Core Pricing in Combinatorial Exchanges with Financially Constrained Buyers: Computational Hardness and Algorithmic Solutions
Published Online:1 Nov 2021https://doi.org/10.1287/opre.2021.2132
References
- (2018) Nash social welfare for indivisible items under separable, piecewise-linear concave utilities. Proc. Twenty-Ninth Annual ACM-SIAM Symposium Discrete Algorithms (SIAM, Philadelphia), 2274–2290.Google Scholar
- (1954) Existence of an equilibrium for a competitive economy. Econometrica 22(3):265–290.Crossref, Google Scholar
- (2006) An efficient dynamic auction for heterogeneous commodities. Amer. Econom. Rev. 96(3):602–629.Crossref, Google Scholar
- (2019) Understanding preferences: “demand types”, and the existence of equilibrium with indivisibilities. Econometrica 87(3):867–932.Crossref, Google Scholar
- (2020) The equilibrium existence duality: Equilibrium with indivisibilities & income effects. Preprint, submitted June 30, https://arxiv.org/abs/2006.16939.Google Scholar
- (2017) The use of auctions for allocating airport access rights. Transp. Res. Part A Policy Pract. 114:186–202.Crossref, Google Scholar
- (1990) A branch and bound algorithm for the bilevel programming problem. SIAM J. Sci. Statist. Comput. 11(2):281–292.Crossref, Google Scholar
- (2001) Multiple-object auctions with budget constrained bidders. Rev. Econom. Stud. 68(1):155–179.Crossref, Google Scholar
- (2016) Frontiers in spectrum auction design. Internat. J. Indust. Organ. 50:372–391.Crossref, Google Scholar
- (2017) Handbook of Spectrum Auction Design (Cambridge University Press, Cambridge, UK).Google Scholar
- (2017) Core and pricing equilibria in combinatorial exchanges. Econom. Lett. 157:145–147.Crossref, Google Scholar
- (2020) Walrasian equilibria from an optimiziation perspective: a guide to the literature. Naval Res. Logist. 68(4):496–513.Crossref, Google Scholar
- (2018) A matter of equality: Linear pricing in combinatorial exchanges. Inform. Systems Res. 29(4):779–1068.Link, Google Scholar
- (2019) Designing combinatorial exchanges for the reallocation of resource rights. Proc. National Academy Sci. 116(3):786–791.Crossref, Google Scholar
- (1997) Competitive equilibrium in an exchange economy with indivisibilities. J. Econom. Theory 74(2):385–413.Crossref, Google Scholar
- (2002) The package assignment model. J. Econom. Theory 107(2):377–406.Crossref, Google Scholar
- (1963) Some applications of linear programming to the theory of cooperative games [in Russian]. Problemy Kibernetiki 10: 119–139.Google Scholar
- (2005) Multi-unit auctions with budget-constrained bidders. Proc. 6th ACM Conf. Electronic Commerce (ACM), 44–51.Google Scholar
- (2007) Dynamics of bid optimization in online advertisement auctions. Proc. 16th Internat. Conf. World Wide Web (ACM, New York), 531–540.Google Scholar
- (2006) Combinatorial auctions for truckload transportation. Cramton P, Shoham Y, Steinberg R, eds. Combinatorial Auctions (MIT Press, Boston), 21:539–571.Google Scholar
- (2011) Airport slot allocation in Europe: economic efficiency and fairness. Internat. J. Rev. Management 6(1-2):28–44.Google Scholar
- (1998) Standard auctions with financially constrained bidders. Rev. Econom. Stud. 65(1):1–21.Crossref, Google Scholar
- (2015) Approximating the nash social welfare with indivisible items. Proc. Forty-Seventh Annual ACM Symposium Theory Comput. 371–380.Google Scholar
- (2018) Approximating the nash social welfare with indivisible items. SIAM J. Comput. 47(3):1211–1236.Crossref, Google Scholar
- (2017) Convex program duality, fisher markets, and nash social welfare. Proc. 2017 ACM Conf. Econom. Comput., 459–460.Google Scholar
