of team Player may race each other to make a common move. Although there exist event structures which support such parallel causes, in which an event is enabled in several compatible ways, they do not support an operation of hiding central to the composition of strategies; nor do they support probability adequately. An extension of traditional event structures is devised which supports parallel causes and hiding, as well as the mix of probability and nondeterminism needed to account for probabilistic distributed strategies. The extension is located within existing models for concurrency and tested in the construction of a bicategory of probabilistic distributed strategies with parallel causes.