منابع مشابه
Convexity and Hamiltonian equations in differential games
We study a zero sum differential game under strong assumptions of convexity — the cost is convex for one player, and concave for the other. An explicit necessary and sufficient condition for a saddle point of the game is given in terms of convex analysis subgradients of the conjugate of the cost function. A generalized Hamiltonian equation is shown to describe saddle trajectories of the game.
متن کاملHamiltonian potential functions for differential games
We introduce the concept of Hamiltonian potential function for noncooperative open-loop differential games and characterise necessary and sufficient conditions for its existence. We also identify a class of games admitting a Hamiltonian potential and illustrate appropriate examples pertaining to oligopoly games where price or quantity competition goes along with noncooperative investments eithe...
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We look at the unbiased Maker-Breaker Hamiltonicity game played on the edge set of a complete graph Kn, where Maker’s goal is to claim a Hamiltonian cycle. First, we prove that, independent of who starts, Maker can win the game for n = 8 and n = 9. Then we use an inductive argument to show that, independent of who starts, Maker can win the game if and only if n ≥ 8. This, in particular, resolve...
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We review some properties of the evolutionary dynamics for asymmetric conflicts, give a simplified approach to them, and present some new results on the stability and bifurcations occurring in these conservative systems. In particular, we compare their dynamics to those of Hamiltonian systems.
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Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to +∞, have been introduced by J.-M. Lasry and P.-L. Lions in [11, 12, 13]. We use a change of variables to transform the mean field games (MFG) equations into a system of simpler coupled partial differential equations, in the case of a quadratic Hamiltonian. This system...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1992
ISSN: 0095-8956
DOI: 10.1016/0095-8956(92)90030-2