Related papers: Backward induction in presence of cycles

This paper considers a game-theoretic framework for distributed machine learning problems over networks where the information acquisition at a node is modeled as a rational choice of a player. In the proposed game, players decide both the…

An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…

This paper considers the distributed strategy design for Nash equilibrium (NE) seeking in multi-cluster games under a partial-decision information scenario. In the considered game, there are multiple clusters and each cluster consists of a…

Two fundamental problems in computational game theory are computing a Nash equilibrium and learning to exploit opponents given observations of their play (opponent exploitation). The latter is perhaps even more important than the former:…

In multi-agent dynamic games, the Nash equilibrium state trajectory of each agent is determined by its cost function and the information pattern of the game. However, the cost and trajectory of each agent may be unavailable to the other…

We consider seeking a Nash equilibrium (NE) of a monotone game, played by dynamic agents which are modeled as a class of lower-triangular nonlinear uncertain dynamics with external disturbances. We establish a general framework that…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

Stochastic differential games have been used extensively to model agents' competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets. The recently…

In this paper, we study Nash equilibrium payoffs for nonzero-sum stochastic differential games via the theory of backward stochastic differential equations. We obtain an existence theorem and a characterization theorem of Nash equilibrium…

We consider a subclass of $n$-player stochastic games, in which players have their own internal state/action spaces while they are coupled through their payoff functions. It is assumed that players' internal chains are driven by independent…

We study the performance of the gradient play algorithm for stochastic games (SGs), where each agent tries to maximize its own total discounted reward by making decisions independently based on current state information which is shared…

A Nash equilibrium has become important solution concept for analyzing the decision making in Game theory. In this paper, we consider the problem of computing Nash equilibria of a subclass of generic finite normal form games. We define…

Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…

Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…

We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…

This paper addresses the problem of fair equilibrium selection in graphical games. Our approach is based on the data structure called the {\em best response policy}, which was proposed by Kearns et al. \cite{kls} as a way to represent all…

Multi-time scale techniques, such as singular perturbations and averaging theory, have played an essential role in the development of distributed Nash equilibrium-seeking algorithms for network systems. Such techniques intrinsically rely on…

$ $This paper addresses the inverse problem for Linear-Quadratic (LQ) nonzero-sum $N$-player differential games, where the goal is to learn parameters of an unknown cost function for the game, called observed, given the demonstrated…

The study of learning in games typically assumes that each player always has access to all of their actions. However, in many practical scenarios, players' available actions might be restricted due to exogenous stochasticity. To model this…