Related papers: Sensitivity Analysis for Markov Decision Process C…
'Rich get richer' rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics…
We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…
We propose a real-time nodal pricing mechanism for cost minimization and voltage control in a distribution network with autonomous distributed energy resources and analyze the resulting market using stochastic game theory. Unlike existing…
Congestion game is a widely used model for modern networked applications. A central issue in such applications is that the selfish behavior of the participants may result in resource overloading and negative externalities for the system…
The proliferation of distributed generation and storage units is leading to the development of local, small-scale distribution grids, known as microgrids (MGs). In this paper, the problem of optimizing the energy trading decisions of MG…
In this paper, we consider an integrated MSP-MDP framework which captures features of Markov decision process (MDP) and multistage stochastic programming (MSP). The integrated framework allows one to study a dynamic decision-making process…
We consider risk-sensitive Markov decision processes (MDPs), where the MDP model is influenced by a parameter which takes values in a compact metric space. We identify sufficient conditions under which small perturbations in the model…
This paper develops a novel econometric framework for static discrete choice games with costly information acquisition. In traditional discrete games, players are assumed to perfectly know their own payoffs when making decisions, ignoring…
Markov decision processes (MDP) are a well-established model for sequential decision-making in the presence of probabilities. In robust MDP (RMDP), every action is associated with an uncertainty set of probability distributions, modelling…
Zero sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics , we completely characterize…
We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…
The paper introduces a new approach to theory of differential games in which entangled players try to predict and influence actions of their adversaries. The entanglement is generated be a joint probability density known by the players.…
This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
We introduce Mean Field Markov games with $N$ players, in which each individual in a large population interacts with other randomly selected players. The states and actions of each player in an interaction together determine the…
We study nonzero-sum stochastic differential games with risk-sensitive ergodic cost criterion. Under certain conditions, using multi-parameter eigenvalue approach, we establish the existence of a Nash equilibrium in the space of stationary…
We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…
Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…
We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with…
Partially observable stochastic games provide a rich mathematical paradigm for modeling multi-agent dynamic decision making under uncertainty and partial information. However, they generally do not admit closed-form solutions and are…