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.
[1] Wilson R. Competitive bidding with asymmetrical information[J]. Management Science, 1967, 13(11):816-820.
[2] Reichert A O. Models for competitive bidding under uncertainty[D].California,U.S.:Department of Operations Research, Stanford University,1968.
[3] Engelbrecht-Wiggans R, Milgrom P, Weber R. Competitive bidding and proprietary information[J]. Journal of Mathematical Economics, 1983,11(2):161-169.
[4] Paul P,Rajdeep S. Using bidder asymmetry to increase seller revenue[J]. Economics Letters, 2004,84(1):17-20.
[5] Bennouri M, Falconieri S. The optimality of uniform pricing in IPOs:An optimal auction approach[J]. Review of Finance, 2008, 12(4), 673-700.
[6] 王彦,李楚霖. 非对称情况下的多物品拍卖[J]. 中国管理科学,2003, 12(06):61-65.
[7] 饶从军,赵勇,王清. 基于可变供给量的可分离物品拍卖及其应用[J]. 中国管理科学. 2012,20(01):129-138.
[8] Shi Xinyan. Common-value auctions with asymmetrically informed bidders and reserve price[J]. International Journal of Economic Theory,2013, 9(2):161-175.
[9] Liu Heng. Equilibrium selection in common-value second-price auctions[J]. Games and Economic Behavior,2014, 84:1-6.
[10] Einy E, Haimanko O,Orzach R,et al. Common-value all-pay auctions with asymmetric information and bid caps[R]. Working Paper,Ben-Gurion University the-Negeu.
[11] Myerson R B. Optimal auction design[J]. Mathematics of operations research, 1981, 6(1):58-73.
[12] Cremer J, McLean R P. Full extraction of the surplus in Bayesian and dominant strategy auctions[J]. Econometrica, 1988, 56(6):1247-1257.
