Ed Green's personal web page
§ 1. Research
“Individual-level randomness in a nonatomic population” is unpublished research that provides a set-theoretic construction of a continuum of i.i.d. random variables, such that the integral of each sample path with respect to a measurable subset of the indexes is the product of the measure of the index subset and the expectation of the random variable. The construction is an alternative to a construction by nonstandard analysis. (Cf. Robert M. Anderson, ”Non-standard analysis with applications to economics,” in W. Hildenbrand and H. Sonnenschein, editors, Handbook of Mathematical Economics, volume 4, chapter 39, pages 2145–2208. Elsevier, 1991.) This paper was rejected for publication, but all of the referees (4 reports were received in total) judged that the results are mathematically sound.
“Iterated elimination of dominated strategies in countable-strategy games” [working title] Draft, 2011.04.28.
“Events concerning knowledge” 2012.04.17. Common knowledge of a Borel event is shown to be a co-analytic event, and is therefore universally measurable. An extension of Aumann's “agreement theorem” regarding common knowledge of posterior probabilities is proved in the framework of a measure space defined on a complete, separable, sigma-compact metric space.
“Embedding an analytic equivalence relation in the transitive closure of a Borel relation [Journal of Logic and Analysis 5:4 (2013)]. The transitive closure of a reflexive, symmetric, Borel relation is an analytic equivalence relation. Does some smaller class contain the transitive closure of every reflexive, symmetric, closed relation? An essentially negative answer is provided here. The Baire space is homeomorphic to an open subset of itself, X, that has an open complement. It is shown that any analytic equivalence relation E on the Baire space can be embedded homeomorphically in the transitive closure of a reflexive, symmetric, closed relation on X. Specifically, the relation can be constructed as the union of two closed equivalence relations. This result shows that Aumann's common-knowledge operator can map individuals' information partitions of low complexity to a considerably more complex common-knowledge partition.
“A parsimonious theory of evidence-based choice” (with Fatemeh Borhani) 2016.01.15. Primitive entities of the theory presented in this article are a body of evidence available to an agent (called an evidential state) and an alternative in a set, from which the agent might choose. Assumptions are stated regarding the space of possible evidential states. Under those assumptions, while the space of evidential states is not necessarily a Boolean algebra, it can be embedded in a structure-preserving way into a canonical sigma-field of events. A plan is a mapping from evidential states to choice alternatives. A consistency condition for plans, reminiscent of Savage's sure-thing principle, is formulated. The condition is neither necessary nor sufficient for a plan to be rationalized by subjective-utility maximization with respect to a probability measure on the canonical sigma-field. A structure of evidential states may contain, or coincide with, a substructure that models a process of experimental learning. A plan specified on such a substructure satisfies the consistency condition if, and only if, it can be rationalized by maximization of subjective conditional expected utility.
“Identifying the presence or absence of cognitive bias in situations resembling the Monty Hall problem” (with Fatemeh Borhani) 2017.06.18. People reason heuristically in situations resembling inferential puzzles such as Bertrand's box paradox and the Monty Hall problem. The practical significance of that fact for economic decision making is uncertain. Criteria are derived here, applicable to both experimental and non-experimental situations, regarding circumstances under which heuristic reasoning in such inferential-puzzle situations does, or does not, lead to “cognitively biased” decisions different from what sound Bayesian reasoning would recommend.
Presentation slides for “A peculiar coin-tossing model”
My CV on the PSU Economics Department website contains further information regarding my published research.
§ 2. Some courses that I have taught
§ 3. PSU Economics Department web page for Ed Green
Go to the Penn State Economics Department web page for Ed Green.
§ 4. Personal information
§ 4.2. Healthcare advance directive
In case of medical emergency, here is my Health Care Power of Attorney and Declaration Regarding Treatment. It is digitally signed with this GPG detached digital signature executed on 2013-05-23. The original, signed, notarized document from which this PDF file was scanned, is on file in my home. By uniform state law (including Pa. Stat. tit. 73 §2260.101 et seq.) and federal law (15 U.S.C. 7001), doctors and hospital administrators can rely directly on this scanned, digitally signed document. In order to verify the signature, use my GPG public key (provided above) and follow the instructions provided in the relevant GPG Handbook chapter.