Game Relations and Metrics

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal (e.g., “reach a target state”), the question of winning is thus a probabilistic one: “what is the maximal probability of winning from a given state?”. On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two states are equivalent if the players can win the same games with the same probability from both states. Metrics provide a bound on the difference in the probabilities of winning across states, capturing a quantitative notion of state “similarity”. We introduce equivalences and metrics for two-player game structures, and we show that they characterize the difference in probability of winnin...

• Type: Conference
• Year: 2007
• Where: LICS
• Authors: Luca de Alfaro, Rupak Majumdar, Vishwanath Raman, Mariëlle Stoelinga
• Keywords: Computer Science, Game Structures, LICS 2007, Two-player Game, finite State Spaces