Average Reward Timed Games

We consider real-time games where the goal consists, for each player, in maximizing the average amount of reward he or she receives per time unit. We consider zero-sum rewards, so that a reward of +r to one player corresponds to a reward of −r to the other player. The games are played on discrete-time game structures which can be specified using a two-player version of timed automata whose locations are labeled by rewards. Even though the rewards themselves are zero-sum, the games are not, due to the requirement that time must progress along a play of the game. Since we focus on control applications, we define the value of the game to a player to be the maximal average reward per time unit that the player can ensure. We show that in general the values to players 1 and 2 do not sum to zero. We provide algorithms for computing the value of the game for either player; the algorithms are based on the relationship between the original, infinite-round, game, and a derived game that is p...

• Type: Conference
• Year: 2005
• Where: FORMATS
• Authors: B. Thomas Adler, Luca de Alfaro, Marco Faella
• Keywords: Discrete-time Game Structures, FORMATS 2005, Time Unit, Zero-sum Rewards