Monograph records
https://feeds.library.caltech.edu/people/Border-K-C/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 17:49:35 +0000Reduced Form Auctions Revisited
https://resolver.caltech.edu/CaltechAUTHORS:20170731-164441362
Authors: Border, Kim C.
Year: 2017
This note uses Farkas's Lemma to prove new results on the implementability of general, asymmetric auctions, and to provide simpler proofs of known results for symmetric auctions. The tradeoff is that type spaces are taken to be finite.https://authors.library.caltech.edu/records/4f7kp-cze06Objective Subjective Probabilities
https://resolver.caltech.edu/CaltechAUTHORS:20170808-151011915
Authors: Border, Kim C.; Ghirardato, Paolo; Segal, Uzi
Year: 2017
This note shows that if the space of events is sufficiently rich and the subjective probability measure of each individual is non-atomic, then there is a σ-algebra of events on which everyone will have the same probability, and moreover, the range of these probabilities is the entire segment [0, 1].https://authors.library.caltech.edu/records/vtw3e-k9969Preferences Over Solution to the Bargaining Problem
https://resolver.caltech.edu/CaltechAUTHORS:20170818-141404867
Authors: Border, Kim C.; Segal, Uzi
Year: 2017
There are several solutions to the Nash bargaining problem in the literature. Since various authors have expressed preferences for one solution over another, we find it useful to study preferences over solutions in their own right. We identify two sets of appealing axioms on such preferences that lead to unanimity in the choice of solution. Thus bargainers may be able to reach agreement on which solution to employ. Under the first set of axioms, the Nash solution is preferred to any other solution, while under the second set, a new solution, which we call the weighted linear solution, is best.https://authors.library.caltech.edu/records/6xdyr-40f88Economies With Many Commodities
https://resolver.caltech.edu/CaltechAUTHORS:20170817-150419178
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Burkinshaw, Owen
Year: 2017
We discuss the two fundamental theorems of welfare economics in the context of the Arrow-Debreu-McKenzie model with an infinite dimensional commodity space. As an application, we prove the existence of competitive equilibrium in the standard single agent growth model.https://authors.library.caltech.edu/records/jjhxf-hrj08Dynamic Consistency Implies Approximately Expected Utility Preferences
https://resolver.caltech.edu/CaltechAUTHORS:20170828-143106635
Authors: Border, Kim C.; Segal, Uzi
Year: 2017
Machina has proposed a definition of dynamic consistency which admits non-expected utility functionals. We show that even under this new definition, a dynamically consistent preference relation that is differentiable becomes arbitrarily close to an expected utility preference after the realization of a low probability event.https://authors.library.caltech.edu/records/yxwaw-esd54Dutch Book Arguments and Subjective Probability
https://resolver.caltech.edu/CaltechAUTHORS:20170831-151749064
Authors: Border, Kim C.; Segal, Uzi
Year: 2017
[No abstract]https://authors.library.caltech.edu/records/0z0pw-6pj51A Theory of Auditing and Plunder
https://resolver.caltech.edu/CaltechAUTHORS:20170915-144256949
Authors: Border, Kim C.; Sobel, Joel
Year: 2017
Taxpayers know their income but the IRS does not. The IRS can audit taxpayers to discover their true income, but auditing is costly. We characterize optimal policies for the IRS when it is free to choose tax levies, audit probabilities and penalties. The main results are that optimal policies involve taxes which are monotonically increasing in reported incomes and audit probabilities are monotonically decreasing in reported income. In general optimal schemes involve stochastic auditing of reports and rebates for telling the truth. A theory of optimal plundering is described.https://authors.library.caltech.edu/records/hq4vr-2ev86More on Harsanyi's Utilitarian Cardinal Welfare Theorem
https://resolver.caltech.edu/CaltechAUTHORS:20170918-163836570
Authors: Border, Kim C.
Year: 2017
If individuals and society both obey the expected utility hypothesis and social alternatives are uncertain, then the social utility must be a linear combination of the individual utilities, provided the society is indifferent when all its members are. This result was first proven by Harsanyi [4] who made implicit assumptions in the proof not actually needed for the result (see [5]). This note presents a straightforward proof of Harsanyi's theorem based on a separating hyperplane argument.https://authors.library.caltech.edu/records/q0pxs-qmw64The Core of a Coalitional Production Economy Without Ordered Preferences
https://resolver.caltech.edu/CaltechAUTHORS:20170926-134414751
Authors: Border, Kim C.
