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Simultaneous auctions with budgets: Equilibrium existence and characterization

Gagan Ghosh

Games and Economic Behavior, 2021, vol. 126, issue C, 75-93

Abstract: We study the sale of two units of a good through simultaneous sealed bid first-price auctions to bidders who have private types and multi-unit demand. Bidders are differentiated based on their valuations and budgets. Under a parametric restriction, we show that this auction game is better-reply secure and thus possesses a Nash equilibrium. In equilibrium, bidders expend their budgets. The equilibrium strategies are essentially pure in the sense that each bidder-type has a unique split (up to a permutation) of her budget between the two auctions. In equilibrium, there always exist bidder-types who submit unequal bids in equilibrium even though they have the same valuations for the units. In addition, the equilibrium is monotone in valuations and budgets: bidders with higher valuations (lower budgets) prefer more unequal splits of their budgets than bidders with lower valuations (higher budgets) and the same budget (valuation).

Keywords: Simultaneous auctions; Private budgets; Multi-dimensional types; Better-reply security (search for similar items in EconPapers)
JEL-codes: C72 D44 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.geb.2020.12.002

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