Jean-Charles Rochet

PLATFORM COMPETITION IN TWO-SIDED MARKETS

Many if not most markets with network externalities are two-sided. To succeed, platforms in industries such as software, portals and media, payment systems and the Internet, must “get both sides of the market on board”. Accordingly, platforms devote much attention to their business model, that is to how they court each side while making money overall. The paper builds a model of platform competition with two-sided markets. It unveils the determinants of price allocation and end-user surplus for different governance structures (profit-maximizing platforms and not-for-profit joint undertakings), and compares the outcomes with those under an integrated monopolist and a Ramsey planner.

Systemic Risk, Interbank Relations and Liquidity Provision by the Central Bank

We model systemic risk in an interbank market. Banks face liquidity needs as consumers are uncertain about where they need to consume. Interbank credit lines allow to cope with these liquidity shocks while reducing the cost of maintaining reserves. However, the interbank market exposes the system to a coordination failure (gridlock equilibrium) even if all banks are solvent. When one bank is insolvent, the stability of the banking system is affected in various ways depending on the patterns of payments across locations. We investigate the ability of the banking system to withstand the insolvency of one bank and whether the closure of one bank generates a chain reaction on the rest of the system. We analyze the coordinating role of the Central Bank in preventing payments systemic repercussions and we examine the justification of the Too-big-to-fail-policy.

Capital requirements and the behaviour of commercial banks

Abstract I study the consequences of capital regulations on the portfolio choices of commercial banks. Elaborating on previous work by Kareken and Wallace (1978), Koehn and Santomero (1980) and Kim and Santomero (1988), I obtain the following results: - If the objective of commercial banks is maximization of the market value of their future profits (value maximizing banks), capital regulations cannot prevent banks from choosing very specialized and very risky portfolios, Risk-based insurance premia are in fact the relevant instrument for that purpose. - On the other hand, if banks behave as portfolio managers (utility maximizing banks) capital regulations can be effective, but only if the weights used in the computation of the ratio are proportional to the systematic risks of the assets (their betas). - Because of limited liability of commercial banks, a minimum capital regulation or a closing rule may become necessary as well to prevent failing banks from ‘betting for resurrection’.

Changes of numeraire, changes of probability measure and option pricing

The use of the risk-neutral probability measure has proved to be very powerful for computing the prices of contingent claims in the context of complete markets, or the prices of redundant securities when the assumption of complete markets is relaxed. We show here that many other probability measures can be defined in the same way to solve different asset-pricing problems, in particular option pricing. Moreover, these probability measure changes are in fact associated with numeraire changes, this feature, besides providing a financial interpretation, permits efficient selection of the numeraire appropriate for the pricing of a given contingent claim and also permits exhibition of the hedging portfolio, which is in many respects more important than the valuation itself. The key theorem of general numeraire change is illustrated by many examples, among which the extension to a stochastic interest rates framework of the Margrabe formula, Geske formula, etc.

A necessary and sufficient condition for rationalizability in a quasi-linear context

Abstract The aim of this note is to give a simple characterization of the rationalizability of decision rules (or action profiles). The necessary and sufficient condition we obtain suggests interesting analogies between the Implementation Problem and Revealed Preference Theory. Two particular cases are examined: 1. (a) The one-dimensional context, which shows that our condition is a generalization of the monotonicity condition of Spence-Mirrlees, 2. (b) The linear set-up, which shows that rationalizability in multiple dimension requires more than monotonicity: it implies also symmetry conditions which are translated by Partial Differential Equations (analogue in this context of Slutsky equations for Revealed Preference Theory).

The Economics of Multidimensional Screening

This chapter, which corresponds to an invited lecture at the Seventh World Congress of the Econometric Society, surveys recent theoretical developments in the use of multidimensional screening models in such applications as contract theory and pricing strategies.

COMPETING MECHANISMS IN A COMMON VALUE ENVIRONMENT

Consider strategic risk-neutral traders competing in schedules to supply liquidity to a risk-averse agent who is privately informed about the value of the asset and his hedging needs. Imperfect competition in this common value environment is analyzed as a multi-principal game in which liquidity suppliers offer trading mechanisms in a decentralized way. Each liquidity supplier behaves as a monopolist facing a residual demand curve resulting from the maximizing behavior of the informed agent and the trading mechanisms offered by his competitors. There exists a unique equilibrium in convex schedules. It is symmetric and differentiable and exhibits typical features of market-power: Equilibrium trading volume is lower than ex ante efficiency would require. Liquidity suppliers charge positive mark-ups and make positive expected profits, but these profits decrease with the number of competitors. In the limit, as this number goes to infinity, ask (resp. bid) prices converge towards the upper (resp. lower) tail expectations obtained in Glosten (1994) and expected profits are zero.

Multi-dimensional screening:: A user's guide

Abstract Multi-dimensional screening models have many potential applications but economists have so far been hindered by the considerable technical difficulties involved in their resolution. This paper studies the simplest formulation of the general screening model, and we provide a complete solution to this case. We then show how this model can be applied to multi-product nonlinear pricing and to multi-product monopoly regulation. Finally, we discuss how the model has been applied to other economic situations of interest, including auction design and optimal taxation.

Large risks, limited liability, and dynamic moral hazard

We study a continuous-time principal-agent model in which a risk-neutral agent with limited liability must exert unobservable effort to reduce the likelihood of large but relatively infrequent losses. Firm size can be decreased at no cost or increased subject to adjustment costs. In the optimal contract, investment takes place only if a long enough period of time elapses with no losses occurring. Then, if good performance continues, the agent is paid. As soon as a loss occurs, payments to the agent are suspended, and so is investment if further losses occur. Accumulated bad performance leads to downsizing. We derive explicit formulae for the dynamics of firm size and its asymptotic growth rate, and we provide conditions under which firm size eventually goes to zero or grows without bounds.

An optimal IPO mechanism

We analyse the optimal Initial Public Offering (IPO) mechanism in a multidimensional adverse selection setting where institutional investors have private information about the market valuation of the shares, the intermediary has private information about the demand, and the institutional investors and intermediary collude. Theorem 1 states that uniform pricing is optimal (all agents pay the same price) and characterizes the IPO price in terms of conditional expectations. Theorem 2 states that the optimal mechanism can be implemented by a non-linear price schedule decreasing in the quantity allocated to retail investors. This is similar to IPO procedures used in the U.K. and France. Relying on French IPO data we perform a GMM structural estimation and test of the model. The price schedule is estimated and the conditions characterizing the optimal mechanism are not rejected.