Randomness for Free

Krishnendu Chatterjee (1) , Laurent Doyen (2) , Hugo Gimbert (3) , Thomas Henzinger (1)

1 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]
2 LSV - Laboratoire Spécification et Vérification [Cachan]
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.

Domaines: Informatique et théorie des jeux [cs.GT]; Analyse numérique [math.NA]

Krishnendu Chatterjee, Laurent Doyen, Hugo Gimbert, Thomas Henzinger. Randomness for Free. MFCS 2010 - 35th International Symposium on Mathematical Foundations of Computer Science, Aug 2010, Brno, Czech Republic. pp.246-257, ⟨10.1007/978-3-642-15155-2_23⟩. ⟨hal-01006409⟩