Related papers: Cellular Games
We consider static finite-player network games and their continuum analogs, graphon games. Existence and uniqueness results are provided, as well as convergence of the finite-player network game optimal strategy profiles to their analogs…
Many real-world domains contain multiple agents behaving strategically with probabilistic transitions and uncertain (potentially infinite) duration. Such settings can be modeled as stochastic games. While algorithms have been developed for…
Evolutionary games are a developing sub-field of game theory. This branch of game theory is used in the study of the adaptation of large, but finite, populations of agents to changes in the environment. It assumes that each agent has no…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
We propose a toy model for a stochastic description of the competition between two athletes of unequal strength, whose average strength difference is represented by a parameter $d$. The athletes interact through the choice of their…
We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. Long-run behavior of stochastic dynamics of spatial games with multiple…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
This work explores dynamics existing in interactions between players. The dynamic system of games is a new attitude to modeling in which an event is modeled using several games. The model allows us to analyze the interplay capabilities and…
Learning in games provides a powerful framework to design control policies for self-interested agents that may be coupled through their dynamics, costs, or constraints. We consider the case where the dynamics of the coupled system can be…
This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the…
We study natural strategic games on directed graphs, which capture the idea of coordination in the absence of globally common strategies. We show that these games do not need to have a pure Nash equilibrium and that the problem of…
The article introduces a notion of a stochastic game with failure states and proposes two logical systems with modality "coalition has a strategy to transition to a non-failure state with a given probability while achieving a given goal."…
Evolutionary game dynamics describes not only frequency dependent genetical evolution, but also cultural evolution in humans. In this context, successful strategies spread by imitation. It has been shown that the details of strategy update…
We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether…
Situations of conflict giving rise to social dilemmas are widespread in society and game theory is one major way in which they can be investigated. Starting from the observation that individuals in society interact through networks of…
In this paper we experiment with a 2-player strategy board game where playing models are evolved using reinforcement learning and neural networks. The models are evolved to speed up automatic game development based on human involvement at…
Causal games are probabilistic graphical models that enable causal queries to be answered in multi-agent settings. They extend causal Bayesian networks by specifying decision and utility variables to represent the agents' degrees of freedom…
In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…
Taking the absolute value of consecutive differences of a cyclicly ordered list of integers constitutes a simple dynamical system. For lists of lenght a power of two the process will terminate in all zeros, but examples with arbitarily long…
The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of three formalisms used for different purposes in reasoning…