- (2011) On multiple round sponsored search auctions with budgets. Preprint, submitted December 29, https://arxiv.org/abs/1112.6361.Google Scholar
- (2017) Multiplicative pacing equilibria in auction markets. Preprint, submitted June 22, https://arxiv.org/abs/1706.07151.Google Scholar
- (2018) Pacing equilibrium in first-price auction markets. Preprint, submitted November 17, https://arxiv.org/abs/1811.07166.Google Scholar
- (2001) Discrete convexity and equilibria in economies with indivisible goods and money. Math. Soc. Sci. 41(3):251–273.Crossref, Google Scholar
- (2012) The quadratic core-selecting payment rule for combinatorial auctions. Oper. Res. 60:588–603.Link, Google Scholar
- (2007) Fair payments for efficient allocations in public sector combinatorial auctions. Management Sci. 53(9):1389–1406.Link, Google Scholar
- (2007) On ascending vickrey auctions for heterogeneous objects. J. Econom. Theory 132(1):95–118.Crossref, Google Scholar
- (2016) Airports in the EU: Challenges ahead. Technical Report PE 583.820, European Parliamentary Research Service.Google Scholar
- (2010) Analysis of electric grid interdiction with line switching. IEEE Trans. Power Systems 25(2):633–641.Crossref, Google Scholar
- (2002) Foundations of Bilevel Programming (Springer, New York).Google Scholar
- (2003) Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optim. 52(3):333–359.Crossref, Google Scholar
- (2008) Multi-unit auctions with budget limits. Foundations Comput. Sci., 2008. FOCS’08, IEEE 49th Annual IEEE Symposium (IEEE, Piscataway, NJ), 260–269.Google Scholar
- (2016) Auctions for heterogeneous items and budget limits. ACM Trans. Econom. Comput. 4(1):4.Google Scholar
- (2003) Decentralized mechanism design for supply chain organizations using an auction market. Inform. Systems Res. 14(1):1–22.Link, Google Scholar
- (2017) A new general-purpose algorithm for mixed-integer bilevel linear programs. Oper. Res. 65(6):1615–1637.Link, Google Scholar
- (2015) Compact bid languages and core pricing in large multi-item auctions. Management Sci. 61(7):1684–1703.Link, Google Scholar
- (1999) Walrasian equilibrium with gross substitutes. J. Econom. Theory 87:95–124.Crossref, Google Scholar
- (2012) A computational analysis of bunding trading markets design for distributed resource allocation. Inform. Systems Res. 23(3-part-1):823–843.Link, Google Scholar
- (2017) Airport slots. Technical report, House of Commons Briefing Paper No CBP 488.Google Scholar
- 2017. Budget Constraints in Combinatorial Clock Auctions (Cambridge University Press, Cambridge, UK), 318–337.Google Scholar
- (1985) The polynomial hierarchy and a simple model for competitive analysis. Math. Programming 32(2):146–164.Crossref, Google Scholar
- (1982) Job matching, coalition formation, and gross substitute. Econometrica 50:1483–1504.Crossref, Google Scholar
- (2008) Scarf is ppad-complete. Preprint, submitted December 9, https://arxiv.org/abs/0812.1601.Google Scholar
- (2010) Auction Theory (Academic Press, San Diego).Google Scholar
- (2017) Apx-hardness of maximizing nash social welfare with indivisible items. Inform. Process. Lett. 122:17–20.Crossref, Google Scholar
- (2006) The winner determination problem. Cramton P, Shoham Y, Steinberg R, eds. Combinatorial Auctions (MIT Press, Boston), 297–318.Google Scholar
- (2017) Gross substitutability: An algorithmic survey. Games Econom. Behav. 106:294–316.Crossref, Google Scholar
- (2000) Toward a universal test suite for combinatorial auction algorithms. Proc. 2nd ACM Conf. Electronic Commerce. (ACM, New York), 66–76.Google Scholar
- (2015) Computationally efficient mip formulation and algorithms for european day-ahead electricity market auctions. Eur. J. Oper. Res. 242(2):580–593.Crossref, Google Scholar
