IST Lunch Bunch

We study games in which each player can simultaneously exert costly
effort to provides different benefits to some of the other players.
The static analysis of the game yields a prediction of no cooperation,
while a standard repeated games approach yields a folk theorem in
which anything goes. To obtain more refined predictions about repeated
play, we start from the observation that outcomes in such settings are
typically negotiated in multilateral meetings involving various
subsets of players. Thus, our goal is to find and describe effort
profiles that can be sustained in equilibrium despite the possibility
of coordinated coalitional deviations.

In general, even the existence of such solutions is a difficult
matter. This paper argues that there are simple, efficient, and
coalition-proof equilibria that can be found by analyzing the setting
as a network of marginal benefit flows among players. In these
equilibria each player's effort is equal to a sum (appropriately
weighted) of the efforts of those whose contributions help him at the
margin; this is an eigenvector centrality condition in the network. To
establish the main result, we study connections among three concepts:
coalition-proof equilibria of a repeated game; Lindahl equilibria
(which are "market" solutions in a static public goods environment);
and effort profiles satisfying the centrality condition. We also find
a simple spectral characterization of Pareto-efficient outcomes of our
public goods environment: they are the ones where a certain marginal
benefits matrix has a largest eigenvalue of 1.