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A PATH GUESSING GAME WITH WAGERING

Published online by Cambridge University Press:  23 April 2010

Marcus Pendergrass
Marcus Pendergrass
Affiliation:
Department of Mathematics and Computer Science, Hampden-Sydney CollegeE-mail: mpendergrass@hsc.edu
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Abstract

We consider a two-player game in which the first player (the Guesser) tries to guess, edge-by-edge, the path that second player (the Chooser) takes through a directed graph. At each step, the Guesser makes a wager as to the correctness of her guess and receives a payoff proportional to her wager if she is correct. We derive optimal strategies for both players for various classes of graphs, and we describe the Markov-chain dynamics of the game under optimal play. These results are applied to the infinite-duration Lying Oracle Game, in which the Guesser must use information provided by an unreliable Oracle to predict the outcome of a coin toss.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 3 , July 2010 , pp. 375 - 396
Copyright
Copyright © Cambridge University Press 2010

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