A Path Guessing Game with Wagering

TL;DR

This paper introduces a strategic path guessing game involving wagering, analyzes optimal strategies on different graph classes, and applies findings to an infinite-duration game with an unreliable oracle, blending game theory and probabilistic analysis.

Contribution

It provides the first comprehensive analysis of optimal strategies for a path guessing game with wagering on various graph structures and extends the results to an infinite-duration setting.

Findings

Derived optimal strategies for the game on different graph classes

Described the Markov-chain dynamics under optimal play

Applied results to the Lying Oracle Game with an unreliable oracle

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 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.