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Equilibrium strategy and population-size effects in lowest unique bid auctions
Simone Pigolotti1, Sebastian Bernhardsson, Jeppe Juul
1Niels Bohr Institute, Copenhagen, Denmark.
Physical Review Letters
|April 3, 2012
Summary
In lowest unique bid auctions, the optimal strategy distribution differs for small and large player groups. For large populations, adapting to find the best bid becomes challenging, questioning collective game adaptation.
Area of Science:
- Game Theory
- Behavioral Economics
- Statistical Mechanics
Background:
- Lowest unique bid auctions incentivize strategic bidding.
- Understanding equilibrium strategies in such games is complex.
- Previous models often simplify population dynamics.
Purpose of the Study:
- To derive an analytical expression for equilibrium strategy distribution in lowest unique bid auctions.
- To investigate how this distribution changes with the number of players (N).
- To compare theoretical predictions with real-world internet auction data.
Main Methods:
- Employed a grand canonical approach from statistical mechanics.
- Derived an analytical expression for the equilibrium strategy distribution.
- Analyzed the solution's properties as a function of mean player number (N).
- Compared theoretical results with a large dataset of internet auctions.
Main Results:
- The theoretical model shows striking accuracy for small population sizes (N).
- For larger N, a qualitatively different strategy distribution emerges.
- This indicates the presence of two distinct regimes: one where adaptation is feasible, and one where it is not.
Conclusions:
- The study reveals a phase transition in strategy adaptation based on population size.
- For large populations, optimal strategy adaptation in this collective game becomes significantly more difficult.
- Results challenge the assumption that large groups can effectively adapt and find optimal strategies in collective decision-making scenarios.
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