Contribution Games in Social Networks

TL;DR

This paper analyzes network contribution games in social networks, exploring equilibrium existence, complexity, and efficiency, with a focus on reward functions and minimum effort scenarios, providing bounds and convergence results.

Contribution

It characterizes equilibrium properties and efficiency bounds in network contribution games with various reward functions, including minimum effort cases.

Findings

Price of anarchy is at most 2 for concave reward functions

Equilibrium existence and complexity depend on reward function types

Tight bounds for approximate equilibria and convergence in minimum effort games

Abstract

We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure the success we use a reward function for each relationship. Every agent is trying to maximize the reward from all relationships that it is involved in. We consider pairwise equilibria of this game, and characterize the existence, computational complexity, and quality of equilibrium based on the types of reward functions involved. For example, when all reward functions are concave, we prove that the price of anarchy is at most 2. For convex functions the same only holds under some special but very natural conditions. A special focus of the paper are minimum effort games, where the reward of a relationship depends only on the minimum effort of any of the participants. Finally, we show tight bounds for approximate equilibria and convergence of dynamics in these games.