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Nonlinear BSDEs with Two Optional Doob’s Class Barriers Satisfying Weak Mokobodzki’s Condition and Extended Dynkin Games
We study reflected backward stochastic differential equations (RBSDEs) on the probability space equipped with a Brownian motion. The main novelty of...
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Stationary fully nonlinear mean-field games
In this paper we examine fully nonlinear mean-field games associated with a minimization problem. The variational setting is driven by a functional...
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Differential Games in a Banach Space without Discrimination
AbstractThe paper is a continuation of author’s research on the existence of an ε-equilibrium in the sense of piecewise program strategies in...
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Well-Posedness of Weakly Cooperative Equilibria for Multi-objective Population Games
In this paper, we construct a bounded rationality function of weakly cooperative equilibrium point of multi-objective population games (WCEPOMPG) by...
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Introspection Dynamics in Asymmetric Multiplayer Games
Evolutionary game theory and models of learning provide powerful frameworks to describe strategic decision-making in social interactions. In the...
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Newton’s Method, Bellman Recursion and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games
Dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics,...
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Games and the Treatment Convexity of Cancer
Evolutionary game theory has been highly valuable in studying frequency-dependent selection and growth between competing cancer phenotypes. We study...
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A Survey of the Latest Advances in Oligopoly Games
AbstractOne of the most important problems of game theory—the game of firms in an oligopoly market—is considered. The survey covers classical and...
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Randomized Lagrangian stochastic approximation for large-scale constrained stochastic Nash games
In this paper, we consider stochastic monotone Nash games where each player’s strategy set is characterized by possibly a large number of explicit...
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On some mean field games and master equations through the lens of conservation laws
In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of...
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Approximation of Deterministic Mean Field Games with Control-Affine Dynamics
We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with...
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Stationary Equilibria in Discounted Stochastic Games
We provide a new characterisation of the set of stationary equilibria for finite discounted N -player stochastic games, based on the definition of an...
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Approximating the Value of Zero-Sum Differential Games with Linear Payoffs and Dynamics
We consider two-player zero-sum differential games of fixed duration, where the running payoff and the dynamics are both linear in the controls of...
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Dynamic Advertising Games in Duopolies Under One-Step-Ahead Optimal Control
In discrete-time Vidale–Wolfe–Deal duopoly models and variants, two firms compete for market share, in a dynamic game setting, described by a pair of...
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Stochastic differential games with controlled regime-switching
In this article, we consider a two-player zero-sum stochastic differential game with regime-switching. Different from the results in existing...
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Two Classes of Signaling Games: Reputation and Information Privacy Games
In the previous chapter, we introduced and analyzed Nash and Stackelberg equilibria of signaling games where the agents have misaligned objectives or...
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Generic Properties of First-Order Mean Field Games
We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear...
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Robustness and Sample Complexity of Model-Based MARL for General-Sum Markov Games
Multi-agent reinforcement learning (MARL) is often modeled using the framework of Markov games (also called stochastic games or dynamic games). Most...
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Stochastic Teams, Games, and Control under Information Constraints
This monograph presents a mathematically rigorous and accessible treatment of the interaction between information, decision, control, and probability...
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Convexification Numerical Method for the Retrospective Problem of Mean Field Games
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field...
