Theoretical Economics 13 (2018), 307–340

Tweet

### Collusion constrained equilibrium

*Rohan Dutta, David K. Levine, Salvatore Modica*

#### Abstract

We study collusion within groups in non-cooperative
games. The primitives are the preferences of the players, their assignment
to non-overlapping groups and the goals of the groups. Our notion
of collusion is that a group coordinates the play of its members among
different incentive compatible plans to best achieve its goals. Unfortunately,
equilibria that meet this requirement need not exist. We instead introduce
the weaker notion of collusion constrained equilibrium. This
allows groups to put positive probability on alternatives that are
suboptimal for the group in certain razor's edge cases where the set
of incentive compatible plans changes discontinuously. These collusion
constrained equilibria exist and are a subset of the correlated equilibria
of the underlying game. We examine four perturbations of the underlying
game. In each case we show that equilibria in which groups choose
the best alternative exist and that limits of these equilibria lead
to collusion constrained equilibria. We also show that for a sufficiently
broad class of perturbations every collusion constrained equilibrium
arises as such a limit. We give an application to a voter participation
game showing how collusion constraints may be socially costly.

Keywords: Collusion, group

JEL classification: C72, D70

Full Text: PRINT VIEW Supplementary appendix