Bidding behavior and equilibrium excursion of uniform price auction mechanism. (English) Zbl 1380.91085
Summary: Multiple equilibria (equilibrium excursion) affects the auction proceeds, and is bad for estimating auction efficiency. This paper examines the relationship between bidding behavior and equilibrium excursion. We analyze a uniform price auction mechanism based on a rationing strategy and common value information. In this uniform price auction mechanism, bidders (strategic and non-strategic) participate in an auction simultaneously, and the auctioneer rations the strategic bidders after observing their bids. The conclusions drawn suggest that a rationing strategy can effectively limit the strategic bidders from manipulating the auction, and the Nash equilibrium may not be unique (i.e., there exists an equilibrium excursion). As the number of bidders increases, or when the quantity that can be allocated to the non-strategic bidders is unconstrained, there exists asymptotically a unique equilibrium price which is the highest price the auctioneer could obtain. Based on these conclusions, we provide some strategies and suggestions on how to induce the equilibrium excursion state to a desired unique equilibrium state.
MSC:
| 91B26 | Auctions, bargaining, bidding and selling, and other market models |
| 91B50 | General equilibrium theory |
| 91A10 | Noncooperative games |
Keywords:
uniform price auction; rationing strategy; equilibrium excursion; pure-strategy symmetric Nash equilibrium; mechanism optimizationReferences:
| [1] | Akaichi, F, Nayga, RM Jr and Gil, JM (2014). Demand reduction in multi-unit auctions with varying number of bidders and units. Economics Letters, 124, 443-445. |
| [2] | Alvarez, F and Mazón, C (2012). Multi-unit auctions with private information: An indivisible unit continuous price model. Economic Theory, 51, 35-70. · Zbl 1247.91069 |
| [3] | Anderson, EJ (2013). On the existence of supply function equilibria. Mathematical Programming, 140, 323-349. · Zbl 1273.91095 |
| [4] | Back, K and Zender, JF (1993). Auctions of divisible goods: On the rationale for the treasury experiment. Review of Financial Studies, 6(1), 733-764. |
| [5] | Back, K and Zender, JF (2001). Auctions of divisible goods with endogenous supply. Economics Letters, 73(1), 29-34. · Zbl 0983.91021 |
| [6] | Benjamin, R (2016). Tacit collusion in electricity markets with uncertain demand. Review of Industrial Organization, 48, 69-93. |
| [7] | Bodoh-Creed, A (2013). Efficiency and information aggregation in large uniform-price auctions. Journal of Economic Theory, 148, 2436-2466. · Zbl 1284.91167 |
| [8] | Bourjade, S (2009). Strategic price discounting and rationing in uniform price auctions. Economics Letters, 105(1), 23-27. · Zbl 1179.91088 |
| [9] | Brenner, M, Galai, D and Sade, O (2009). Sovereign debt auctions: Uniform or discriminatory?Journal of Monetary Economics, 56(2), 267-274. |
| [10] | Bresky, M (2013). Revenue and efficiency in multi-unit uniform-price auctions. Games and Economic Behavior, 82, 205-217. · Zbl 1282.91122 |
| [11] | Burinskiene, M and Rudzkis, P (2010). Feasibility of the liberal electricity market under conditions of a small and imperfect market. Technological and Economic Development of Economy, 16(3), 555-566. |
| [12] | Chakraborty, I and Engelbrecht-Wiggans, R (2005). Asymptotic prices in uniform-price multi-unit auctions summary. Economic Theory, 26(4), 983-987. · Zbl 1116.91038 |
| [13] | Cheng, CB (2011). Reverse auction with buyer-supplier negotiation using bi-level distributed programming. European Journal of Operational Research, 211(3), 601-611. |
| [14] | Damianov, DS and Becker, JG (2010a). Auctions with variable supply: Uniform price versus discriminatory. European Economic Review, 54, 571-593. |
| [15] | Damianov, DS, Oechssler, J and Becker, JG (2010b). Uniform vs. discriminatory auctions with variable supply-experimental evidence. Games and Economic Behavior, 68, 60-76. · Zbl 1197.91105 |
| [16] | Feng, J and Chatterjee, K (2010). Simultaneous vs. sequential sales: Bidder competition and supply uncertainty. Decision Support Systems, 49, 251-260. |
| [17] | Genc, TS (2009). Discriminatory versus uniform-price electricity auctions with supply function equilibrium. Journal of Optimization Theory and Applications, 140, 9-31. · Zbl 1177.91077 |
| [18] | Gurnani, H, Gümüs, M, Ray, S and Ray, T (2012). Optimal procurement strategy under supply risk. Asia-Pacific Journal of Operational Research, 29(1), 1240006-1-1240006-31. · Zbl 1237.90042 |
| [19] | Jiang, ZZ, Fang, SC, Fan, ZP and Wang, D (2013). Selecting optimal selling format of a product in B2C online auctions with bounded rational customers. European Journal of Operational Research, 226(1), 139-153. · Zbl 1292.91083 |
