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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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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.
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!