Related papers: The Modified Stochastic Games
In this paper, we analyze mean-field game modulated by finite states markov chains. We first develop a sufficient stochastic maximum principle for the optimal control of a Markov-modulated stochastic differential equation (SDE) of…
We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…
In this paper, we study the number of equilibria of the replicator-mutator dynamics for both deterministic and random multi-player two-strategy evolutionary games. For deterministic games, using Decartes' rule of signs, we provide a formula…
Distributed Nash equilibrium (NE) seeking problem for multi-coalition games has attracted increasing attention in recent years, but the research mainly focuses on the case without agreement demand within coalitions. This paper considers a…
Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…
In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…
We show that every two-player stochastic game with finite state and action sets and bounded, Borel-measurable, and shift-invariant payoffs, admits an $\ep$-equilibrium for all $\varepsilon>0$.
This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated It\^o-diffusion via a two-sided singular stochastic control…
High performance machine learning models have become highly dependent on the availability of large quantity and quality of training data. To achieve this, various central agencies such as the government have suggested for different data…
In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
In this note, we prove the existence of an equilibrium concept, dubbed conditional strategy equilibrium, for non-cooperative games in which a strategy of a player is a function from the other players' actions to her own actions. We study…
We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and…
We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…
We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a…
We consider a finite state, finite action, zero-sum stochastic games with data defining the game lying in the ordered field of algebraic numbers. In both the discounted and the limiting average versions of these games we prove that the…
This paper proposes and studies a general form of dynamic $N$-player non-cooperative games called $\alpha$-potential games, where the change of a player's value function upon her unilateral deviation from her strategy is equal to the change…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
In this paper we define the canonical mixed extension of a decision form game. We motivate the necessity to introduce this concept and we show several examples about the new concept. In particular we focus our study upon the mixed…
In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…
We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to symmetric additively-separable hedonic games, which are a nontrivial subclass of…