Simultaneous auctions with budgets: Equilibrium existence and characterization
Games and Economic Behavior, 2021, vol. 126, issue C, 75-93
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)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:126:y:2021:i:c:p:75-93
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