COMPARATIVE STATICS AND LAWS OF SCARCITY FOR GAMES

A 2law of scarcity2 is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we demonstrate conditions under which all payoffs in the core of any game in a parametized collection have an equal treatment property and 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. Results are compared to the developments in the literature on matching markets, pregames and general equilibrium. This paper expands on results published in Kovalenkov and Wooders, Economic Theory )to appear).