Infinite Choice Transferable Utility Games and a n Application to Wage Distribution in Firms

Abstract

Much work has been done on extending the Shapley value tofinite multi-choice transferable utility games. However, little of this work has dealt with infinite choice games. Thispaper extends the Shapley value to infinite choice games and shows that this Shapley value satisfies six simple axioms: weak symmetry, efficiency, additivity, the null worker axiom,no poy for no work and strong scale invariance. In addition, this paper gives a similar axiomatizationfor extending the Shapley value tofinite multi-choice games. Justification for using this axiomatization for wage distribution infirm problems is given and compared to thejustificati onfor the Aumann-Shapley value. Taking advantage of thefact that total-factor productivity ispositively correlated withfirm size, this paper uses 2012 Current Population Survey data to test if workers ore being paid their expected Shapley value in earnings. Union membership is found to have a positive effect on bargaining strength that is statistically significant at the 9596 confidence level.