Winning, Losing and Drawing in Concurrent Games with Perfect or Imperfect Information

Abstract

AbstractNondeterministic concurrent strategies—those strategies compatible with copy-cat behaving as identity w.r.t. composition—have been characterised as certain maps of event structures. This leads to a bicategory of general concurrent games in which the maps are nondeterministic concurrent strategies. This paper explores the consequences of extending concurrent games with (1) winning, losing and, implicitly, neutral configurations, and (2) access levels, to address situations where Player or Opponent have imperfect information as to what has occurred in the game. In both cases winning strategies are shown to form bicategories of games. The bicategories become equivalent to order-enriched categories when restricted to deterministic strategies.