| [20] | Klemperer, P (1989). Supply function equilibria in oligopoly under uncertainty. Econometrica, 57(6), 1243-1277. · Zbl 0684.90008 |
| [21] | Kremer, I and Nyborg, K (2004a). Divisible-good auctions: The role of allocation rules. Rand Journal of Economics, 35(1), 147-159. |
| [22] | Kremer, I and Nyborg, K (2004b). Underpricing and market power in uniform price auctions. Review of Financial Studies, 17(1), 849-877. |
| [23] | Lee, PJ, Taylor, SL and Walter, TS (1999). IPO underpricing explanations: Implications from investor application and allocation schedules. Journal of Financial and Quantitative Analysis, 34, 425-444. |
| [24] | Lengwiler, Y (1999). The multiple unit auction with variable supply. Economic Theory, 14(2), 373-392. · Zbl 0942.91036 |
| [25] | LiCalzi, M and Pavan, A (2005). Tilting the supply schedule to enhance competition in uniform-price auctions. European Economic Review, 49(1), 227-250. |
| [26] | Liu, SR, Zhu, YM and Hu, QY (2015). Optimal inventory control and allocation for sequential internet auctions. Asia-Pacific Journal of Operational Research, 32(2), 1550003-1-1550003-32. · Zbl 1319.90011 |
| [27] | Ljungqvist, AP and Wilhelm, WJ (2002). IPO allocations: Discriminatory or discretionary?Journal of Financial Economics, 65, 167-201. |
| [28] | Lorentziadis, PL (2012). Optimal bidding in auctions of mixed populations of bidders. European Journal of Operational Research, 217(3), 653-663. · Zbl 1244.91043 |
| [29] | McAdams, D (2002). Modifying the uniform-price auction to eliminate ‘collusive seeming equilibria’. Working Paper, MIT. |
| [30] | McAdams, D (2007). Adjustable supply in uniform price auctions: Non-commitment as a strategic tool. Economics Letters, 95(1), 48-53. · Zbl 1255.91164 |
| [31] | Mezzetti, C, Pekěc, A Saša and Tsetlin, I (2008). Sequential vs. single-round uniform-price auctions. Games and Economic Behavior, 62, 591-609. · Zbl 1137.91414 |
| [32] | Milgrom, P (2006). Putting Auction Theory to Work. Beijing: Tsinghua University Press. |
| [33] | Pant, KP (2015). Uniform-price reverse auction for estimating the costs of reducing open-field burning of rice residue in Nepal. Environmental and Resource Economics, 62, 567-581. |
| [34] | Rao, CJ and Li, P (2013). Multi-stage sequential uniform price auction mechanism for divisible goods. Expert Systems with Applications, 40(15), 6105-6114. |
| [35] | Rao, CJ and Peng, J (2009). Fuzzy group decision making model based on credibility theory and gray relative degree. International Journal of Information Technology & Decision Making, 8(3), 515-527. · Zbl 1187.68562 |
| [36] | Rao, CJ and Zhao, Y (2010). Mechanism design for optimal auction of divisible goods. International Journal of Information Technology & Decision Making, 9(5), 831-845. · Zbl 1231.91128 |
| [37] | Rao, CJ and Zhao, Y (2011a). Optimal multi-attribute auctions for divisible goods. International Journal of Information Technology and Decision Making, 10(5), 891-911. · Zbl 1241.91056 |
| [38] | Rao, CJ and Zhao, Y (2011b). Incentive mechanism for allocating total permitted pollution discharge capacity and evaluating the validity of free allocation. Computers & Mathematics with Applications, 62(8), 3037-3047. · Zbl 1232.91555 |
| [39] | Rao, CJ, Zhao, Y and Wang, Q (2010). Uniform price auctions of divisible goods with variable supply. ICIC Express Letters, 4(4), 1127-1134. |
| [40] | Rao, CJ, Zhao, Y and Li, CF (2012a). Asymmetric Nash equilibrium in emission rights auctions. Technological Forecasting and Social Change, 79(3), 429-435. |
| [41] | Rao, CJ, Zhao, Y and Ma, SH (2012b). Procurement decision making mechanism of divisible goods based on multi-attribute auction. Electronic Commerce Research and Applications, 11(4), 397-406. |
| [42] | Rao, CJ, Zhao, Y, Zheng, JJ, Wang, C and Chen, ZW (2016). An extended uniform-price auction mechanism of homogeneous divisible goods: Supply optimisation and non-strategic bidding. International Journal of Production Research54(13), 4028-4042. |
| [43] | Rao, CJ, Zhao, Y and Chen, Y (2015). Uniform price auction of divisible goods based on multiple rounds linear bidding and its equilibrium analysis. Technological and Economic Development of Economy, 21(1), 96-117. |
| [44] | Wang, JJD and Zender, JF (2002). Auctioning divisible goods. Economic Theory, 19(3), 673-705. · Zbl 1011.91033 |
| [45] | Wilson, R (1979). Auctions of share. The Quarterly Journal of Economics, 93(4), 675-689. · Zbl 0414.90011 |
| [46] | Zhang, P (2009). Uniform price auctions and fixed price offerings in IPOs: An experimental comparison. Experimental Economics, 12, 202-219. · Zbl 1175.91081 |
| [47] | Zhang, LH, Jia, SF, Leung, CK and Guo, LP (2013). An analysis on the transaction costs of water markets under DPA and UPA auctions. Water Resource Management, 27, 475-484. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
