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Worstcase equilibria
 IN PROCEEDINGS OF THE 16TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 1999
"... In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a ver ..."
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Cited by 631 (19 self)
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In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.
A Network Game with Attacker and Protector Entities
 Proceedings of the 16th Annual International Symposium on Algorithms and Computation
, 2005
"... Consider an information network with harmful procedures called attackers (e.g., viruses); each attacker uses a probability distribution to choose a node of the network to damage. Opponent to the attackers is the system protector scanning and cleaning from attackers some part of the network (e.g., an ..."
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Cited by 9 (6 self)
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Consider an information network with harmful procedures called attackers (e.g., viruses); each attacker uses a probability distribution to choose a node of the network to damage. Opponent to the attackers is the system protector scanning and cleaning from attackers some part of the network (e.g., an edge or a path), which it chooses independently using another probability distribution. Each attacker wishes to maximize the probability of escaping its cleaning by the system protector; towards a conflicting objective, the system protector aims at maximizing the expected number of cleaned attackers. We model this network scenario as a noncooperative strategic game on graphs. We focus on the special case where the protector chooses a single edge. We are interested in the associated Nash equilibria, where no network entity can unilaterally improve its local objective. We obtain the following results: • No instance of the game possesses a pure Nash equilibrium. • Every mixed Nash equilibrium enjoys a graphtheoretic structure, which enables a (typically exponential) algorithm to compute it.
On the Complexity of Equilibria \Lambda
"... ABSTRACT We prove complexity, approximability, and inapproximability results for the problem of finding an exchange equilibrium in markets with indivisible (integer) goods, most notably a polynomialtime algorithm that approximates the market equilibrium arbitrarily closely when the number of goods ..."
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ABSTRACT We prove complexity, approximability, and inapproximability results for the problem of finding an exchange equilibrium in markets with indivisible (integer) goods, most notably a polynomialtime algorithm that approximates the market equilibrium arbitrarily closely when the number of goods is bounded and the utilities are linear. We also show a communication complexity lower bound, implying that the ideal informational economy of a market with unique individual optima is unattainable in general. 1. INTRODUCTION The existence of equilibria in markets, a longstanding conjecture proved rigorously in the 1950's [1], is one of the most fundamental results in Mathematical Economics. Imagine n agents in a market with m kinds of goods (or commodities), each agent with an initial allocation, or endowment, ei 2!