# Complete Submodularity Characterization in the Comparative Independent Cascade Model

## TL;DR

This paper provides a complete characterization of submodularity in the comparative independent cascade model for two ideas, analyzing competing and complementary scenarios, and introduces a One-Shot model where only the strongest idea propagates.

## Contribution

It offers the first full characterization of submodularity in the Com-IC model and introduces the One-Shot model to analyze idea propagation with less patience.

## Key findings

- Submodularity is fully characterized for competing and complementary ideas.
- In the One-Shot model, only the strongest idea exhibits submodularity.
- The One-Shot model captures less patient agent behavior in idea spread.

## Abstract

We study the propagation of comparative ideas or items in social networks. A full characterization for submodularity in the comparative independent cascade (Com-IC) model of two-idea cascade is given, for competing ideas and complementary ideas respectively, with or without reconsideration. We further introduce One-Shot model where agents show less patience toward ideas, and show that in One-Shot model, only the strongest idea spreads with submodularity.