Kim C. Border
Kim Border's recent research is in the areas of decision theory and incentive design. He is interested in applying insights from mathematical areas such as convex analysis and network flow programming to design incentives to solve resource allocation problems and to address issues of making decisions under risk. He's particularly interested in the mathematical characterizations of the behavior implied by expected utility theory and some of its alternatives. He has extended classic "Dutch book" arguments in favor of acting according to the classical rationality embodied in the expected utility hypothesis (EUH). (A Dutch book is a situation in which a decision maker who violates the EUH can be forced to lose money.) On the other hand, Border and Uzi Segal have constructed examples of game-theoretic situations in which an expected utility odds-maker constructs a Dutch book in response to the presence of non–expected-utility decision makers. In other words, classically rational behavior may not be the classically rational best response to non-classically rational behavior. Along with Paolo Ghirardato, Border and Segal have also investigated the extent to which subjective probabilities must agree. They showed that if the subjective probabilities are atomless—that is, every event can be subdivided into events of positive probability—then there is a very rich set of events for which everyone must agree on the probability. There is renewed interest in some of his earlier work on characterizing feasibility in auctions. He is now investigating the mathematical structure of related problems, including unexpected connection to axioms in revealed preference theory.
At Caltech, Border was the director of graduate studies for the social sciences from 1994 to 1996, executive officer for the social sciences from 1995 to 1999, and chair of the faculty from 1999 to 2001. Previously, he was a visitor at the Institute for Advanced Studies at the Hebrew University of Jerusalem in the summer of 1983. He was on the editorial board of Economic Theory from 1990 to 2000 and was a panelist for the National Science Foundation's Research Fellowship Program in 2003 and 2004.
- Fixed Point Theorems with Application to Economics and Game Theory. Cambridge University Press, Cambridge, 1985. Corrected 3rd. printing and paperback edition, 1989.
- Positive Operators, Riesz Spaces, and Economics, editor, with C. D. Aliprantis and W. A. J. Luxemburg. Springer–Verlag, Berlin, 1991.
- Infinite Dimensional Analysis: A Hitchhiker's Guide, with C. D. Aliprantis. Springer–Verlag, Berlin, 1994. 2nd. edition, 1999. 3rd. edition, 2006.
- Expectations equilibrium with expectations conditioned on past data, with J. S. Jordan. Journal of Economic Theory 22: 395–406, 1980. (doi:10.1016/0022-0531(80)90050-2)
- Straightforward elections, unanimity, and phantom voters, with J. S. Jordan. Review of Economic Studies 50: 153–170, 1983. (JSTOR)
- Social welfare functions for economic environments with and without the Pareto principle. Journal of Economic Theory 29: 205–216, 1983. (doi:10.1016/0022-0531(83)90045-5)
- A core existence theorem for games without ordered preferences. Econometrica 52: 1537–1542, 1984. (JSTOR)
- An impossibility theorem for spatial models. Public Choice 43: 293–303, 1984. (doi:10.1007/BF00118938)
- More on Harsanyi's cardinal welfare theorem. Social Choice and Welfare 1: 279–281, 1985. (doi:10.1007/BF00649263)
- Samurai accountant: a theory of auditing and plunder, with J. Sobel. Review of Economic Studies 5: 525–540, 1987. (JSTOR) Reprinted in The Economics of Information, S. A. Lippman and D. K. Levine (editors). Edward Elgar, Cheltenham, UK, 1995. (Elgar)
- Implementation of reduced form auctions: a geometric approach. Econometrica 59: 1175–1187, 1991. (JSTOR)
- Functional analytic tools in expected utility theory, in K. C. Border, C. D. Aliprantis, and W. A. J. Luxemburg (editors), Positive Operators, Riesz Spaces, and Economics, pages 69–88. Springer–Verlag, Berlin, 1991.
- Revealed preference, stochastic dominance, and the expected utility hypothesis. Journal of Economic Theory 56: 20–42, 1992. (doi:10.1016/0022-0531(92)90067-R)
- Dutch books and conditional probability, with U. Segal. Economic Journal 104: 71–75, 1994. (JSTOR)
- Dynamic consistency implies approximately expected utility preferences, with U. Segal. Journal of Economic Theory 63: 170–188, 1994. (doi:10.1006/jeth.1994.1038)
- Preferences over solutions to the bargaining problem, with U. Segal. Econometrica 65: 1–18, 1997. (JSTOR) Reprinted in Bargaining and the Theory of Cooperative Games: John Nash and Beyond, William Thomson (editor). Edward Elgar, Cheltenham, UK, 2010.
- Economies with many commodities, with C. D. Aliprantis and O. Burkinshaw. Journal of Economic Theory 74: 62–105, 1997. (doi:10.1006/jeth.1996.2240)
- Market economies with many commodities, with C. D. Aliprantis and O. Burkinshaw. Decisions in Economics and Finance (formerly Rivista di Matematica per le Scienze Economiche e Sociali) 19: 113–185, 1996. (doi:10.1007/BF02441265)
- A new proof of the existence of equilibrium in the single sector growth model, with C. D. Aliprantis and O. Burkinshaw. Macroeconomic Dynamics 1: 669–679, 1997. (doi:10.1017/S1365100597005014)
- Coherent odds and subjective probability, with U. Segal. Journal of Mathematical Psychology, 46:253–268, 2002. (doi:10.1006/jmps.2001.1387)
- Reduced form auctions revisited. Economic Theory, 31:167–181, 2007. (doi:10.1007/s00199-006-0080-z)
- Unanimous subjective probabilities, with Paolo Ghirardato and Uzi Segal. Economic Theory, 34:383–387, 2008. (doi:10.1007/s00199-006-0174-7)