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 (players interact simultaneously); and (b) turn-based (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. 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.
This research was supported by the European Union project COMBEST and the European Network of Excellence ArtistDesign.
246 - 257
MFCS: Mathematical Foundations of Computer Science
Brno, Czech Republic
2010-08-23 – 2010-08-27
Chatterjee K, Doyen L, Gimbert H, Henzinger TA. Randomness for free. In: Vol 6281. Springer; 2010:246-257. doi:10.1007/978-3-642-15155-2_23
Chatterjee, K., Doyen, L., Gimbert, H., & Henzinger, T. A. (2010). Randomness for free (Vol. 6281, pp. 246–257). Presented at the MFCS: Mathematical Foundations of Computer Science, Brno, Czech Republic: Springer. https://doi.org/10.1007/978-3-642-15155-2_23
Chatterjee, Krishnendu, Laurent Doyen, Hugo Gimbert, and Thomas A Henzinger. “Randomness for Free,” 6281:246–57. Springer, 2010. https://doi.org/10.1007/978-3-642-15155-2_23.
K. Chatterjee, L. Doyen, H. Gimbert, and T. A. Henzinger, “Randomness for free,” presented at the MFCS: Mathematical Foundations of Computer Science, Brno, Czech Republic, 2010, vol. 6281, pp. 246–257.
Chatterjee K, Doyen L, Gimbert H, Henzinger TA. 2010. Randomness for free. MFCS: Mathematical Foundations of Computer Science, LNCS, vol. 6281. 246–257.
Chatterjee, Krishnendu, et al. Randomness for Free. Vol. 6281, Springer, 2010, pp. 246–57, doi:10.1007/978-3-642-15155-2_23.
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