Evolutionary stability of first price auctions

Louge F, Riedel F (2010) Working Papers. Institute of Mathematical Economics; 435.
Bielefeld: Universität Bielefeld.

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Abstract
This paper studies the evolutionary stability of the unique Nash equilibrium of a first price sealed bid auction. It is shown that the Nash equilibrium is not asymptotically stable under payoff monotonic dynamics for arbitrary initial populations. In contrast, when the initial population includes a continuum of strategies around the equilibrium, the replicator dynamic does converge to the Nash equilibrium. Simulations are presented for the replicator and Brown-von Neumann-Nash dynamics. They suggest that the convergence for the replicator dynamic is slow compared to the Brown-von Neumann-Nash dynamics.
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Louge F, Riedel F. Evolutionary stability of first price auctions. Working Papers. Institute of Mathematical Economics. Vol 435. Bielefeld: Universität Bielefeld; 2010.
Louge, F., & Riedel, F. (2010). Evolutionary stability of first price auctions (Working Papers. Institute of Mathematical Economics, 435). Bielefeld: Universität Bielefeld.
Louge, F., and Riedel, F. (2010). Evolutionary stability of first price auctions. Working Papers. Institute of Mathematical Economics, 435, Bielefeld: Universität Bielefeld.
Louge, F., & Riedel, F., 2010. Evolutionary stability of first price auctions, Working Papers. Institute of Mathematical Economics, no.435, Bielefeld: Universität Bielefeld.
F. Louge and F. Riedel, Evolutionary stability of first price auctions, Working Papers. Institute of Mathematical Economics, vol. 435, Bielefeld: Universität Bielefeld, 2010.
Louge, F., Riedel, F.: Evolutionary stability of first price auctions. Working Papers. Institute of Mathematical Economics, 435. Universität Bielefeld, Bielefeld (2010).
Louge, Fernando, and Riedel, Frank. Evolutionary stability of first price auctions. Bielefeld: Universität Bielefeld, 2010. Working Papers. Institute of Mathematical Economics. 435.
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