The lying oracle game with a biased coin
Robb Koether, Marcus Pendergrass, and John Osoinach
Source: Adv. in Appl. Probab. Volume 41, Number 4
(2009), 1023-1040.
Abstract
The lying oracle problem is a problem of finding the optimal
strategies in a two-person game where an oracle predicts the
outcomes of coin flips and a player bets on the outcomes. The
oracle announces whether the coin will land heads or tails, but
may at times lie. We analyze the variant of the game which uses a
biased coin, where the probability p that the coin lands heads
is common knowledge. We determine optimal strategies for both the
oracle and player, and we give an explicit expression for the
expected payoff to the player when the coin is flipped $n$ times
and the oracle may lie at most k times.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1261669584
Digital Object Identifier: doi:10.1239/aap/1261669584
Zentralblatt MATH identifier: 05706688
Mathematical Reviews number (MathSciNet): MR2663234
References
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Koether, R. (2007). The generalized paper-scissors-stone game. Preprint.
Koether, R. T. and Osoinach, J. K. (2005). Outwitting the lying oracle. Math. Mag. 78, 98--109.
Pendergrass, M. (2009). A path guessing game with wagering. Preprint. Available at http://arxiv.org/ abs/0907.2196.
Ravikumar, B. (2005). Some connections between the lying oracle problem and Ulam's search problem. In Proc. Australasian Workshop Combinatorial Algorithms (Ballarat, September 2005), eds J. Ryan et al., University of Ballarat, pp. 269--277.
Rivest, R. L., Mayer, A. R., Kleitman, D. J. and Winklemann, K. (1980). Coping with errors in binary search procedures. J. Comput. System Sci. 20, 396--404.
Mathematical Reviews (MathSciNet):
MR584867
