Abstract
We introduce a discrete-time search game, in which two players compete to find an invisible object first. The object moves according to a time-varying Markov chain on finitely many states. The players are active in turns. At each period, the active player chooses a state. If the object is there then he finds the object and wins. Otherwise the object moves and the game enters the next period. We show that this game admits a value, and for any error-term epsilon > 0 , each player has a pure (subgame-perfect) epsilon-optimal strategy. Interestingly, a 0-optimal strategy does not always exist. We derive results on the analytic and structural properties of the value and the epsilon-optimal strategies. We devote special attention to the important timehomogeneous case, where we show that (subgame-perfect) optimal strategies exist if the Markov chain is irreducible and aperiodic.
Original language | English |
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Pages (from-to) | 945-957 |
Number of pages | 13 |
Journal | European Journal of Operational Research |
Volume | 303 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Dec 2022 |
Keywords
- Game Theory
- Search game
- Two-player zero-sum game
- Optimal strategies
- Discrete time-varying Markov process
- PERFECT-INFORMATION GAMES
- INTELLIGENT EVADER
- IMMOBILE HIDER
- EQUILIBRIA
- MODEL