Ranking asymmetric auctions

Gavious, Arieh; Minchuk, Yizhaq

doi:10.1007/s00182-013-0383-9

Cited by 13 publications

(8 citation statements)

References 25 publications

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“…However, the opposite holds for large values of K. Using a different approximation technique, Fibich and Gavish [6] provided an example in which it is also the case that s falls below the common mean. This observation is also consistent with Gavious and Minchuk [10] who noted that if both bidders' distributions are "almost" uniform, small asymmetries between them will tend to suppress s. In comparison, if the two bidders are symmetric, then it is well known that s will equal the mean of the distribution.…”

Section: Proof See the Appendixsupporting

confidence: 87%

“…In figure 2, we plot the absolute differences in the approximate equilibrium inverse-bid functionsD 1,2 (s) when the order of the approximating polynomials K increases from three to five to twenty-five. 10 We denote by s K the approximated high bid in the case when an order K polynomial is used to approximate the equilibrium inverse-bid functions. When K equals three, the absolute difference in the approximate equilibrium inverse-bid functions and the theoretical absolute difference coincide exactly.…”

Section: Proof See the Appendixmentioning

confidence: 99%

See 1 more Smart Citation

Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions

2012

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In models of first-price auctions, when bidders are ex ante heterogenous, deriving explicit equilibrium bid functions is typically impossible, so numerical methods (such as polynomial approximations) are often employed to find approximate solutions. Recent theoretical research concerning asymmetric auctions has determined conditions under which equilibrium bid functions must cross. When equilibrium bid functions are approximated by low-order polynomials, however, such polynomials may not be flexible enough to satisfy the qualitative predictions of the theory. Plotting the relative expected pay-offs of bidders is a quick, informative way to decide whether the approximate solutions are consistent with theory.

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Section: Proof See the Appendixsupporting

confidence: 87%

Section: Proof See the Appendixmentioning

confidence: 99%

Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions

2012

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“…For some particular distributions, revenue in a FPA is higher than in a SPA (see, e.g., Maskin and Riley, 2000). This ranking does not always hold, as Gavious and Minchuk (2014) show that revenue in a SPA can be higher than that in a FPA under asymmetry.…”

Section: Revenue Comparisonmentioning

confidence: 93%

“…Nevertheless, even for two bidders with asymmetrically drawn valuations from the same support, no general closed-form solution is known. The first-price and second-price auctions no longer yield the same revenue under asymmetric value distributions, with the revenue ranking depending on the asymmetry of the value distributions (Maskin and Riley, 2000;Cantillon, 2008;Gavious and Minchuk, 2014).…”

Section: Introductionmentioning

confidence: 99%

Asymmetric budget constraints in a first-price auction

Bobkova

2020

Journal of Economic Theory

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I solve a first-price auction for two bidders with asymmetric budget distributions and known valuations for one object. I show that in any equilibrium, the expected utilities and bid distributions of both bidders are unique. If budgets are sufficiently low, the bidders will bid their entire budget in any equilibrium. For sufficiently high budgets, mass points in the equilibrium strategies arise. A less restrictive budget distribution could make both bidders strictly worse off. If the budget distribution of a bidder is dominated by the budget distribution of his opponent in the reverse-hazardrate order, the weaker bidder will bid more aggressively than his stronger opponent. In contrast to existing results for symmetric budget distributions, with asymmetric budget distributions, a second-price auction can yield a strictly higher revenue than a first-price auction. Under an additional assumption, I derive the unique equilibrium utilities and bid distributions of both bidders in an all-pay auction.

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“…In the binary setting with equal low values, Maskin and Riley (1983) show that the SPA is better than the FPA if the bidders' high values are approximately equal, or if the probabilities of a high value are approximately equal. Gavious and Minchuk (2013) study environments such that the valuations' distributions are close to the uniform distribution and in this framework they identify cases in which the SPA dominates the FPA.…”

Section: Related Literaturementioning

confidence: 98%

Revenue Comparison in Asymmetric Auctions with Discrete Valuations

Doni

Menicucci

2013

The B.E. Journal of Theoretical Economics

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We consider an asymmetric auction setting with two bidders such that the valuation of each bidder has a binary support. First, we characterize the unique equilibrium outcome in the first price auction for any values of parameters. Then we compare the first price auction with the second price auction in terms of expected revenue. Under the assumption that the probabilities of low values are the same for the two bidders, we obtain two main results: (i) the second price auction yields a higher revenue unless the distribution of a bidder's valuation first-order stochastically dominates the distribution of the other bidder's valuation "in a strong sense" and (ii) introducing reserve prices implies that the first price auction is never superior to the second price auction. In addition, in some cases, the revenue in the first price auction decreases when all the valuations increase.

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Ranking asymmetric auctions

Cited by 13 publications

References 25 publications

Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions

Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions

Asymmetric budget constraints in a first-price auction

Revenue Comparison in Asymmetric Auctions with Discrete Valuations

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