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Given this, our main contribution is a poly-time approximation algorithm that achieves stability without sacrificing too much welfare. Our Model. Given an instance (N , P, (vk )k∈P ) with N agents (N ) and m projects, a solution is an allocation S = (S1 , . . , Sm ) of agents to projects along with a vector of payments (¯ p)i∈N . With unlimited copies of a project, core stability refers to the inability of any set of agents to form a group on their own and obtain more value than the payments they receive.

Sekar Effect of Monopolies on the Efficiency of Equilibrium In this paper, we are interested in settings where approximately efficient outcomes are reached despite the presence of self-interested sellers with monopolizing power. While for general functions λ(x) obeying the MPE condition, the efficiency can be exponentially bad, we show that for many natural classes of functions it is much better, even in the presence of monopolies. , when M = 0, the efficiency is 1. This result is only a starting point for us since it is the addition of monopolies that leads to interesting behavior.

There is a unique non-trivial equilibrium that satisfies Local Dominance. (or) 2. All non-trivial equilibria that satisfy Local Dominance maximize welfare. Moreover, we can compute this equilibrium efficiently. For the purposes of studying efficiency, the above theorem provides a useful baseline: either all equilibria are fully efficient or it suffices to bound the efficiency of the unique equilibrium that satisfies Corollary 5 (which we do in Sect. 4). ), “computing” a solution means getting within arbitrary precision of the desired solution; the exact solution could be irrational.

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23 Internet Myths Exposed by Darrell Jackson

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