Kempten Autumn Talks

Title of the lecture

“Values of cooperative games: marginalism, egalitarianism and implementation”

Abstract

The central problem in the theory of cooperative games is how to divide among players the gain resulting from the cooperation of all of them. "Values" are allocation rules designed to solve the problem and specifying, for each game, one well-defined division. The first and foremost of them, the Shapley value, relies on "marginalism": the share of each player is determined solely by his contributions to all coalitions. Many attempts to reconcile this approach with the egalitarian one have led to numerous classes of values with various appealing properties. An important problem is that of "implementation" of such values, i.e. constructing mechanisms under which the division prescribed by the value under consideration will result. Two approaches to this problem co-exist in the literature: a "procedural" one starting from the classical probabilistic interpretation of the Shapley value and adapting it to other values, and a dynamic one aimed at obtaining the relevant values as subgame-perfect Nash equilibria of appropriate
non-cooperative games. This talk will focus on how some of the above classes of values can be implemented along these lines.

Slides of the lecure