Year: 2017
It is shown that the core of a coalitional production economy with a balanced technology (Bohm [1974]) is nonempty, even if the consumers have preferences which are intransitive, provided the preferences are convex and continuous. Since such preferences cannot be represented by utility functions, this result does not follow from the nonemptiness of the core of a characteristic function game. Rather, the approach is closer to that of Ichiishi's [1981] social coalitional equilibrium.https://authors.library.caltech.edu/records/t18hp-r5w51On Equilibria of Excess Demand Correspondences
https://resolver.caltech.edu/CaltechAUTHORS:20170926-135446678
Authors: Border, Kim C.
Year: 2017
A new lemma on the existence of maximal elements of binary relations is proved and applied to a revealed preference relation on price vectors. The resulting maximal elements are equilibrium prices. This technique allows one to generalize results of Aliprantis and Brown [1982], Neuefeind [1980], and Geistdoerfer-Florenzano [1982].https://authors.library.caltech.edu/records/e31jk-6s897An Impossibility Theorem for Spatial Models
https://resolver.caltech.edu/CaltechAUTHORS:20171002-150117835
Authors: Border, Kim C.
Year: 2017
This paper examines the implications for social welfare functions of restricting the domain of individual preferences lo type-one preferences. Type-one preferences assume that each person has a most preferred alternative in a euclidean space and that alternatives are ranked according to their euclidean distance from this point. The result is that if we impose Arrow's conditions of collective rationality, IIA, and the Pareto principle on the social welfare function, then it must be dictatorial. This result may not seem surprising, but it stands in marked contrast to the problem considered by Gibbard and Saiterthwaite of finding a social-choice function. With unrestricted domain, under the Gibbard-Satterthwaite hypotheses, choices must be dictatorial. With type-one preferences this result has been previously shown not to be true. This finding identifies a significant difference between the Arrow and the Gibbard-Satterwaite hypothesis.https://authors.library.caltech.edu/records/e3phc-jcr89Noncooperative Games, Abstract Economies, and Walrasian Equilibria
https://resolver.caltech.edu/CaltechAUTHORS:20171004-164203686
Authors: Border, Kim C.
Year: 2017
The introduction of an additional player to serve as coordinator in an N-person abstract economy leads in a natural way to an N+1-person noncooperative game. Sufficient conditions on the abstract economy are considered which lead to the existence of equilibrium in the resulting game and hence for the abstract economy.https://authors.library.caltech.edu/records/z8ajz-55h10Straightforward Elections, Unanimity, and Phantom Voters
https://resolver.caltech.edu/CaltechAUTHORS:20171005-161613179
Authors: Border, Kim C.; Jordan, J. S.
Year: 2017
Nonmanipulable direct revelation social choice functions are characterized for societies where the space of alternatives is a euclidean space and all voters have separable preferences with a global optimum. If a nonmanipulable choice function satisfies a weak unanimity-respecting condition (which is equivalent to having an unrestricted range) then it will depend only on voters' ideal points. Further, such a choice function will decompose into a product of one-dimensional mechanisms in the sense that each coordinate of the chosen point depends only on the respective coordinate of the voter's ideal points. Each coordinate function will also be nonmanipulable and respect unanimity. Such one-dimensional mechanisms are uncompromising in the sense that voters cannot take an extreme position to influence the choice to their advantage. Two characterizations of uncompromising choice functions are presented. One is in terms of a continuity condition, the other in terms of "phantom voters," i.e., those points which are chosen which are not any voter's ideal point. There are many such mechanisms which are not dictatorial. However, if differentiability is required of the choice function, this forces it to be either constant or dictatorial. In the multidimensional case, nonseparability of preferences leads to dictatorship, even if preferences are restricted to be quadratic.https://authors.library.caltech.edu/records/wckbb-nkp96Social Welfare Functions for Economic Environments with and without the Pareto Principle
https://resolver.caltech.edu/CaltechAUTHORS:20171012-170534239
Authors: Border, Kim C.
Year: 2017
Social welfare functions for private goods economies with classical preferences are considered. It is shown that every social welfare function satisfying a weak nonimposition condition and the independence of irrelevant alternatives axiom is of one of the following forms. It is either null or the class of decisive coalitions is an ultrafilter or the class of anti-decisive coalitions is an ultrafilter.https://authors.library.caltech.edu/records/2nh7t-93726