Scheduling a Cascade with Opposing Influences

TL;DR

This paper studies how to optimally schedule the spread of ideas in a society considering opposing influences, generalizing existing models to account for diverse behaviors and analyzing the complexity of strategy design.

Contribution

It introduces a generalized model for influence propagation with opposing effects, analyzes the difficulty of designing non-adaptive strategies, and provides algorithms under certain conditions.

Findings

Influences help or hurt propagation depending on idea appeal.

Hardness results for non-adaptive strategy computation.

Algorithm for optimal non-adaptive strategies with i.i.d. behavior probabilities.

Abstract

Adoption or rejection of ideas, products, and technologies in a society is often governed by simultaneous propagation of positive and negative influences. Consider a planner trying to introduce an idea in different parts of a society at different times. How should the planner design a schedule considering this fact that positive reaction to the idea in early areas has a positive impact on probability of success in later areas, whereas a flopped reaction has exactly the opposite impact? We generalize a well-known economic model which has been recently used by Chierichetti, Kleinberg, and Panconesi (ACM EC'12). In this model the reaction of each area is determined by its initial preference and the reaction of early areas. We generalize previous works by studying the problem when people in different areas have various behaviors. We first prove, independent of the planner's schedule, influences help (resp., hurt) the planner to propagate her idea if it is an appealing (resp., unappealing) idea. We also study the problem of designing the optimal non-adaptive spreading strategy. In the non-adaptive spreading strategy, the schedule is fixed at the beginning and is never changed. Whereas, in adaptive spreading strategy the planner decides about the next move based on the current state of the cascade. We demonstrate that it is hard to propose a non-adaptive spreading strategy in general. Nevertheless, we propose an algorithm to find the best non-adaptive spreading strategy when probabilities of different behaviors of people in various areas drawn i.i.d from an unknown distribution. Then, we consider the influence propagation phenomenon when the underlying influence network can be any arbitrary graph. We show it is $\#P$-complete to compute the expected number of adopters for a given spreading strategy.