Displaying similar documents to “Differential Games and Nonlinear First Order PDE on Bounded Domains.”

Viscosity solutions of the Isaacs equation οn an attainable set

Leszek Zaremba (1994)

Applicationes Mathematicae

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We apply a modification of the viscosity solution concept introduced in [8] to the Isaacs equation defined on the set attainable from a given set of initial conditions. We extend the notion of a lower strategy introduced by us in [17] to a more general setting to prove that the lower and upper values of a differential game are subsolutions (resp. supersolutions) in our sense to the upper (resp. lower) Isaacs equation of the differential game. Our basic restriction is that the variable...

Method of construction of the evasion strategy for differential games with many pursuers

Witold Rzymowski

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CONTENTSIntroduction...........................................................................51. Preliminaries.....................................................................6 1.1. Notation........................................................................6 1.2. Control systems. Strategies..........................................72. Main lemma......................................................................93. Avoidance of many pursuers..........................................14 3.1....

Equilibria in constrained concave bimatrix games

Wojciech Połowczuk, Tadeusz Radzik (2013)

Applicationes Mathematicae

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We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to -∞. The first of these results is a discrete...

An axiomatization of the aspiration core

Hans Keiding (2006)

Banach Center Publications

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The aspiration core of a TU game was introduced by Bennett [1] as a payoff vector which is undominated and achievable in the sense that each player belongs to a coalition which can obtain the specified payoff for its members, and which minimizes the distance to the set of aggregate feasible payoffs among all such payoff vectors. In the paper a set of axioms is proposed which characterize the aspiration core, which may be considered as an extension of the core to a much larger set of...