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Generalised Fictitious Play for a Continuum of Anonymous Players

Generalised Fictitious Play for a Continuum of Anonymous Players
Generalised Fictitious Play for a Continuum of Anonymous Players
Recently, efficient approximation algorithms for finding Nash equilibria have been developed for the interesting class of {\it anonymous games}, where a player's utility does not depend on the identity of its opponents. In this paper, we tackle the problem of computing equilibria in such games with {\it continuous player types}, extending the framework to encompass settings with imperfect information. In particular, given the existence result for pure Bayes-Nash equilibiria in these games, we generalise the {\it fictitious play algorithm} by developing a novel procedure for finding a best response strategy, which is specifically designed to deal with continuous and, therefore, infinite type spaces. We then combine the best response computation with the general fictitious play structure to obtain an equilibrium. To illustrate the power of this approach, we apply our algorithm to the domain of simultaneous auctions with continuous private values and discrete bids, in which the algorithm shows quick convergence.
245-250
Rabinovich, Zinovi
573422bf-523d-466b-a047-7a92917102e7
Gerding, Enrico
d9e92ee5-1a8c-4467-a689-8363e7743362
Polukarov, Maria
bd2f0623-9e8a-465f-8b29-851387a64740
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Rabinovich, Zinovi
573422bf-523d-466b-a047-7a92917102e7
Gerding, Enrico
d9e92ee5-1a8c-4467-a689-8363e7743362
Polukarov, Maria
bd2f0623-9e8a-465f-8b29-851387a64740
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30

Rabinovich, Zinovi, Gerding, Enrico, Polukarov, Maria and Jennings, Nicholas R. (2009) Generalised Fictitious Play for a Continuum of Anonymous Players. Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI), United States. pp. 245-250 .

Record type: Conference or Workshop Item (Paper)

Abstract

Recently, efficient approximation algorithms for finding Nash equilibria have been developed for the interesting class of {\it anonymous games}, where a player's utility does not depend on the identity of its opponents. In this paper, we tackle the problem of computing equilibria in such games with {\it continuous player types}, extending the framework to encompass settings with imperfect information. In particular, given the existence result for pure Bayes-Nash equilibiria in these games, we generalise the {\it fictitious play algorithm} by developing a novel procedure for finding a best response strategy, which is specifically designed to deal with continuous and, therefore, infinite type spaces. We then combine the best response computation with the general fictitious play structure to obtain an equilibrium. To illustrate the power of this approach, we apply our algorithm to the domain of simultaneous auctions with continuous private values and discrete bids, in which the algorithm shows quick convergence.

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Published date: July 2009
Additional Information: to appear
Venue - Dates: Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI), United States, 2009-07-01
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 267271
URI: http://eprints.soton.ac.uk/id/eprint/267271
PURE UUID: 1638ce08-84c1-4040-ad1b-c67d03fe9055
ORCID for Enrico Gerding: ORCID iD orcid.org/0000-0001-7200-552X

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Date deposited: 10 Apr 2009 12:31
Last modified: 10 Dec 2019 01:44

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Contributors

Author: Zinovi Rabinovich
Author: Enrico Gerding ORCID iD
Author: Maria Polukarov
Author: Nicholas R. Jennings

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