在卖者面对两个风险厌恶的信息不对称知情投标者和一个风险中性的不知情投标者的假设下,研究可分公共物品的拍卖机制设计问题。通过最大化卖者的期望收入,同时满足所有投标者的理性参与约束与知情投标者的激励相容约束,建立了最优机制设计模型;给出了知情投标者的激励相容约束成立的充要条件,并用来简化了卖者的期望收入最大化问题。当不考虑随机性的卖方期望收入最大化问题时,利用Kuhn-Tucker条件进行求解,得到对每个知情投标者都存在一个临界值。当且仅当所报告的估价大于该值时,知情投标者可分配到一定数量拍品;同时,投标者报告的估值越高,就越能获得更多数量的拍品。研究结果对股票或债券发行的机制设计有参考价值,这是因为它们可看做可分的具有公共价值的商品。
In this paper problem of optimal auction design of selling a divisible common-value object under an assumption that the seller faces two asymmetrically informed risk-averse bidders and one uninformed risk-neutral bidder is analyzed. The optimal mechanism design model is established for maximizing seller's expected revenue under all bidders' rational participation constraints and informed bidders' incentive compatibility constraints. The necessary and sufficient condition for the informed bidders' incentive compatibility constraints to be satisfied is given used and to simplify the seller's expected revenue maximization problem. The seller's revenue maximization problem is solved by ignoring its randomness and find that the seller allocates some goods to the informed bidder if and only if his reported value is higher than a particular threshold; the higher the reported value by the informed bidders is, the more goods will be allocated to him. Our research results can provide some suggestions for mechanism design for stock or bond issuance because the shares and bonds can be seen divisible and common-valued goods.
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