Related papers: Selfish Cops and Active Robber: Multi-Player Pursu…

We consider a variant of Cops and Robbers in which the robber may traverse as many edges as he likes in each turn, with the constraint that he cannot pass through any vertex occupied by a cop. We study this model on several classes of…

These are some personal notes about the pursuit game of Cops and Robbers that I made starting in 2007. More old and new problems (and some solutions) will be added in future versions of these notes.

We provide a game theoretic framework for the game of cops and robbers (CR). Within this framework we study certain assumptions which underlie the concepts of optimal strategies and capture time. We also point out a connection of these…

This paper investigates the encirclement control problem involving two groups using a non-cooperative differential game approach. The active group seeks to chase and encircle the passive group, while the passive group responds by fleeing…

We define new graph parameters, called flip-width, that generalize treewidth, degeneracy, and generalized coloring numbers for sparse graphs, and clique-width and twin-width for dense graphs. The flip-width parameters are defined using…

We show that the cop number of every generalized Petersen graph is at most 4. The strategy is to play a modified game of cops and robbers on an infinite cyclic covering space where the objective is to capture the robber or force the robber…

We consider a variant of the hide-and-seek game in which a seeker inspects multiple hiding locations to find multiple items hidden by a hider. Each hiding location has a maximum hiding capacity and a probability of detecting its hidden…

In the context of multi-player, general-sum games, there is an increasing interest in solution concepts modeling some form of communication among players, since they can lead to socially better outcomes with respect to Nash equilibria, and…

Nash equilibrium (NE) assumes that players always make a best response. However, this is not always true; sometimes people cooperate even it is not a best response to do so. For example, in the Prisoner's Dilemma, people often cooperate.…

This paper studies a two-person linear-quadratic-Gaussian pursuit-evasion differential game with costly but controlled information. One player can decide when to observe the other player's state. However, one observation of another player's…

We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from…

In this paper we will be introducing a type of game which as far as this author is aware has never been studied before. These are games where there are two players, one who is trying to get one of his pieces, called a King to a predefined…

The game of cops and robber has been studied for many years. Denoting $\mathsf{Forb}(4K_1)$ to be the family of all graphs that contain no induced subgraph isomorphic to $4K_1$ (e.g., with independence number less than $4$), we prove that…

We consider the problem of computing Nash equilibria in potential games where each player's strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network…

Interdicting a criminal with limited police resources is a challenging task as the criminal changes location over time. The size of the large transportation network further adds to the difficulty of this scenario. To tackle this issue, we…

We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a…

Recently, a new model extending the standard replicator equation to a finite set of players connected on an arbitrary graph was developed in evolutionary game dynamics. The players are interpreted as subpopulations of multipopulations…

This paper considers the problem of Nash equilibrium (NE) seeking in aggregative games, where the payoff function of each player depends on an aggregate of all players' actions. We present a distributed continuous time algorithm such that…

A qualitative account is given of a differential pursuit/evasion game. A criterion for the existence of an intercept solution is obtained using future cones that contain all attainable trajectories of target or interceptor originating from…

Evolutionary anti-coordination games on networks capture real-world strategic situations such as traffic routing and market competition. In such games, agents maximize their utility by choosing actions that differ from their neighbors'…