相关论文: Stopping times in the game Rock-Paper-Scissors

Dynamical mechanisms that can stabilize the coexistence or diversity in biology are generally of fundamental interest. In contrast to many two-strategy evolutionary games, games with three strategies and cyclic dominance like the…

We construct and study the transition probability matrix of evolutionary games in which the number of players is finite (and relatively small) of such games. We use a simplified version of the population games studied by Sandholm. After…

We consider multi-player stopping games in continuous time. Unlike Dynkin games, in our games the payoff of each player is revealed after all the players stop. Moreover, each player can adjust her own stopping strategy by observing other…

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that…

Three notions of random stopping times exist in the literature. We introduce two concepts of equivalence of random stopping times, motivated by optimal stopping problems and stopping games respectively. We prove that these two concepts…

In a two-person Rock-Paper-Scissors (RPS) game, if we set a loss worth nothing and a tie worth 1, and the payoff of winning (the incentive a) as a variable, this game is called as generalized RPS game. The generalized RPS game is a…

Two concepts of random stopping times in continuous time have been defined in the literature, mixed stopping times and randomized stopping times. We show that under weak conditions these two concepts are equivalent, and, in fact, that all…

We analyze the replicator-mutator equations for the Rock-Paper-Scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional mutation pathway between two of the species, to global…

The Rock-Paper-Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained…

Predicting and modeling human behavior and finding trends within human decision-making processes is a major problem of social science. Rock Paper Scissors (RPS) is the fundamental strategic question in many game theory problems and…

When playing games in groups, it is an advantage for individuals to have accurate statistical information on the strategies of their opponents. Such information may be obtained by remembering previous interactions. We consider a…

Markov chains are an important example for a course on stochastic processes because simple board games can be used to illustrate the fundamental concepts. For example, a looping board game (like Monopoly) consists of all recurrent states,…

We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing…

We consider a zero-sum stochastic game for continuous-time Markov chain with countable state space and unbounded transition and pay-off rates. The additional feature of the game is that the controllers together with taking actions are also…

We consider (N,r) games of predation with N species and r < N prey and predators, acting in a cyclic way. Further basic reactions include reproduction, decay and diffusion over a regular grid, without a hard constraint on the occupation…

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and…

We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with…

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and…

The Rock-Scissors-Paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic…