The tree search game for two players
Ravi B. Boppana, Joel Brewster Lewis

TL;DR
This paper analyzes a two-player game on trees where players alternately guess vertices to find a hidden target, revealing subtrees after each guess, and determines winning probabilities under various strategies.
Contribution
It introduces a new two-player search game on trees and characterizes winning probabilities under optimal and random strategies.
Findings
Optimal play yields approximately 50% win probability for each player.
Mixed strategies result in win probabilities between 9/16 and 2/3.
Random play leads to win probabilities between 13/30 and 17/30.
Abstract
We consider a two-player search game on a tree . One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess is not the target, then both players are informed in which subtree of the target lies. The winner is the player who guesses the target. When both players play optimally, we show that each of them wins with probability approximately . When one player plays optimally and the other plays randomly, we show that the player with the optimal strategy wins with probability between and (asymptotically). When both players play randomly, we show that each wins with probability between and (asymptotically).
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Taxonomy
TopicsGame Theory and Applications · Computability, Logic, AI Algorithms · Optimization and Search Problems
