Towards a theory of platform dynamics

• DOI: http://doi.org/10.1111/jems.12312
• Author: Luís Cabral
• Date: 01 January 2019
• Published date: 01 January 2019

Received: 19 August 2018

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Accepted: 20 August 2018

DOI: 10.1111/jems.12312

ORIGINAL ARTICLE

Towards a theory of platform dynamics

Luís Cabral

1,2

1

Department of Economics, Stern School

of Business/Kaufman Management

Center, New York University, New York

City, New York

2

CEPR, London, UK

Correspondence

Luís Cabral, Department of Economics,

Stern School of Business/Kaufman

Management Center, New York

University, New York City, NY 10012.

Email: lcabral@stern.nyu.edu

Abstract

I introduce a dynamic framework to analyze platforms. The (single) platform

owner sets prices at the beginning of each period. Agents (buyers, sellers,

readers, consumers, merchants, etc.) make platform membership decisions

occasionally. I show that an optimal platform pricing addresses two

externalities: across sides and across time periods. This results in optimal

prices which depend on platform size in a nontrivial way. By means of

numerical simulations, I examine the determinants of equilibrium platform

size, showing that the stationary distribution of platform size may be bimodal,

that is, with some probability the platform remains very low or takes very long

to increase in size. I also contrast the dynamics of proprietary versus

nonproprietary (i.e., zero‐priced) platforms, and consider the specific case of

asymmetric platforms (one side cares about the other but not vice versa).

KEYWORDS

dynamics, platforms, two‐sided markets

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INTRODUCTION AND OVERVIEW

Market platforms are as old as human society. However, as the “digital revolution”unfolds, their number and economic

importance grows considerably. Some platforms are household names (Alibaba, Airbnb, Uber, Apple’s iOS, and Sony’s

PlayStation); many other are less known or have fallen into oblivion: For each successful platform, there are dozens of

other platforms that “failed to launch.”

This observation motivates much of my analysis, which addresses a number of issues related to two‐sided platforms,

both positive and normative issues: Why do some platforms succeed while others fail? To what extent is there a

chicken‐and‐egg problem in platform formation (e.g., buyers do not want to join a trading platform unless there are

sellers, and vice versa)? If so, should a platform owner subsidize membership? More generally, what is the optimal

pricing policy for a platform owner? Is welfare higher or lower in a proprietary platform vis‐à‐vis a nonproprietary one

(where prices are uniformly set a marginal cost level)? How does platform size evolve over time?

These and various other questions have been addressed in past research by a series of papers on two‐sided markets.

One common feature of most of these papers is that they are static: Both platform owners and agents make one‐time

decisions regarding prices, membership, and use. Static models have a long tradition in economics, and for a good

reason, they provide a good approximation for equilibrium “once the dust settles,”that is, once convergence to

equilibrium takes place.

However, anecdotal evidence from many markets suggests that time plays an important role in agents’decisions.

Specifically, inertia is an important force in many agents’decisions. Take smartphones, for example, while usage

decisions are made on a regular basis, “membership”decisions are only made at irregular moments in time: you do not

decide everyday which phone to own, much less which smartphone operating system to use. In other words, platform

membership decisions are durable decisions.

J Econ Manage Strat. 2019;28:60–72.wileyonlinelibrary.com/journal/jems60

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© 2019 Wiley Periodicals, Inc.