The Affiliation Effect in First‐Price Auctions

We study the monotonicity of the equilibrium bid with respect to the number of bidders n in affiliated private‐value models of first‐price sealed‐bid auctions and prove the existence of a large class of such models in which the equilibrium bid function is not increasing in n. We moreover decompose the effect of a change in n on the bid level into a competition effect and an affiliation effect. The latter suggests to the winner of the auction that competition is less intense than she had thought before the auction. Since the affiliation effect can occur in both private‐ and common‐value models, a negative relationship between the bid level and n does not allow one to distinguish between the two models and is also not necessarily (only) due to bidders taking account of the winner's curse.     

Common Value Auctions with Insider Information

Bidding is studied in first-price common value auctions where an insider is better informed than other bidders (outsiders) about the value of the item. With inexperienced bidders, having an insider does not materially reduce the severity of the winner's curse compared to auctions with a symmetric information structure (SIS). In contrast, super-experienced bidders, who have largely overcome the winner's curse, satisfy the comparative static predictions of equilibrium bidding theory: (i) average seller's revenue is larger with an insider than in SIS auctions, (ii) insiders make substantially greater profits, conditional on winning, than outsiders, and (iii) insiders increase their bids in response to more rivals. Further, changes in insiders' bids are consistent with directional learning theory (Selten and Buchta (1994)).     

Cursed Equilibrium

There is evidence that people do not fully take into account how other people's actions depend on these other people's information. This paper defines and applies a new equilibrium concept in games with private information, cursed equilibrium, which assumes that each player correctly predicts the distribution of other players' actions, but underestimates the degree to which these actions are correlated with other players' information. We apply the concept to common‐values auctions, where cursed equilibrium captures the widely observed phenomenon of the winner's curse, and to bilateral trade, where cursedness predicts trade in adverse‐selections settings for which conventional analysis predicts no trade. We also apply cursed equilibrium to voting and signalling models. We test a single‐parameter variant of our model that embeds Bayesian Nash equilibrium as a special case and find that parameter values that correspond to cursedness fit a broad range of experimental datasets better than the parameter value that corresponds to Bayesian Nash equilibrium.     

Can Relaxation of Beliefs Rationalize the Winner's Curse?: An Experimental Study

We use a second‐price common‐value auction, called the maximal game, to experimentally study whether the winner's curse (WC) can be explained by models which retain best‐response behavior but allow for inconsistent beliefs. We compare behavior in a regular version of the maximal game, where the WC can be explained by inconsistent beliefs, to behavior in versions where such explanations are less plausible. We find little evidence of differences in behavior. Overall, our study casts a serious doubt on theories that posit the WC is driven by beliefs.     

在线拍卖中的“托”出价研究

本文分析了独立的私人估价环境下最优保留价格与竞买人数之间的关系,纠正了最优保留价格与竞买人数无关的传统观点.在此基础上,讨论了卖者可能递交"托"出价的条件以及拍卖中只剩下一个竞买人时卖者的最优"托"出价.     

The Effect of Timing on Jump Bidding in Ascending Auctions

We investigate the role of timing in ascending auctions under the premise that time is a valuable resource. Traditional models of the English auction ignore timing issues by assuming that the auction occurs instantaneously. However, when auctions are slow, as Internet auctions used for procurement often are, there are significant opportunity or monitoring costs to bidders, and the choice of the size of the jump bid becomes a strategic decision. We study the choice in the experimental laboratory by systematically varying the opportunity costs associated with fast bidding. When time is more valuable bidders respond by choosing larger jump bids. Surprisingly, the economic performance of the auction is not significantly affected. We develop a simple model of ascending auctions with impatient bidders that provides insights into the effect jump bids have on auction performance.     

Level‐k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private‐Value Auctions?

This paper proposes a structural nonequilibrium model of initial responses to incomplete‐information games based on “level‐k” thinking, which describes behavior in many experiments with complete‐information games. We derive the model's implications in first‐ and second‐price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level‐k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common‐value auctions and overbidding in those independent‐private‐value auctions without the uniform value distributions used in most experiments.     

Behavior in Multi‐Unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions

We experimentally investigate the sensitivity of bidders demanding multiple units of a homogeneous commodity to the demand reduction incentives inherent in uniform price auctions. There is substantial demand reduction in both sealed bid and ascending price clock auctions with feedback regarding rivals' drop‐out prices. Although both auctions have the same normal form representation, bidding is much closer to equilibrium in the ascending price auctions. We explore the behavioral process underlying these differences along with dynamic Vickrey auctions designed to eliminate the inefficiencies resulting from demand reduction in the uniform price auctions.     

