Laws of scarcity for a finite game - exact bounds on estimations

Summary. A law of scarcity is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we show that equal treatment core payoff vectors satisfy a condition of cyclic monotonicity. Our results are developed for parameterized collections of games and exact bounds on the maximum possible deviation of approximate core payoff vectors from satisfying a law of scarcity are stated in terms of the parameters describing the games. We note that the parameters can, in principle, be estimated.Received: 21 November 2002, Revised: 7 October 2003, JEL Classification Numbers: C71, C78, D41. Correspondence to: Myrna WoodersThis research was initiated in 1994 when the first author was in the IDEA Ph.D. Program of the Autonomous University of Barcelona. Support by the IBM Fund Award, the Latané Fund, the University of North Carolina Research Council, and the Warwick Centre for Public Economics is acknowledged. The second author gratefully acknowledges the support of the Direccio General dUniversitats of Catalonia, the Social Sciences and Humanities Research Council of Canada, and the Department of Economics of the Autonomous University of Barcelona. This article is dedicated to Marcel (Ket) Richter, a distinguished researcher and a wonderful teacher and mentor to his students. We are delighted to contribute our paper to this special issue of Economic Theory in his honor.