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_ k+2 for sufficiently large k? Conway and Guy showed that the answer is affirmative (unpublished) .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 <...

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 ...

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...

In the ultimatum game, two players are asked to split a certain sum of money. The proposer has to make an offer. If the responder accepts the offer, the money will be shared accordingly. If the responder rejects the offer, both players receive nothing. The rational solution is for the proposer to offer the smallest possible share, and for the responder to accept it. Human players, in contrast, ...

We have benefited from the helpful comments of Dan Kovenock, Wolfgang Leininger, and participants in the presentation at the CESifo Summer Institute Workshop on Advances in the Theory of Contests and its Applications. Brian Roberson Miami University, Department of Economics, Richard T. Farmer School of Business, 208 Laws Hall, Oxford, OH 45056-3628 USA t: 513-529-0416, f: 513-529-8047, E-mail: ...

This note addresses scenarios of buyers purchasing rate along paths in a nonhierarchical communication network. A sum bid game is proposed in which each buyer submits a bid, also equal to a payment, and the network allocates rate in a weighted proportionally fair fashion, with the bids as the weights. This is in contrast to an itemized bid game, considered recently by Johari and Tsitsiklis, und...

While the idea of a matching pennies game may seem contrived, it is merely the simplest example of a general class of zero-sum games, where the total payoff of the players is constant regardless of the outcome. Consequently gains for one player can only come from losses of the other. For this reason, zero-sum games will rarely have a pure strategy Nash equilibrium. Examples would be chess, or m...

This chapter provides a comprehensive review of the domain of game theory based physical layer security in wireless communications. By exploiting the wireless channel characteristic and secure cooperation of nodes, physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without relying on higher-layer encry...

It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence a...