Nonparametric Identification of Risk Aversion in First‐Price Auctions Under Exclusion Restrictions

This paper studies the nonparametric identification of the first‐price auction model with risk averse bidders within the private value paradigm. First, we show that the benchmark model is nonindentified from observed bids. We also derive the restrictions imposed by the model on observables and show that these restrictions are weak. Second, we establish the nonparametric identification of the bidders' utility function under exclusion restrictions. Our primary exclusion restriction takes the form of an exogenous bidders' participation, leading to a latent distribution of private values that is independent of the number of bidders. The key idea is to exploit the property that the bid distribution varies with the number of bidders while the private value distribution does not. We then extend these results to endogenous bidders' participation when the exclusion restriction takes the form of instruments that do not affect the bidders' private value distribution. Though derived for a benchmark model, our results extend to more general cases such as a binding reserve price, affiliated private values, and asymmetric bidders. Last, possible estimation methods are proposed.     

风险规避与一级密封拍卖的有限腐败——模型及实验

在风险中性假设的有限腐败一级密封拍卖模型基础上,构建容纳风险规避的有限腐败一级密封拍卖的一般模型,依据模型进行基于计算机局域网的多组并行的实验室实验;实验包含一个作为基准的无腐败一级密封拍卖和三种有限腐败程度的一级密封拍卖,并设计两种收益计算方式和保留价设置,实验研究对比两种模型的预测力,考察存在有限腐败的一级密封拍卖的效率和竞标人行为。研究结果表明,有限腐败机制不影响一级密封拍卖的效率,成交价格方面有腐败与无腐败的拍卖之间没有显著差异;腐败者的期望收益有所上升,高报价更为激进而低报价更为保守;腐败者是异质的,其报价行为具有禀赋依赖性;非腐败者的行为和卖者收益没有显著变化。实验结果表明包含腐败者风险规避特征的模型预测力更好。     

主体风险规避情形下多属性逆向拍卖利润分配研究

本文针对采供双方风险规避的多属性逆向拍卖环境下的利润分配与采供关系建立问题,构建了非合作与合作博弈模型,分析了主体风险态度对利润分配结果的影响,得出建立和发展合作关系的条件,并确定了利润最优分配比例。结合仿真实验得出：1）采供双方非合作时,影响双方利润的因素：供应商成本参数,参与拍卖的供应商数量等。2）双方合作时,对利润的分配比例,受双方风险规避系数的影响;采购商提供给供应商的补贴受双方风险规避系数和讨价还价能力的影响。3）双方建立合作的基本条件需同时满足集体理性和个体理性,而长期合作的必要条件是双方效用最大化前提下的确定最优分配比例。     

关键词拍卖中基于广义第一价格的投标价格决策分析

在关键词拍卖中,由于广告商不能保证对关键词的估价是最优投标价格,因此如何选取最优的关键词投标价格一直是广告商急于解决的问题。基于与Friedman投标模型假设条件等价的关键词拍卖投标假设条件,计算了各个关键词广告位置的胜标概率,并在广义第一价格拍卖机制下建立了关键词投标价格决策模型。该模型可以使广告商选取最优的关键词投标价格。最后通过仿真验证了该模型的有效性。     

Optimal Reserve Prices in Name‐Your‐Own‐Price Auctions with Bidding and Channel Options

Few papers have explored the optimal reserve prices in the name‐your‐own‐price (NYOP) channel with bidding options in a multiple channel environment. In this paper, we investigate a double‐bid business model in which the consumers can bid twice in the NYOP channel, and compare it with the single‐bid case. We also study the impact of adding a retailer‐own list‐price channel on the optimal reserve prices. This paper focuses on achieving some basic understanding on the potential gain of adding a second bid option to a single‐bid system and on the potential benefits of adding a list‐price channel by the NYOP retailer. We show that a double‐bid scenario can outperform a single‐bid scenario in both single‐channel and dual‐channel situations. The optimal reserve price in the double‐bid scenario is no less than that in the single‐bid case. Furthermore, the addition of a retailer‐own list‐price channel could push up the reserve prices in both single‐bid and double‐bid scenarios.     

On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games

We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure‐strategy equilibria in Bayesian games. We allow action spaces to be compact locally complete metric semilattices and type spaces to be partially ordered probability spaces. Our proof is based on contractibility rather than convexity of best‐reply sets. Several examples illustrate the scope of the result, including new applications to multi‐unit auctions with risk‐averse bidders.