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Control of multi-agent systems via game theory is investigated. Assume a system level object is given, the utility functions for individual agents are designed to convert a multi-agent system into a potential game. First, for fixed…
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of Bayesian games and deterministic aggregative games. We handle the aggregation…
In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive discounted-cost optimality criterion. Risk-sensitivity is introduced for each agent (player) via an exponential utility function. In…
We consider quadratic, nonmonotone generalized Nash equilibrium problems with symmetric interactions among the agents. Albeit this class of games is known to admit a potential function, its formal expression can be unavailable in several…
The concept of Nash equilibrium in behavioral strategies (NashEBS) was formulated By Nash~\cite{Nash (1951)} for an extensive-form game through global rationality of nonconvex payoff functions. Kuhn's payoff equivalence theorem resolves the…
Equilibria of realistic multiplayer games constitute a key solution concept both in practical applications, such as online advertising auctions and electricity markets, and in analytical frameworks used to study strategic voting in…
We consider a non-zero-sum linear quadratic Gaussian (LQG) dynamic game with asymmetric information. Each player observes privately a noisy version of a (hidden) state of the world $V$, resulting in dependent private observations. We study…
We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE.…
Evolution of agents' dynamics of multiagent systems under consensus protocol in the face of jamming attacks is discussed, where centralized parties are able to influence the control signals of the agents. In this paper we focus on a…
Multi-leader multi-follower games are a class of hierarchical games in which a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
A Bayesian player acting in an infinite multi-player game learns to predict the other players' strategies if his prior assigns positive probability to their play (or contains a grain of truth). Kalai and Lehrer's classic grain of truth…
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…
The behavior of rational and selfish players (receivers) over a multiple-input multiple-output Gaussian broadcast channel is investigated using the framework of noncooperative game theory. In contrast to the game-theoretic model of the…
We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…
The strategic selection of resources by selfish agents is a classic research direction, with Resource Selection Games and Congestion Games as prominent examples. In these games, agents select available resources and their utility then…
This paper develops a unified framework for testing monotonicity of Bayesian Nash equilibrium strategies in unobserved types in games of incomplete information. We show that, under symmetric independent private types, monotonicity of…
This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for correlation is crucial in global games and in models with social interactions as it represents correlated…