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

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. Copyright Springer-Verlag Berlin/Heidelberg 2005