In this paper, we shall give a brief account of the main ideas in the theory of differential games. Our presentation will be limited to two player, zero sum, differential games, except for a few words regarding the situations where there are more than two players or where the game is not zero sum. To begin with, recall the game formulation when there are two players, I and II. The actions (stra...

William D. Hamilton famously stated that “human life is a many person game and not just a disjoined collection of two person games”. However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inh...

The slow-coloring game is played by Lister and Painter on a graph G. On each round, Lister marks a nonempty subsetM of the uncolored vertices, scoring ∣M ∣ points. Painter then gives a color to a subset of M that is independent in G. The game ends when all vertices are colored. Painter and Lister want to minimize and maximize the total score, respectively. The best score that each player can gu...

(3) f(x) = (log x/log 2) + 0(1)? 1\Mloser and I asked : Is it true that f(2 11) >_ k+2 for sufficiently large k? Conway and Guy showed that the answer is affirmative (unpublished) . P. Erdös, Problems and results in additive number theory, Colloque, Théorie des Nombres, Bruxelles 1955, p . 137 . 2. Let 1 < a 1< . . . < ak <_ x be a sequence of integers so that all the sums ai,+ . . .+ais, i 1 <...

amino acid (aa) content of six meat and bone meal (mbm) samples was determined by ion-exchange chromatography. true aa digestibility of amino acids were determined of using precise sibbald&apos;s feeding method. metionin and lucien, with averages of 0.35 and 2.29 percent, had the lowest and highest values among essential aa of mbm samples. average content of individual aa, sum of essential and ...

We examine experimentally how humans behave when they play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects’ play was consistent with their Nash equilibrium strategy, while a larger percentage of subjects’ play was more consistent with different mod...

This paper considers an optimization problem of sum-rate in the Gaussian frequency-selective channel. We construct a competitive game with an asymptotically optimal compensation to approximate the optimization problem of sum-rate. Once the game achieves the Nash equilibrium, all users in the game will operate at the optimal sum-rate boundary. The contributions of this paper are twofold. On the ...

We show that the value of a zero-sum Bayesian game is a Lipschitz continuous function of the players’common prior belief, with respect to the total variation metric on beliefs. This is unlike the case of general Bayesian games, where lower semi-continuity of Bayesian equilibrium (BE) payo¤s rests on the "almost uniform" convergence of conditional beliefs. We also show upper semi-continuity (USC...

Game playing is one of the most important areas in AI. Chess is a very popular two-player strategy board game. In the context of AI, chess falls under the category of adversarial games where the opponent tries to reduce your chance of winning as much as possible. Being a classic example of a two-player zero sum game (sum of the utilities of agent and opponent is zero), the game of chess provide...