Equilibrium Strategy and Population-Size Effects in Lowest Unique Bid Auctions

Simone Pigolotti; Per Johan Sebastian Bernhardsson; Jeppe Søgaard Juul; Gorm Galster; Pierpaolo Vivo

Equilibrium Strategy and Population-Size Effects in Lowest Unique Bid Auctions

Simone Pigolotti, Per Johan Sebastian Bernhardsson, Jeppe Søgaard Juul, Gorm Galster, Pierpaolo Vivo

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12 Citationer (Scopus)

Abstract

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.

Originalsprog	Engelsk
Tidsskrift	Physical Review Letters
Vol/bind	108
Udgave nummer	8
Sider (fra-til)	088701
Antal sider	5
ISSN	0031-9007
Status	Udgivet - 22 feb. 2012

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http://link.aps.org/doi/10.1103/PhysRevLett.108.088701

Citationsformater

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title = "Equilibrium Strategy and Population-Size Effects in Lowest Unique Bid Auctions",

abstract = "In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.",

author = "Simone Pigolotti and Bernhardsson, {Per Johan Sebastian} and Juul, {Jeppe S{\o}gaard} and Gorm Galster and Pierpaolo Vivo",

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T1 - Equilibrium Strategy and Population-Size Effects in Lowest Unique Bid Auctions

AU - Pigolotti, Simone

AU - Bernhardsson, Per Johan Sebastian

AU - Juul, Jeppe Søgaard

AU - Galster, Gorm

AU - Vivo, Pierpaolo

PY - 2012/2/22

Y1 - 2012/2/22

N2 - In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.

AB - In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.

M3 - Journal article

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VL - 108

SP - 088701

JO - Physical Review Letters

JF - Physical Review Letters

IS - 8

ER -

Equilibrium Strategy and Population-Size Effects in Lowest Unique Bid Auctions

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