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In many real-world settings agents engage in strategic interactions with multiple opposing agents who can employ a wide variety of strategies. The standard approach for designing agents for such settings is to compute or approximate a…

We improve the framework of open games with agency by showing how the players' counterfactual analysis giving rise to Nash equilibria can be described in the dynamics of the game itself (hence diegetically), getting rid of devices such as…

We introduce an analytical model to study the evolution towards equilibrium in spatial games, with `memory-aware' agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner's…

A robust game is a distribution-free model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worst-case optimizers and a solution, called robust-optimization…

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

We consider the existence and computational complexity of coalitional stability concepts based on social networks. Our concepts represent a natural and rich combinatorial generalization of a recent approach termed partition equilibrium. We…

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…

We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…

We study stochastic mean-field games among finite number of teams with large finite as well as infinite number of decision makers. For this class of games within static and dynamic settings, we establish the existence of a Nash equilibrium,…

We consider the problem of computing a mixed-strategy generalized Nash equilibrium (MS-GNE) for a class of games where each agent has both continuous and integer decision variables. Specifically, we propose a novel Bregman…

The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…

We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…

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, the problem of finding a generalized Nash equilibrium (GNE) of a networked game is studied. Players are only able to choose their decisions from a feasible action set. The feasible set is considered to be a private linear…

Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more…

We consider a large population dynamic game in discrete time where players are characterized by time-evolving types. It is a natural assumption that the players' actions cannot anticipate future values of their types. Such games go under…

This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

Nash equilibrium is used as a model to explain the observed behavior of players in strategic settings. For example, in many empirical applications we observe player behavior, and the problem is to determine if there exist payoffs for the…

Nash equilibrium serves as a fundamental mathematical tool in economics and game theory. However, it classically assumes knowledge of player utilities, whereas economics generally regards preferences as more fundamental. To leverage…