English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce and study the game of "Selfish Cops and Active Robber" (SCAR)which can be seen as an multiplayer variant of the "classic" two-player Copsand Robbers (CR) game. In classic CR all cops are controlled by a singleplayer, who has no preference over which cop captures the robber. In SCAR, onthe other hand, each of N-1 cops is controlled by a separate player, and asingle robber is controlled by the N-th player; and the capturing cop playerreceives a higher reward than the non-capturing ones. Consequently, SCAR is anN-player pursuit game on graphs, in which each cop player has an increasedmotive to be the one who captures the robber. The focus of our study is theexistence and properties of SCAR Nash Equilibria (NE). In particular, we provethat SCAR always has one NE in deterministic positional strategies and (for Ngreater than two) another in deterministic nonpositional strategies.Furthermore, we study conditions which, at equilibrium, guarantee eithercapture or escape of the robber and show that (because of the antagonismbetween the "selfish" cop players) the robber may, in certain SCARconfigurations, be captured later than he would be in classic CR, or even notcaptured at all. Finally we define the selfish cop number of a graph and studyits connection to the classic cop number.

Selfish Cops and Active Robber: Multi-Player Pursuit Evasion on Graphs