Centripetal and Centrifugal Influence: When Positive Network Effects Stabilize Competition

What the paper says

A central issue in price competition with positive network effects is the potential for small price changes to trigger abrupt chain reactions, leading to market tipping, winner-take-all scenarios, and zero-profit equilibria. We show that in a duopoly where consumers are not anonymous but partitioned into at least two groups, a simple group-based network structure can, by itself, generate downward-sloping demand and support profitable shared-market equilibria. These are subgame-perfect pure price equilibria in which both firms earn strictly positive profit. Triggering a bandwagon effect and tipping the market remains possible, but requires aggressive price deviations, or price shocks, that produce demand jumps. However, this is not always profitable, and the fear of bankruptcy can be sufficient to stabilize firms in equilibrium. The result relies on having one group with centripetal influence (stronger impact on peers) and another with centrifugal influence (stronger impact on outsiders). It requires no additional sources of heterogeneity or product differentiation. This mechanism shows that positive network effects – when group structured – can endogenously generate stability in price competition. The analysis reconciles the coexistence of local stability and the potential for tipping, offering a unified explanation of how markets with strong network effects can sustain both competition and profitability. We draw a parallel to Turing’s reaction–diffusion patterns and reinterpret Becker’s intuition that social influence can produce stable outcomes, even when demand may exhibit upward-sloping segments.