A competitive search game with a moving target
Benoit Duvocelle, J\'anos Flesch, Mathias Staudigl, Dries Vermeulen

TL;DR
This paper introduces a discrete-time competitive search game with a moving target modeled by a Markov chain, establishing the existence of approximate strategies and analyzing their robustness and structural properties.
Contribution
It develops the theory of $ ext{eps}$-optimal strategies in a competitive search game with a moving target, including their robustness and structural analysis.
Findings
Existence of a game value and $ ext{eps}$-optimal strategies.
Robustness of strategies over finite horizons and discounted games.
Analysis of finite truncation strategies and special results for time-homogeneous cases.
Abstract
We introduce a discrete-time search game, in which two players compete to find an object first. The object moves according to a time-varying Markov chain on finitely many states. The players know the Markov chain and the initial probability distribution of the object, but do not observe the current state of the object. The players are active in turns. The active player chooses a state, and this choice is observed by the other player. If the object is in the chosen state, this player wins and the game ends. Otherwise, the object moves according to the Markov chain and the game continues at the next period. We show that this game admits a value, and for any error-term , each player has a pure (subgame-perfect) -optimal strategy. Interestingly, a 0-optimal strategy does not always exist. The -optimal strategies are robust in the sense that they are -optimal…
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