Comparative statics and laws of scarcity for games

Alexander Kovalenkov and Myrna Wooders
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Alexander Kovalenkov: University of North Carolina

A chapter in Rationality and Equilibrium, 2006, pp 141-167 from Springer

Abstract: Summary A “law of scarcity” 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 parameterized 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 (26, 383–396, 2005).

Keywords: Monotonicity; cooperative games; clubs; games with side payments (TU games); cyclic monotonicity; law of scarcity; law of demand; approximate cores; effective small groups; parameterized collections of games (search for similar items in EconPapers)
Date: 2006
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Related works:
Working Paper: Comparative statics and laws of scarcity for games (2004)
Working Paper: COMPARATIVE STATICS AND LAWS OF SCARCITY FOR GAMES (2004)
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DOI: 10.1007/3-540-29578-X_8

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