On authority distributions in organizations: Equilibrium.

*(English)*Zbl 1054.91011Summary: One assumption in the Shapley-Shubik power index is that there is no interaction nor influence among the voting members. This paper will apply the command structure of L. S. Shapley [A Boolean model of organization authority based on the theory of simple games. Mimeo (1994)] to model members’ interaction relations by simple games. An equilibrium authority distribution is then formulated by the power-in/power-out mechanism. It turns out to have much similarity to the invariant measure of a Markov chain and therefore some similar interpretations are followed for the new setting. In some sense, one’s authority distribution quantifies his general administrative power in the organization and his long-run influence on all members. We provide a few applications in conflict resolution, college and journal ranking, and organizational choice.

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\textit{X. Hu} and \textit{L. S. Shapley}, Games Econ. Behav. 45, No. 1, 132--152 (2003; Zbl 1054.91011)

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