TROPICAL GEOMETRY TO ANALYSE DEMAND

Duality techniques from convex geometry, extended by the recently-developed mathematics of tropical geometry, provide a powerful lens to study demand. We propose a new framework of \demand types", for categorising and understanding demand; our classication

[1]  F. Echenique,et al.  A Theory of Stability in Many-to-Many Matching Markets , 2004 .

[2]  G. Mikhalkin Enumerative tropical algebraic geometry , 2003 .

[3]  Paul Milgrom,et al.  Assignment Messages and Exchanges , 2009 .

[4]  Ennio Stacchetti,et al.  The English Auction with Differentiated Commodities , 2000, J. Econ. Theory.

[5]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[6]  Andreas Gathmann,et al.  Tropical algebraic geometry , 2006 .

[7]  F. Echenique Contracts versus Salaries in Matching , 2012 .

[8]  V. Danilov,et al.  Unimodular systems of vectors are embeddable in the (0, 1)-cube , 2010 .

[9]  V. Crawford,et al.  Job Matching, Coalition Formation, and Gross Substitutes , 1982 .

[10]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[11]  A.J.J. Talman,et al.  A Model of Partnership Formation , 2008 .

[12]  G. van der Laan,et al.  Existence of an Equilibrium in a Competitive Economy with Indivisibilities and Money , 1997 .

[13]  Faruk Gul,et al.  WALRASIAN EQUILIBRIUM WITH GROSS SUBSTITUTES , 1999 .

[14]  L. Shapley,et al.  The assignment game I: The core , 1971 .

[15]  Zaifu Yang,et al.  On a class of discrete convolution concave functions and their applications , 2008 .

[16]  Bettina Klaus,et al.  Consistency in one-sided assignment problems , 2010, Soc. Choice Welf..

[17]  Paul Fisher Paul Fisher: Recent developments in the sterling monetary framework , 2011 .

[18]  Zaifu Yang,et al.  Equilibrium, Auction, Multiple Substitutes and Complements , 2013 .

[19]  Pierre-Andre Chiappori,et al.  The Roommate Problem Is More Stable than You Think , 2012, SSRN Electronic Journal.

[20]  Paul D. Seymour,et al.  Decomposition of regular matroids , 1980, J. Comb. Theory, Ser. B.

[21]  Eugenii Shustin,et al.  Tropical Algebraic Geometry , 2007 .

[22]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[23]  Viatcheslav P. Grishukhin,et al.  Maximal Unimodular Systems of Vectors , 1999, Eur. J. Comb..

[24]  Zaifu Yang,et al.  A Note on Kelso and Crawford's Gross Substitutes Condition , 2003, Math. Oper. Res..

[25]  Scott Duke Kominers,et al.  Multilateral matching , 2011, EC '11.

[26]  B. Sturmfels,et al.  First steps in tropical geometry , 2003, math/0306366.

[27]  M. Ostrovsky,et al.  Stability and Competitive Equilibrium in Trading Networks , 2013, Journal of Political Economy.

[28]  M. Ostrovsky Stability in Supply Chain Networks , 2005 .

[29]  Oswald Veblen,et al.  On Matrices Whose Elements Are Integers , 1921 .

[30]  G. Koshevoy,et al.  Equilibria in Markets with Indivisible Goods , 2013 .

[31]  Paul Milgrom,et al.  Substitute goods, auctions, and equilibrium , 2009, J. Econ. Theory.

[32]  N. M. Fehr,et al.  Designing and Structuring Auctions for Firm and Interruptible Gas Supply Contracts in Colombia , 2011 .

[33]  G. Koshevoy,et al.  Equilibria with indivisible goods and package-utilities , 2008 .

[34]  John William Hatfield,et al.  Substitutes and stability for matching with contracts , 2010, J. Econ. Theory.

[35]  Kazuo Murota,et al.  Discrete convexity and equilibria in economies with indivisible goods and money , 2001, Math. Soc. Sci..

[36]  T. Frost,et al.  Innovations in the Bank's Provision of Liquidity Insurance via Indexed Long-Term Repo (ILTR) Operations , 2015 .

[37]  Zaifu Yang,et al.  A Double‐Track Adjustment Process for Discrete Markets With Substitutes and Complements , 2009 .

[38]  Stephen H. Friedberg,et al.  Elementary Linear Algebra , 2007 .

[39]  Christine Lang,et al.  Gross substitution, discrete convexity, and submodularity , 2003, Discret. Appl. Math..

[40]  Alexey Kushnir,et al.  A Geometric Approach to Mechanism Design , 2013, Journal of Political Economy Microeconomics.

[41]  Paul R. Milgrom,et al.  Matching with Contracts , 2005 .

[42]  Mamoru Kaneko,et al.  Cores of partitioning games , 1982, Math. Soc. Sci..

[43]  Alexander Teytelboym,et al.  Gross Substitutes and Complements: A Simple Generalization , 2013 .

[44]  Kim-Sau Chung,et al.  On the Existence of Stable Roommate Matchings , 2000, Games Econ. Behav..

[45]  P. Cramton,et al.  Introduction to Combinatorial Auctions , 2006 .

[46]  Marilda Sotomayor Three remarks on the many-to-many stable matching problem , 1999 .

[47]  C. A. Rogers,et al.  An Introduction to the Geometry of Numbers , 1959 .

[48]  F. Kojima,et al.  Matching with Contracts: Comment , 2008 .

[49]  K. Murota Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10 , 2003 .

[50]  M. Utku Ünver,et al.  Credible group stability in many-to-many matching problems , 2006, J. Econ. Theory.

[51]  Zaifu Yang,et al.  Equilibria and Indivisibilities: Gross Substitutes and Complements , 2006 .

[52]  Lawrence M. Ausubel,et al.  Ascending Auctions with Package Bidding , 2002 .

[53]  Lawrence M. Ausubel,et al.  Auctioning Many Divisible Goods , 2004 .

[54]  ENUMERATIVE TROPICAL ALGEBRAIC GEOMETRY IN R , 2004 .

[55]  Paul R. Milgrom,et al.  Putting Auction Theory to Work: The Simultaneous Ascending Auction , 1999, Journal of Political Economy.

[56]  Henri Poincaré,et al.  Second Complément à l'Analysis Situs , 1900 .

[57]  Peter Cramton,et al.  Auction Design for Wind Rights , 2012 .

[58]  S. Bikhchandani,et al.  Competitive Equilibrium in an Exchange Economy with Indivisibilities , 1997 .

[59]  Grigory Mikhalkin Decomposition into pairs-of-pants for complex algebraic hypersurfaces , 2002 .

[60]  Kimmo Eriksson,et al.  Stable outcomes of the roommate game with transferable utility , 2000, Int. J. Game Theory.

[61]  P. Klemperer The Product-Mix Auction: A New Auction Design for Differentiated Goods , 2010 .

[62]  Brian Osserman,et al.  Lifting Tropical Intersections , 2010, 1007.1314.

[63]  Walzl Markus,et al.  Stable Many-to-Many Matchings with Contracts , 2006 .

[64]  V. I. Danilov,et al.  Discrete convexity and unimodularity—I , 2003 .

[65]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .