In real life auctions, a widely observed phenomenon is the winner's curse -- the winner's high bid implies that the winner often over-estimates the value of the good for sale, resulting in an incurred negative utility. The seminal work of Eyster and Rabin [Econometrica'05] introduced a behavioral model aimed to explain this observed anomaly. We term agents who display this bias "cursed agents". We adopt their model in the interdependent value setting, and aim to devise mechanisms that prevent the cursed agents from obtaining negative utility. We design mechanisms that are cursed ex-post IC, that is, incentivize agents to bid their true signal even though they are cursed, while ensuring that the outcome is individually rational -- the price the agents pay is no more than the agents' true value. Since the agents might over-estimate the good's value, such mechanisms might require the seller to make positive transfers to the agents to prevent agents from over-paying. For revenue maximization, we give the optimal deterministic and anonymous mechanism. For welfare maximization, we require ex-post budget balance (EPBB), as positive transfers might lead to negative revenue. We propose a masking operation that takes any deterministic mechanism, and imposes that the seller would not make positive transfers, enforcing EPBB. We show that in typical settings, EPBB implies that the mechanism cannot make any positive transfers, implying that applying the masking operation on the fully efficient mechanism results in a socially optimal EPBB mechanism. This further implies that if the valuation function is the maximum of agents' signals, the optimal EPBB mechanism obtains zero welfare. In contrast, we show that for sum-concave valuations, which include weighted-sum valuations and l_p-norms, the welfare optimal EPBB mechanism obtains half of the optimal welfare as the number of agents grows large.
翻译:在现实生活中拍卖中,一个广泛观察到的现象是赢家的诅咒 -- 赢家的高出价意味着赢家往往高估出售的好东西的价值,从而产生负面效用。Eyster和Rabin[Economica'05]的开创性工作引入了一个旨在解释所观察到的异常现象的行为模式。我们将显示这种偏差的代理人定义为“弯曲的代理人 ” 。我们在相互依存的价值设置中采用他们的模式,并设计防止被诅咒的代理人获得负面效用的机制。我们设计了被诅咒的后方IC机制,即激励代理人提出其真实的估价信号,尽管他们被诅咒了,同时确保结果是个人理性的。Eyster和Rabin[Economica'05] 的开创了一种行为模式模式。由于代理人可能高估了所观察到的好东西的价值,这种机制可能要求卖方向代理人进行积极的转移,以防止代理人过度支付。为了实现收入最大化,我们提供了最佳的确定性和匿名机制。关于福利最大化,我们需要前方预算平衡(EPBB),因为积极转移可能使运作机制成为正性机制。