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Approximating Mixed Nash Equilibria using Smooth Fictitious Play in Simultaneous Auctions

Approximating Mixed Nash Equilibria using Smooth Fictitious Play in Simultaneous Auctions
Approximating Mixed Nash Equilibria using Smooth Fictitious Play in Simultaneous Auctions
We investigate equilibrium strategies for bidding agents that participate in multiple, simultaneous second-price auctions with perfect substitutes. For this setting, previous research has shown that it is a best response for a bidder to participate in as many such auctions as there are available, provided that other bidders only participate in a single auction. In contrast, in this paper we consider equilibrium behaviour where all bidders participate in multiple auctions. For this new setting we consider mixed-strategy Nash equilibria where bidders can bid high in one auction and low in all others. By discretising the bid space, we are able to use smooth fictitious play to compute approximate solutions. Specifically, we find that the results do indeed converge to $\epsilon$-Nash mixed equilibria and, therefore, we are able to locate equilibrium strategies in such complex games where no known solutions previously existed.
1577-1580
Gerding, Enrico
d9e92ee5-1a8c-4467-a689-8363e7743362
Rabinovich, Zinovi
573422bf-523d-466b-a047-7a92917102e7
Byde, Andrew
cdfddb83-7ad2-4274-a048-343b1c0783d8
Elkind, Edith
7a013473-5cd0-4e41-b907-66b30a04a400
Jennings, N. R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Gerding, Enrico
d9e92ee5-1a8c-4467-a689-8363e7743362
Rabinovich, Zinovi
573422bf-523d-466b-a047-7a92917102e7
Byde, Andrew
cdfddb83-7ad2-4274-a048-343b1c0783d8
Elkind, Edith
7a013473-5cd0-4e41-b907-66b30a04a400
Jennings, N. R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30

Gerding, Enrico, Rabinovich, Zinovi, Byde, Andrew, Elkind, Edith and Jennings, N. R. (2008) Approximating Mixed Nash Equilibria using Smooth Fictitious Play in Simultaneous Auctions. The 7th International Conference on Autonomous Agents and Multiagent Systems, Portugal. 12 - 16 May 2008. pp. 1577-1580 .

Record type: Conference or Workshop Item (Poster)

Abstract

We investigate equilibrium strategies for bidding agents that participate in multiple, simultaneous second-price auctions with perfect substitutes. For this setting, previous research has shown that it is a best response for a bidder to participate in as many such auctions as there are available, provided that other bidders only participate in a single auction. In contrast, in this paper we consider equilibrium behaviour where all bidders participate in multiple auctions. For this new setting we consider mixed-strategy Nash equilibria where bidders can bid high in one auction and low in all others. By discretising the bid space, we are able to use smooth fictitious play to compute approximate solutions. Specifically, we find that the results do indeed converge to $\epsilon$-Nash mixed equilibria and, therefore, we are able to locate equilibrium strategies in such complex games where no known solutions previously existed.

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More information

Published date: May 2008
Additional Information: Event Dates: May 12-16
Venue - Dates: The 7th International Conference on Autonomous Agents and Multiagent Systems, Portugal, 2008-05-12 - 2008-05-16
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 265133
URI: http://eprints.soton.ac.uk/id/eprint/265133
PURE UUID: 4feb3f50-be00-4837-b6c8-3de9c9e23449
ORCID for Enrico Gerding: ORCID iD orcid.org/0000-0001-7200-552X

Catalogue record

Date deposited: 04 Feb 2008 10:27
Last modified: 20 Jul 2019 00:56

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Contributors

Author: Enrico Gerding ORCID iD
Author: Zinovi Rabinovich
Author: Andrew Byde
Author: Edith Elkind
Author: N. R. Jennings

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