DeepAI AI Chat
Log In Sign Up

Public Goods Games in Directed Networks

by   Christos Papadimitriou, et al.

Public goods games in undirected networks are generally known to have pure Nash equilibria, which are easy to find. In contrast, we prove that, in directed networks, a broad range of public goods games have intractable equilibrium problems: The existence of pure Nash equilibria is NP-hard to decide, and mixed Nash equilibria are PPAD-hard to find. We define general utility public goods games, and prove a complexity dichotomy result for finding pure equilibria, and a PPAD-completeness proof for mixed Nash equilibria. Even in the divisible goods variant of the problem, where existence is easy to prove, finding the equilibrium is PPAD-complete. Finally, when the treewidth of the directed network is appropriately bounded, we prove that polynomial-time algorithms are possible.


page 1

page 2

page 3

page 4


Computing Equilibria in Binary Networked Public Goods Games

Public goods games study the incentives of individuals to contribute to ...

Strategic Payments in Financial Networks

In their seminal work on systemic risk in financial markets, Eisenberg a...

Selfish Caching Games on Directed Graphs

Caching networks can reduce the routing costs of accessing contents by c...

Computing Bayes-Nash Equilibria in Combinatorial Auctions with Verification

Combinatorial auctions (CAs) are mechanisms that are widely used in prac...

On the Existence and Structure of Mixed Nash Equilibria for In-Band Full-Duplex Wireless Networks

This article offers the first characterisation of mixed Nash equilibria ...

A Note on Optimal Fees for Constant Function Market Makers

We suggest a framework to determine optimal trading fees for constant fu...

Pure-Circuit: Strong Inapproximability for PPAD

The current state-of-the-art methods for showing inapproximability in PP...