Farsighted manipulation and exploitation in networks

Péter Bayer,P Jean-Jacques Herings,Ronald Peeters

doi:10.1016/j.jet.2021.105311

Péter Bayer, P Jean-Jacques Herings + Show 1 more

Open Access

https://doi.org/10.1016/j.jet.2021.105311

Copy DOI

Abstract

Farsighted economic agents can use their advantage to exploit their more myopic counterparts. In public goods games played on networks, such an agent will attempt to manipulate as many of his neighbors as possible to contribute to the public good. We study the exploitation of a myopic population by a single farsighted player in such games. We show the existence and payoff-uniqueness of optimal farsighted strategies in every network structure. For all optimal strategies, the set of absorbing effort profiles is non-empty and is generally neither a subset or a superset of the set of Nash equilibria of the static game. Optimal long-run effort profiles for the farsighted player can be reached via a simple dependence-withdrawal strategy and the farsighted player's effects on the myopic players are only felt locally. We characterize the lower and upper bounds of long-run payoffs the farsighted player can attain in a given network and examine comparative statics with respect to adding a new link. The farsighted player always benefits from linking to more opponents and is always harmed by his neighbors linking to each other.

Highlights

In many social and economic settings, agents produce goods for their own consumption with other agents benefitting from these goods as a form of externality
Proposition 3.8 identifies an effort profile which is both acceptable for the myopic players, as they are playing best responses, and for the farsighted player, who gets the maximum instantaneous payoff attainable from this position. By this construction we show that the set of absorbing effort profiles is non-empty for every SSPE of Γ, and that it has a non-empty intersection with the set of Nash equilibria of the static game Γ
In this paper we consider the private provision of local public goods game, a gameclass with a wide array of applicability and a strong body of theoretical contributions

Summary

Introduction

In many social and economic settings, agents produce goods for their own consumption with other agents benefitting from these goods as a form of externality. The farsighted player’s optimal outcome is to exploit the myopic neighbors belonging to the maximum independent set of his neighborhood and this outcome can be reached by a simple dependence-withdrawal strategy. For strategy profile sand a T -long history h ∈ HT , let ut0(h, s) denote the expected instantaneous payoff that player 0 receives in period T +t−1. It holds that u10(h, s) = π0(siT (h), xT−−iT1) = π0(xT ). For J ⊆ I0, let RsJ (x) ⊆ Rs(x) denote the set of effort profiles that are reachable from x in s if updates are restricted to the players in J.

No exit

Conclusion

A Appendix