Hansen, Kristoffer; Ibsen-Jensen, RasmusIST Austria ; Koucký, Michal
We study repeated games with absorbing states, a type of two-player, zero-sum concurrent mean-payoff games with the prototypical example being the Big Match of Gillete (1957). These games may not allow optimal strategies but they always have ε-optimal strategies. In this paper we design ε-optimal strategies for Player 1 in these games that use only O(log log T) space. Furthermore, we construct strategies for Player 1 that use space s(T), for an arbitrary small unbounded non-decreasing function s, and which guarantee an ε-optimal value for Player 1 in the limit superior sense. The previously known strategies use space Ω(log T) and it was known that no strategy can use constant space if it is ε-optimal even in the limit superior sense. We also give a complementary lower bound. Furthermore, we also show that no Markov strategy, even extended with finite memory, can ensure value greater than 0 in the Big Match, answering a question posed by Neyman .
64 - 76
SAGT: Symposium on Algorithmic Game Theory
Liverpool, United Kingdom
2016-09-19 – 2016-09-21
Hansen K, Ibsen-Jensen R, Koucký M. The big match in small space. In: Vol 9928. Springer; 2016:64-76. doi:10.1007/978-3-662-53354-3_6
Hansen, K., Ibsen-Jensen, R., & Koucký, M. (2016). The big match in small space (Vol. 9928, pp. 64–76). Presented at the SAGT: Symposium on Algorithmic Game Theory, Liverpool, United Kingdom: Springer. https://doi.org/10.1007/978-3-662-53354-3_6
Hansen, Kristoffer, Rasmus Ibsen-Jensen, and Michal Koucký. “The Big Match in Small Space,” 9928:64–76. Springer, 2016. https://doi.org/10.1007/978-3-662-53354-3_6.
K. Hansen, R. Ibsen-Jensen, and M. Koucký, “The big match in small space,” presented at the SAGT: Symposium on Algorithmic Game Theory, Liverpool, United Kingdom, 2016, vol. 9928, pp. 64–76.
Hansen K, Ibsen-Jensen R, Koucký M. 2016. The big match in small space. SAGT: Symposium on Algorithmic Game Theory, LNCS, vol. 9928, 64–76.
Hansen, Kristoffer, et al. The Big Match in Small Space. Vol. 9928, Springer, 2016, pp. 64–76, doi:10.1007/978-3-662-53354-3_6.