A competitive search game with a moving target

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

Multiagent Online Learning in Time-Varying Games

We examine the long-run behavior of multiagent online learning in games that evolve over time. Specifically, we focus on a wide class of policies based on mirror descent, and we show that the induced sequence of play (a) converges to a Nash equilibrium in time-varying games that stabilize in the long run to a strictly monotone limit, and (b) it stays asymptotically close to the evolving equilibrium of the sequence of stage games (assuming they are strongly monotone). Our results apply to both gradient- and payoffbased feedback???that is, when players only get to observe the payoffs of their chosen actions

A competitive search game with a moving target

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