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Approximate Competitive Equilibrium with Generic Budget

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Algorithmic Game Theory (SAGT 2021)

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Abstract

We study the existence of approximate competitive equilibrium in the Fisher market with generic budgets. We show that for any number of buyers and any number of goods, when the preferences are identical and budgets are generic, a 2 approximation of competitive equilibrium (2-\(\mathsf {CE}\)) always exists. By 2-\(\mathsf {CE}\) we mean that every buyer receives a bundle with a value at least half of the value of her most desirable bundle that fits within her budget, and the market clears. We also present a polynomial time algorithm to obtain a 2-\(\mathsf {CE}\).

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Notes

  1. 1.

    An allocation is envy-free if each agent prefers her share to other agent’s share.

  2. 2.

    Note that our greedy algorithm might leave some of the goods un-allocated.

  3. 3.

    allocation that maximizes the utility product of the agents.

  4. 4.

    For the missing proofs, we refer to the complete version of the paper.

  5. 5.

    Here we need to extend Definition 9 for \(i=n\): there is a cut on buyer n if she is not satisfied.

  6. 6.

    Note that Lemma 8 holds regardless of the method by which we update the bundles.

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Ghiasi, A., Seddighin, M. (2021). Approximate Competitive Equilibrium with Generic Budget. In: Caragiannis, I., Hansen, K.A. (eds) Algorithmic Game Theory. SAGT 2021. Lecture Notes in Computer Science(), vol 12885. Springer, Cham. https://doi.org/10.1007/978-3-030-85947-3_16

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  • DOI: https://doi.org/10.1007/978-3-030-85947-3_16

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