[Paper Review] Maximal Information Propagation with Budgets

Haomin Shi, Yao Zhang+3 more|arXiv (Cornell University)|Dec 9, 2019

Game Theory and Applications16 references4 citations

TL;DR

This paper proposes a novel budget-balanced reward mechanism for incentivizing full information propagation in social networks, where agents are rewarded based on hierarchical contributions to maximize reach. The mechanism ensures propagation is a dominant strategy, fully spends the budget, and maintains time efficiency through dynamic reward allocation.

ABSTRACT

In this paper, we present an information propagation game on a network where the information is originated from a sponsor who is willing to pay a fixed total budget to the players who propagate the information. Our solution can be applied to real world situations such as advertising via social networks with limited budgets. The goal is to design a mechanism to distribute the budget such that all players in the social network are incentivized to propagate information to all their neighbours. We propose a family of mechanisms to achieve the goal, where propagating information to all neighbours is a dominant strategy for all players. Furthermore, we also consider the cases where the budget has to be completely shared.

Motivation & Objective

• Address the challenge of incentivizing full propagation of information in social networks under a fixed budget constraint.
• Design a reward mechanism that ensures all agents propagate to all neighbors as a dominant strategy.
• Achieve complete budget utilization (budget balance) while maintaining incentive compatibility.
• Ensure timely propagation by making early action a dominant strategy to prevent deadlocks.
• Provide a practical, scalable mechanism applicable to real-world scenarios like viral marketing and survey distribution.

Proposed method

• Define an information propagation game on a network graph with a sponsor providing a fixed total budget.
• Introduce a hierarchical reward distribution scheme where rewards are shared based on contribution chains and ancestor counts.
• Use a recursive reward allocation algorithm that assigns base rewards (Vb) and hierarchical rewards (Vh) to nodes based on propagation depth and parent contributions.
• Apply a parameterized discount factor α to reduce future rewards, ensuring earlier propagation is more beneficial.
• Formalize the mechanism using a prisoners’ dilemma framework to prove strong propagation incentive compatibility (PIC).
• Introduce a time vector and prove time efficiency by showing that delaying propagation reduces expected rewards due to compounding discounting.

Experimental results

Research questions

• RQ1 How can a fixed budget be allocated to ensure all agents propagate information to all their neighbors?
• RQ2 What reward mechanism guarantees that propagating to all neighbors is a dominant strategy for every agent?
• RQ3 How can the entire budget be fully spent while maintaining incentive compatibility?
• RQ4 What conditions ensure that agents propagate as early as possible to avoid propagation deadlocks?
• RQ5 Can the mechanism be extended to handle practical issues like Sybil attacks or real-time propagation timing?

Key findings

• The proposed mechanism achieves strong propagation incentive compatibility (PIC), ensuring that propagating to all neighbors is a dominant strategy for every agent.
• The mechanism is budget balanced, meaning the entire fixed budget is fully spent through recursive reward allocation.
• Time efficiency is proven: delaying propagation reduces expected rewards due to compounding discounting, making immediate propagation dominant.
• The reward distribution scheme uses a hierarchical structure where rewards depend on the number of ancestors (m), ensuring fairness and incentive alignment.
• A prisoners’ dilemma framework with parameters α and ε is used to formally prove that propagation dominates non-propagation in all cases.
• The mechanism is robust in tree-like network structures and can be extended to general graphs with appropriate modifications.