We focus on the problem of learning equilibria in a particular routing game similar to the Wardrop traffic model. We describe a routing game played by a large number of players and present a distributed learning algorithm that we prove to (weakly) converge to equilibria for the system. The proof of convergence is based on a differential equation governing the global evolution of the system that...

Nonlinear parametric excitation refers to the nonlinear analysis of a system of ordinary differential equations with periodic coefficients. In contrast to linear parametric excitation, which offers determinations of the stability of equilibria, nonlinear parametric excitation has as its goal the structure of the phase space, as given by a portrait of the Poincare map. In this article, perturbat...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon. The performance function is assumed to be indefinite and the underlying system affine. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.

We consider the following differential game of pursuit and evasion involving two unmanned aerial vehicle agents (UAVs): an evading UAV (“evader”), which has limited maneuverability, and a pursuing UAV (“pursuer”), which is assumed to be completely agile. The two UAVs move on the Euclidean plane with different but constant speeds. Whereas the pursuer can change the orientation of its velocity ve...

We study how continuous time Bertrand and Cournot competitions, in which firms producing similar goods compete with one another by setting prices or quantities respectively, can be analyzed as continuum dynamic mean field games. Interactions are of mean field type in the sense that the demand faced by a producer is affected by the others through their average price or quantity. Motivated by ene...

SPATIAL EVOLUTIONARY GAME THEORY: DETERMINISTIC APPROXIMATIONS, DECOMPOSITIONS, AND HIERARCHICAL MULTI-SCALE MODELS SEPTEMBER 2011 SUNGHA HWANG, B.A., SEOUL NATIONAL UNIVERSITY M.A., SEOUL NATIONAL UNIVERSITY Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Luc Rey-Bellet Evolutionary game theory has recently emerged as a key paradigm in various behavioral science disciplines. ...

In this paper, we propose a method of designing energy tax rate based on game theory. Through this method, the effect of energy tax on encouraging manufacturers’ improvement in energy efficiency is enhanced. Consequently policy makers can reduce the average burden of manufacturers brought by energy tax. Through utilizing game theory in a numerical example, we explain the effect of energy tax on...

It is known that the Hamiltonian of the eikonal equation for an anisotropic medium may be nonconvex, which excludes the application of Fermat’s minimum-time principle related to minimum-time control problems. The idea proposed in this paper consists in finding a conflict control problem (differential game) whose Hamiltonian coincides with the Hamiltonian of the eikonal equation. It turns out th...

This paper studies the finite-horizon H∞-optimal control problem for linear hyperbolic systems when only time-sampled values of the state are available, with control acting on the boundary. The problem is formulated in a differential game framework by associating a zero-sum differential game with the original disturbance attenuation problem. The minimizing player’s minimax strategy in this game...

This paper addresses a theoretical issue related to combined dynamic traffic assignment and signal control under conditions of congestion through a brief review of previous research and the discussion on interaction between dynamic traffic assignment and signal control. The dynamic characteristics of the interaction are approached using a differential game modeling approach here to formulate th...