The Adjusted Winner Procedure: Characterizations and Equilibria

Aziz, Haris; Brânzei, Simina; Filos-Ratsikas, Aris; Frederiksen, Søren Kristoffer Stiil

The Adjusted Winner Procedure: Characterizations and Equilibria

Haris Aziz, Simina Brânzei, Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen

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Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence. Main Track. Pages 454-459.

Abstract

The Adjusted Winner procedure is an important mechanism proposed by Brams and Taylor for fairly allocating goods between two agents. It has been used in practice for divorce settlements and analyzing political disputes. Assuming truthful declaration of the valuations, it computes an allocation that is envy-free, equitable and Pareto optimal. We show that Adjusted Winner admits several elegant characterizations, which further shed light on the outcomes reached with strategic agents. We find that the procedure may not admit pure Nash equilibria in either the discrete or continuous variants, but is guaranteed to have Îµ-Nash equilibria for each Îµ > 0. Moreover, under informed tie-breaking, exact pure Nash equilibria always exist, are Pareto optimal, and their social welfare is at least 3/4 of the optimal.

Haris Aziz, Simina Brânzei, Aris Filos-Ratsikas, and Søren Kristoffer Stiil Frederiksen. 2015. The Adjusted Winner Procedure: Characterizations and Equilibria. In Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-15. IJCAI, 454–459. https://ijcai.org/proceedings/2015/70

@inproceedings{ijcai2015p70,
  title     = {The Adjusted Winner Procedure: Characterizations and Equilibria},
  author    = {Aziz, Haris and Brânzei, Simina and Filos-Ratsikas, Aris and Frederiksen, Søren Kristoffer Stiil},
  booktitle = {Proceedings of the Twenty-Fourth International Joint Conference on
               Artificial Intelligence, {IJCAI-15}},
  publisher = {International Joint Conferences on Artificial Intelligence},
  editor    = {Qiang Yang and Michael Wooldridge},
  pages     = {454--459},
  year      = {2015},
  month     = {7},
  note      = {Main Track},
  url       = {https://ijcai.org/proceedings/2015/70},
}

TY  - CPAPER
TI  - The Adjusted Winner Procedure: Characterizations and Equilibria
AU  - Aziz, Haris
AU  - Brânzei, Simina
AU  - Filos-Ratsikas, Aris
AU  - Frederiksen, Søren Kristoffer Stiil
T2  - Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-15
PB  - International Joint Conferences on Artificial Intelligence
PY  - 2015
SP  - 454
EP  - 459
UR  - https://ijcai.org/proceedings/2015/70
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