Infinite Horizon Noncooperative Differential Games with Non-Smooth Costs

In the present paper, we consider a class of two players infinite horizon differential games, with piecewise smooth costs exponentially discounted in time. Through the analysis of the value functions, we study in which cases it is possible to establish the existence Nash equilibrium solutions in feedback form. We also provide examples of piecewise linear costs whose corresponding games have either infinitely many Nash equilibria or no solutions at all.Comment: 17 pages, 5 figure

Markov approximations of nonzero-sum differential games

The paper is concerned with approximate solutions of nonzero-sum differential games. An approximate Nash equilibrium can be designed by a given solution of an auxiliary continuous-time dynamic game. We consider the case when dynamics is determined by a Markov chain. For this game the value function is determined by an ordinary differential inclusion. Thus, we obtain a construction of approximate equilibria with the players' outcome close to the solution of the differential inclusion. Additionally, we propose a way of designing a continuous-time Markov game approximating the original dynamics. © 2020 Udmurt State University. All rights reserved.Russian Science Foundation, RSF: 17-11-01093Funding. This work was funded by the Russian Science Foundation (Project No. 17-11-01093)

Foraging swarms as Nash equilibria of dynamic games

Cataloged from PDF version of article.The question of whether foraging swarms can form as a result of a noncooperative game played by individuals is shown here to have an affirmative answer. A dynamic game played by N agents in 1-D motion is introduced and models, for instance, a foraging ant colony. Each agent controls its velocity to minimize its total work done in a finite time interval. The game is shown to have a unique Nash equilibrium under two different foraging location specifications, and both equilibria display many features of a foraging swarm behavior observed in biological swarms. Explicit expressions are derived for pairwise distances between individuals of the swarm, swarm size, and swarm center location during foraging. © 2013 IEEE

Universal Nash Equilibrium Strategies for Differential Games

The paper is concerned with a two-player nonzero-sum differential game in the case when players are informed about the current position. We consider the game in control with guide strategies first proposed by Krasovskii and Subbotin. The construction of universal strategies is given both for the case of continuous and discontinuous value functions. The existence of a discontinuous value function is established. The continuous value function does not exist in the general case. In addition, we show the example of smooth value function not being a solution of the system of Hamilton--Jacobi equation.Comment: 23 page

Infinite Horizon Noncooperative Differential Games

For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value functions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability.Comment: 25 pages, 7 figure

On feedback strategies in control problems and differential games

This thesis consists of two parts. In the first part we study the existence and uniqueness of Nash equilibrium solutions for a class of infinite horizon, non-cooperative differential games. The second part is concerned with the construction of nearly-optimal patchy feedbacks, for problems of optimal control

Approximate public-signal correlated equilibria for nonzero-sum differential games

We construct an approximate public-signal correlated equilibrium for a nonzero-sum differential game in the class of stochastic strategies with memory. The construction is based on a solution of an auxiliary nonzero-sum continuous-time stochastic game. This class of games includes stochastic differential games and continuous-time Markov games. Moreover, we study the limit of approximate equilibrium outcomes in the case when the auxiliary stochastic games tend to the original deterministic one. We show that it lies in the convex hull of the set of equilibrium values provided by deterministic punishment strategies.Comment: 35 page

Learning multi-robot coordination from demonstrations

This paper develops a Distributed Differentiable Dynamic Game (DDDG) framework, which enables learning multi-robot coordination from demonstrations. We represent multi-robot coordination as a dynamic game, where the behavior of a robot is dictated by its own dynamics and objective that also depends on others' behavior. The coordination thus can be adapted by tuning the objective and dynamics of each robot. The proposed DDDG enables each robot to automatically tune its individual dynamics and objectives in a distributed manner by minimizing the mismatch between its trajectory and demonstrations. This process requires a new distributed design of the forward-pass, where all robots collaboratively seek Nash equilibrium behavior, and a backward-pass, where gradients are propagated via the communication graph. We test the DDDG in simulation with a team of quadrotors given different task configurations. The results demonstrate the capability of DDDG for learning multi-robot coordination from demonstrationsComment: 6 figure