Agent Failures in Totally Balanced Games and Convex Games

  • Yoram Bachrach
  • Ian Kash
  • Nisarg Shah
Conference paper

DOI: 10.1007/978-3-642-35311-6_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)
Cite this paper as:
Bachrach Y., Kash I., Shah N. (2012) Agent Failures in Totally Balanced Games and Convex Games. In: Goldberg P.W. (eds) Internet and Network Economics. WINE 2012. Lecture Notes in Computer Science, vol 7695. Springer, Berlin, Heidelberg

Abstract

We examine the impact of independent agents failures on the solutions of cooperative games, focusing on totally balanced games and the more specific subclass of convex games. We follow the reliability extension model, recently proposed in [1] and show that a (approximately) totally balanced (or convex) game remains (approximately) totally balanced (or convex) when independent agent failures are introduced or when the failure probabilities increase. One implication of these results is that any reliability extension of a totally balanced game has a non-empty core. We propose an algorithm to compute such a core imputation with high probability. We conclude by outlining the effect of failures on non-emptiness of the core in cooperative games, especially in totally balanced games and simple games, thereby extending observations in [1].

Keywords

Totally Balanced Games Convex Games Agent Failures Cooperative Game Theory 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yoram Bachrach
    • 1
  • Ian Kash
    • 1
  • Nisarg Shah
    • 2
  1. 1.Microsoft Research LtdCambridgeUK
  2. 2.Computer Science DepartmentCarnegie Mellon UniversityUSA

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