Related papers: Prisoners, Rooms, and Lightswitches
There is a growing interest in the use of video sensor networks in surveillance applications in order to detect intruders with low cost. The essential concern of such networks is whether or not a specified target can pass or intrude the…
We study a condition of favoring cooperation in a Prisoner's Dilemma game on complex networks. There are two kinds of players: cooperators and defectors. Cooperators pay a benefit b to their neighbors at a cost c, whereas defectors only…
We discuss ``puzzles of prisoners and hats`` with infinitely many prisoners and more than two hat colors. Assuming that the set of hat colors is equipped with a commutative group structure, we prove strategic equivalence among puzzles of…
Escape rooms present a unique cognitive challenge that demands exploration-driven planning: with the sole instruction to 'escape the room', players must actively search their environment, collecting information, and finding solutions…
We extend a relaxation technique due to Bertsimas and Nino-Mora for the restless bandit problem to the case where arbitrary costs penalize switching between the bandits. We also construct a one-step lookahead policy using the solution of…
A simple model for cooperation between "selfish" agents, which play an extended version of the Prisoner's Dilemma(PD) game, in which they use arbitrary payoffs, is presented and studied. A continuous variable, representing the probability…
Repeated game has long been the touchstone model for agents' long-run relationships. Previous results suggest that it is particularly difficult for a repeated game player to exert an autocratic control on the payoffs since they are jointly…
In this paper, we study inference for chains of variable order under two distinct contamination regimes. Consider we have a chain of variable memory on a finite alphabet containing zero. At each instant of time an independent coin is…
Resistive switching is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start…
A deadlock occurs in a network when two or more items prevent each other from moving and are stalled. In a general model, items are stored at vertices and each vertex $v$ has a buffer with $b(v)$ slots. Given a route for each item toward…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
This study introduces "Haunted House" a novel text-based game designed to compare the performance of humans and large language models (LLMs) in model-based reasoning. Players must escape from a house containing nine rooms in a 3x3 grid…
We study an evolutionary version of the spatial prisoner's dilemma game, where the agents are placed in a random graph. For lattices with fixed connectivity, $\alpha$, we show that for low values of $\alpha$ the final density of cooperating…
Prisoner's Dilemma is a game theory model used to describe altruistic behavior seen in various populations. This theoretical game is important in understanding why a seemingly selfish strategy does persist and spread throughout a population…
The increasing rate of crime, attacks by thieves, intruders and vandals, despite all forms of security gadgets and locks still need the attention of researchers to find a permanent solution to the well being of lives and properties of…
This paper investigates the minimal number of inputs/outputs required to guarantees the controllability/observability of a system, under the condition that its state transition matrix (STM) is prescribed. It has been proved that this…
The Prisoner's Dilemma (PD) deals with the cooperation/defection conflict between two agents. The agents are represented by a cell of $L \times L$ square lattice. The agents are initially randomly distributed according to a certain…
This paper examines different evacuation strategies for systems where several rooms evacuate trough the same means of egress, using microscopic pedestrian simulation.As a case study, a medium-rise office building is considered. It was found…
We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its…
In the last few decades, numerous experiments have shown that humans do not always behave so as to maximize their material payoff. Cooperative behavior when non-cooperation is a dominant strategy (with respect to the material payoffs) is…