This paper is motivated by accusations of G. Engl and S. Scotchmer that a paper of mine duplicated results of theirs, dated 1991-1996. They also claim my results, showing cores of large games treat similar players similarly, are subsequent to theirs. My results date back to Stony Brook Working Paper #184, 1977. Some of these are reported in Bennett and Wooders (1979). See especially Theorem 9 of that paper, stating that approximate core payoffs have the property that most players who are similar are treated nearly identically. This result also appears in a 1982 Cowles Foundation Discussion Paper with Martin Shubik, available on my web pages. This result is extended in my paper in the 1994 Mertens-Sorin volume, where it appears as Propostion A.1.1 (in the Appendix) and A.1.2. Thus, the Engl-Scotchmer claim that this research on the equal treatment property of approximate cores of games with many players is subsequent to theirs is foolish. Moreover, while it can be shown that my results on equal treatment imply theirs, the converse is unknown.
Scotchmer also claim that the attribute core in my research is taken from their work -- the attribute core is just a name for the equal treatment core of a game where the players are interpreted as units of commodities or as possible attributes of players. Both the equal treatment core and interpreting players as commodities has a long history, going back to research of Shubik, Owen and others -- I cannot credit either the concept or the name to Engl-Scotchmer and I surely cannot take credit for the concept myself. The core concept in Engl-Scotchmer is distinct. Here is a simple example. In addition, my paper also points out that in fact Engl and Scotchmer mis-represent the literature and accord to themselves results and concepts that have been in the published literature for over a decade. Moreover, changes in their papers to obtain results very similar to prior results in my research are documented and careful citations of papers published in journals or by universities are provided. (Here is a funny --but sad -- story). The link above describes in more detail some of the events leading to the publication of my paper.
Working Paper version.
(With fewer typos than the published version.)
The following paper has been published in Journal of Mathematical Economics 36, Issue 4, 15 December 2001, Pages 295-309, the only definitive repository of the content that has been certified and accepted after peer review. DOI: 10.1016/S0304-4068(01)00078-7
Copyright © 2001 Elsevier Science B.V. All rights reserved.
(Some errors were introduced in the final printed version of this paper -- some changes due to Elsevier and without my permission in the form (although not the meaning) of quotations, some spelling errors, and so on. One of the most bothersome errors is a "stutter" on page 306. The sentence beginning in the third line of page 306 with "As" should read:"As noted, the relationship between exhaustion of gains to scale and per capita boundedness in E&S (1996), Proposition 1, is very similar to one direction of MW (1994), Theorem 4 and, for this author, has origins in research dating back to 1979 -- games satisfying PCB can be approximated by games satisfying MES or, in other words, exhaustion of gains to scale." Also, on the same page, the sentence "Thus, I would surely not claim that the E&S convergence result duplicates either my prior or concurrent research" should be earlier in the paragraph.)
Myrna H. Wooders, Department of Economics, University of Warwick, Coventry CV47AL, UK Received 27 January 2000; revised 18 July 2001; accepted 17 September 2001 Available online 11 December 2001.
Some assertions in Engl and Scotchmer [J. Math. Econ. 26 (1996)209] concerning prior literature are corrected. In addition, I discuss the differences between the convergence results of Engl and Scotchmer [J.Math. Econ. 26 (1996) 209], and those of this author, alone and with Martin Shubik, dating from 1980. Our prior and concurrent results show that (approximate) epsilon-cores of games with many players treat most similar players nearly equally; that is, approximate cores of large games have the equal treatment property. The convergence result of Engl and Scotchmer shows that, in per capita terms, epsilon-core payoffs to sufficiently large groups of players can be approximated by equal-treatment payoffs.
Core; Hedonic core; Equal-treatment;Monotonicity; Convergence; Conduct in science
JEL classification codes: C7; D4; D7
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