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Computational Aspects of Equilibria

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Algorithmic Game Theory (SAGT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5814))

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Abstract

Equilibria play a central role in game theory and economics. They characterize the possible outcomes in the interaction of rational, optimizing agents: In a game between rational players that want to optimize their payoffs, the only solutions in which no player has any incentive to switch his strategy are the Nash equilibria. Price equilibria in markets give the prices that allow the market to clear (demand matches supply) while the traders optimize their preferences (utilities). Fundamental theorems of Nash [34] and Arrow-Debreu [2] established the existence of the respective equilibria (under suitable conditions in the market case). The proofs in both cases use a fixed point theorem (relying ultimately on a compactness argument), and are non-constructive, i.e., do not yield an algorithm for constructing an equilibrium. We would clearly like to compute these predicted outcomes. This has led to extensive research since the 60’s in the game theory and mathematical economics literature, with the development of several methods for computation of equilibria, and more generally fixed points. More recently, equilibria problems have been studied intensively in the computer science community, from the point of view of modern computation theory. While we still do not know definitely whether equilibria can be computed in general efficiently or not, these investigations have led to a better understanding of the computational complexity of equilibria, the various issues involved, and the relationship with other open problems in computation. In this talk we will discuss some of these aspects and our current understanding of the relevant problems. We outline below the main points and explain some of the related issues.

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Authors and Affiliations

  1. Department of Computer Science, Columbia University,  

    Mihalis Yannakakis

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  1. Mihalis Yannakakis
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Editors and Affiliations

  1. Department of Computer Science, University of Cyprus, 75 Kallipoleos Str., P.O. Box 20537, CY-1678, Nicosia, Cyprus

    Marios Mavronicolas

  2. Department of Computer Science and Engineering, European University Cyprus, 6 Diogenes Str., CY-1516, Nicosia, Cyprus

    Vicky G. Papadopoulou

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Yannakakis, M. (2009). Computational Aspects of Equilibria. In: Mavronicolas, M., Papadopoulou, V.G. (eds) Algorithmic Game Theory. SAGT 2009. Lecture Notes in Computer Science, vol 5814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04645-2_2

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  • DOI: https://doi.org/10.1007/978-3-642-04645-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04644-5

  • Online ISBN: 978-3-642-04645-2

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