Chatterjee, KrishnenduIST Austria ; Doyen, Laurent ; Singh, Rohit
Owe, Olaf ; Steffen, Martin ; Telle, Jan Arne
In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.
148 - 159
FCT: Fundamentals of Computation Theory
2011-08-22 – 2011-08-25
Chatterjee K, Doyen L, Singh R. On memoryless quantitative objectives. In: Owe O, Steffen M, Telle JA, eds. Vol 6914. Springer; 2011:148-159. doi:10.1007/978-3-642-22953-4_13
Chatterjee, K., Doyen, L., & Singh, R. (2011). On memoryless quantitative objectives. In O. Owe, M. Steffen, & J. A. Telle (Eds.) (Vol. 6914, pp. 148–159). Presented at the FCT: Fundamentals of Computation Theory, Oslo, Norway: Springer. https://doi.org/10.1007/978-3-642-22953-4_13
Chatterjee, Krishnendu, Laurent Doyen, and Rohit Singh. “On Memoryless Quantitative Objectives.” edited by Olaf Owe, Martin Steffen, and Jan Arne Telle, 6914:148–59. Springer, 2011. https://doi.org/10.1007/978-3-642-22953-4_13.
K. Chatterjee, L. Doyen, and R. Singh, “On memoryless quantitative objectives,” presented at the FCT: Fundamentals of Computation Theory, Oslo, Norway, 2011, vol. 6914, pp. 148–159.
Chatterjee K, Doyen L, Singh R. 2011. On memoryless quantitative objectives. FCT: Fundamentals of Computation Theory, LNCS, vol. 6914. 148–159.
Chatterjee, Krishnendu, et al. On Memoryless Quantitative Objectives. Edited by Olaf Owe et al., vol. 6914, Springer, 2011, pp. 148–59, doi:10.1007/978-3-642-22953-4_13.
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