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Stackelberg games have been widely used to model interactive decision-making problems in a variety of domains such as energy systems, transportation, cybersecurity, and human-robot interaction. However, existing algorithms for solving…

Zero-sum Markov Games (MGs) has been an efficient framework for multi-agent systems and robust control, wherein a minimax problem is constructed to solve the equilibrium policies. At present, this formulation is well studied under tabular…

In this paper, we consider the problem of optimization and learning for constrained and multi-objective Markov decision processes, for both discounted rewards and expected average rewards. We formulate the problems as zero-sum games where…

Zero-sum Markov Stackelberg games can be used to model myriad problems, in domains ranging from economics to human robot interaction. In this paper, we develop policy gradient methods that solve these games in continuous state and action…

Dynamic game theory offers a toolbox for formalizing and solving for both cooperative and non-cooperative strategies in multi-agent scenarios. However, the optimal configuration of such games remains largely unexplored. While there is…

Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…

We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

Several recent works have studied the societal effects of AI; these include issues such as fairness, robustness, and safety. In many of these objectives, a learner seeks to minimize its worst-case loss over a set of predefined distributions…

Long studied as a toy model, quantum zero-sum games have recently resurfaced as a canonical playground for modern areas such as non-local games, quantum interactive proofs, and quantum machine learning. In this simple yet fundamental…

Economic ensembles can be modeled as networks of interacting agents whose be-haviors are described in terms of game theory. The evolutionary paradigm has been applied to two-person games to discover strategies in this context.…

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…

The interplay between exploration and exploitation in competitive multi-agent learning is still far from being well understood. Motivated by this, we study smooth Q-learning, a prototypical learning model that explicitly captures the…

We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…

With the digitalization of the financial market, dealers are increasingly handling market-making activities by algorithms. Recent antitrust literature raises concerns on collusion caused by artificial intelligence. This paper studies the…

Zero-determinant strategies are a class of strategies in repeated games which unilaterally control payoffs. Zero-determinant strategies have attracted much attention in studies of social dilemma, particularly in the context of evolution of…

Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…

Zero-sum Linear Quadratic (LQ) games are fundamental in optimal control and can be used (i)~as a dynamic game formulation for risk-sensitive or robust control and (ii)~as a benchmark setting for multi-agent reinforcement learning with two…

Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…

Scale-invariance in games has recently emerged as a widely valued desirable property. Yet, almost all fast convergence guarantees in learning in games require prior knowledge of the utility scale. To address this, we develop learning…