Math/Economic Theory Seminar: Generalized Shapley axioms and value allocation in cooperative games via Hodge theory on graphs

Zoom Meeting Room
Passcode: 830278

Website

Hosts: Ari Stern and Jonathan Weinstein

Abstract:
Lloyd S. Shapley introduced a set of axioms in 1953, now called the Shapley axioms, and showed that the axioms characterize a natural allocation among the players who are in grand coalition of a cooperative game. Recently, A. Stern and A. Tettenhorst showed that a cooperative game can be decomposed into a sum of component games, one for each player, whose value at the grand coalition coincides with the Shapley value.  The component games are defined by the solutions to the naturally defined system of least squares - or Poisson - equations via the framework of the Hodge decomposition on the hypercube graph.
 
In this talk we propose a new set of axioms which characterizes the component games. Furthermore, we realize them through an intriguing stochastic path integral driven by a canonical Markov chain. The integrals are natural representation for the expected total contribution made by the players for each coalition, and hence can be viewed as their fair share. This allows us to interpret the component game values for each coalition also as a valid measure of fair allocation among the players in the coalition. Finally, we extend the path integrals on general graphs and discover a fundamental connection between stochastic integrations and Hodge theory on graphs.

16th Annual Economics Graduate Student Conference

About Our Conference

The EGSC is a student-run conference that has been held every fall since 2006 by the Department of Economics at Washington University.

The goal of the conference is to provide graduate students from all fields of economics an opportunity to present their work to their fellow students from across the country.