Simultaneously Moving Cops and Robbers
Georgios Konstantinidis, Athanasios Kehagias

TL;DR
This paper introduces and analyzes the concurrent cops and robbers game, proving that the concurrent cop number equals the classical cop number and establishing the existence of optimal strategies for both players.
Contribution
It demonstrates that the concurrent cop number matches the classical one and proves the existence of optimal strategies and a well-defined game value in the concurrent setting.
Findings
Concurrent cop number equals classical cop number
Existence of a game value and optimal strategies for both players
Robber has epsilon-optimal strategies for any epsilon>0
Abstract
In this paper we study the concurrent cops and robber (CCCR) game. CCCR follows the same rules as the classical, turn-based game, except for the fact that the players move simultaneously. The cops' goal is to capture the robber and the concurrent cop number of a graph is defined the minimum number of cops which guarantees capture. For the variant in which it it required to capture the robber in the shortest possible time, we let time to capture be the payoff function of CCCR; the (game theoretic) value of CCCR is the optimal capture time and (cop and robber) time optimal strategies are the ones which achieve the value. In this paper we prove the following. (1) For every graph G, the concurrent cop number is equal to the "classical" cop number. (2) For every graph G, CCCR has a value, the cops have an optimal strategy and, for every epsilon>0, the robber has an epsilon-optimal…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
