Group network effects in price competition

TL;DR

This paper analyzes how social groupings and network effects influence price competition in duopolies, revealing multiple pure equilibrium outcomes depending on group structure and interaction asymmetries.

Contribution

It introduces a model of price competition with demand influenced by network effects partitioned into groups, showing diverse equilibrium outcomes.

Findings

Multiple pure price equilibria exist under group-based network effects.

Asymmetry in group interactions reduces the number of groups needed for equilibrium.

Symmetric undirected networks require at least five groups for diverse outcomes.

Abstract

The partition of society into groups, polarization, and social networks are part of most conversations today. How do they influence price competition? We discuss Bertrand duopoly equilibria with demand subject to network effects. Contrary to models where network effects depend on one aggregate variable (demand for each choice), partitioning the dependence into groups creates a wealth of pure price equilibria with profit for both price setters, even if positive network effects are the dominant element of the game. If there is some asymmetry in how groups interact, two groups are sufficient. If network effects are based on undirected and unweighted graphs, at least five groups are required but, without other differentiation, outcomes are symmetric.