Games and Strategies as Event Structures

TL;DR

This paper revisits and extends Rideau and Winskel's framework of concurrent games and strategies modeled as event structures, establishing a bicategory with a compact closed structure for semantics of concurrent higher-order computation.

Contribution

It provides a detailed, updated account of strategies as event structures, characterizes strategies preserved under composition, and constructs a bicategory with a compact closed structure.

Findings

Strategies form a bicategory with a compact closed structure.

Characterization of strategies preserved by composition.

Foundation for semantics of concurrent higher-order computation.

Abstract

In 2011, Rideau and Winskel introduced concurrent games and strategies as event structures, generalizing prior work on causal formulations of games. In this paper we give a detailed, self-contained and slightly-updated account of the results of Rideau and Winskel: a notion of pre-strategy based on event structures; a characterisation of those pre-strategies (deemed strategies) which are preserved by composition with a copycat strategy; and the construction of a bicategory of these strategies. Furthermore, we prove that the corresponding category has a compact closed structure, and hence forms the basis for the semantics of concurrent higher-order computation.