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This paper aims at investigating the problem of fast convergence to the Nash equilibrium (NE) for N-Player noncooperative differential games. The proposed method is such that the players attain their NE point without steady-state…
The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear…
This paper investigates Nash equilibrium (NE) seeking problems for noncooperative games over multi-players networks with finite bandwidth communication. A distributed quantized algorithm is presented, which consists of local gradient play,…
We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the…
In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost…
The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many…
In practical applications, decision-makers with heterogeneous dynamics may be engaged in the same decision-making process. This motivates us to study distributed Nash equilibrium seeking for games in which players are mixed-order (first-…
This paper studies a class of network games with linear-quadratic payoffs and externalities exerted through a strictly concave interaction function. This class of game is motivated by the diminishing marginal effects with peer influences.…
In this paper, we investigate the noncooperative games of multi-agent systems. Different from existing noncooperative games, our formulation involves the high-order nonlinear dynamics of players, and the communication topologies among…
We apply control theoretic and optimization techniques to adaptively design incentives. In particular, we consider the problem of a planner with an objective that depends on data from strategic decision makers. The planner does not know the…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
For the characterization of Feedback Nash Equilibria (FNE) in linear quadratic games, this paper provides a detailed analysis of the discrete-time discounted coupled best-response equations for the scalar two-player setting, together with a…
Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed…
This paper investigates Nash equilibria in pure strategies for quantum approach to the Prisoner's Dilemma. The quantization process involves extending the classical game by introducing two additional unitary strategies. We consider five…
Given a bimatrix game, the associated leadership or commitment games are defined as the games at which one player, the leader, commits to a (possibly mixed) strategy and the other player, the follower, chooses his strategy after having…
Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural…
We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that…