- (2014) Strict linear prices in non-convex european day-ahead electricity markets. Optim. Methods Software 29(1):189–221.Google Scholar
- (1995) Microeconomic Theory, vol. 1 (Oxford University Press, New York).Google Scholar
- (2007) Package auctions and exchanges. Econometrica 75(4):935–965.Crossref, Google Scholar
- (2009) Substitute goods, auctions, and equilibrium. J. Econom. Theory 144(1):212–247.Crossref, Google Scholar
- (1990) The mixed integer linear bilevel programming problem. Oper. Res. 38(5):911–921.Link, Google Scholar
- (2009) Google’s auction for TV ads. Internat. Colloquium Automata, Languages, Programming (Springer, Berlin), 309–327.Google Scholar
- (2014) Optimal auctions with financially constrained buyers. J. Econom. Theory 150:383–425.Crossref, Google Scholar
- (2003) Combinatorial auction design. Management Sci. 49(11):1485–1503.Link, Google Scholar
- (2012) Secondary trading of airport slots as a combinatorial exchange. Transportation Res., Part E Logist. Trans. Rev. 48(5):1009–1022.Crossref, Google Scholar
- (1982) A combinatorial auction mechanism for airport time slot allocation. Bell J. Econom. 13(2):402–417.Crossref, Google Scholar
- (2015) Why prices need algorithms. Proc. Sixteenth ACM Conf. Econom. Comput. (ACM, New York), 19–36.Google Scholar
- (2012) Very-large-scale generalized combinatorial multi-attribute auctions: Lessons from conducting $60 billion of sourcing. Vulkan N, Roth AE, Neeman Z, eds. The Handbook of Market Design (Oxford University Press, Oxford, UK).Google Scholar
- (2002) Winner determination in combinatorial auction generalizations. Proc. First Internat. Joint Conf. Autobomous Agents Multiagent Systems: Part I (ACM, New York), 69–76.Google Scholar
- (2008) A bilevel mixed-integer program for critical infrastructure protection planning. Comput. Oper. Res. 35(6):1905–1923.Crossref, Google Scholar
- (1967) The core of an n person game. Econometrica 35(1):50–69.Crossref, Google Scholar
- (2009) A combinatorial intra-enterprise exchange for logistics services. Inform. Systems E-Bus. Management 7(4):447–471.Crossref, Google Scholar
- (1967) On balanced sets and cores. Naval Res. Logist. 14(4):453–460 (NRL).Crossref, Google Scholar
- (1971) The assignment game I: The core. Internat. J. Game Theory 1(1):111–130.Crossref, Google Scholar
- (1976) The polynomial-time hierarchy. Theoret. Comput. Sci. 3(1):1–22.Crossref, Google Scholar
- (2017) A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation. Math. Programming Comput. 12:529–568.Crossref, Google Scholar
- (2007) Combinatorial algorithms for market equilibria. Nisan N, Roughgarden T, Tardos E, Vazirani V, eds. Algorithmic Game Theory (Cambridge University Press, New York), 103–134.Google Scholar
- (2011) Market equilibrium under separable, piecewise-linear, concave utilities. J. ACM 58(3):10.Crossref, Google Scholar
- (1934) Marktform und Gleichgewicht (Springer, Berlin and Vienna).Google Scholar
- (2000) Combinatorial auctions for supply chain formation. Proceedings of the 2nd ACM Conference on Electronic Commerce. EC ’00 (ACM, New York), 260–269.Google Scholar
- (2018) Budget constrained bidding by model-free reinforcement learning in display advertising. Proc. 27th ACM Internat. Conf. Inform. Knowledge Management, 1443–1451.Google Scholar
- (2014) An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions. Comput. Oper. Res. 41:309–318.Crossref, Google Scholar
- (2014) Solving bilevel mixed integer program by reformulations and decomposition. Optimization Online 1–34. Accessed August 14, 2021, http://www.optimization-online.org/DB_FILE/2014/07/4455.pdf.Google Scholar

