There is limited formal mathematical analysis of one type of games — dynamic sequential games with large, or even infinitely large, planning horizons, from the point view of system controls. In this paper, we use a zero-sum game theoretical approach to address the disturbance attenuation analysis of state feedback Nash strategies for Dynamic Linear Quadratic Sequential Games (LQSGs) with uncert...

We prove the stability of equilibrium in a completely decentralized Walrasian general equilibrium economy in which prices are fully controlled by economic agents, with production and trade occurring out of equilibrium. Journal of Economic Literature Classifications: C62—Existence and Stability Conditions of Equilibrium D51—Exchange and Production Economies D58—Computable and Other Applied Gener...

For some of the EOS models the dimension of equilibrium problem can be reduced. Stability and difficulties in implementation are among the problems of flash calculation. In this work, a new reduction technique is presented to prepare a reduced number of equilibrium equations. Afterwards, a number of appropriate solution variables are selected for the prepared equation system to solve the equati...

In this article, a new fractional order one–country game model (OCGM) with distinct incidence is explored. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the interior equilibrium are determined. The basic reproduction numbers R0 = β (α+1)(γ+μ) and R∗ 0 = E rv are found. It is shown that the...

A finite game of several players in the case of linear payoff functions is considered. Stability of the problem of finding the set of Nash equilibrium situations is investigated. The formula of the stability radius of this problem is derived. AMS Mathematics Subject Classification: 90C27, 90C29.

This paper studies the Nash stability in hedonic coalition formation games. We address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition? We propose the definition of the Nash-stable core and we analyze the conditions for having a non-empty Nash-stable core. More precisely, we prove that using relaxed efficiency in ut...

We report on the formalization in Ssreflect/Coq of a number of concepts and results from algorithmic game theory, including potential games, smooth games, solution concepts such as Pure and Mixed Nash Equilibria, Coarse Correlated Equilibria, -approximate equilibria, and behavioral models of games such as better-response dynamics. We apply the formalization to prove Price of Stability bounds fo...

In a network creation game, initially proposed by Fabrikant et. al. [FLM+03], selfish players build a network by buying links to each other. Each player pays a fixed price per link α > 0, and suffers an additional cost that is the sum of distances to all other players. We study an extension of this game where each player is only interested in its distances to a certain subset of players, called...

For one-dimensional system of dissipative balance laws endowed with a convex entropy we prove, under natural assumptions, that a constant equilibrium state is asymptotically L 2 ?stable under a zero-mass initial disturbance. The technique is based on the construction of an appropriate Liapunov functional involving the entropy and a so-called compensation term.