Juuso Välimäki

A Robust Folk Theorem for the Prisoner's Dilemma☆

We prove the folk theorem for the Prisoners dilemma using strategies that are robust to private monitoring. From this follows a limit folk theorem: when players are patient and monitoring is sufficiently accurate, (but private and possibly independent) any feasible individually rational payoff can be obtained in sequential equilibrium. The strategies used can be implemented by finite (randomizing) automata.

Learning and Strategic Pricing

The authors consider a single consumer buying a stream of goods from different sellers over time. The true value of each sellers product is initially unknown. Additional information is obtained by experimentation. For exogenous prices, this is a multiarmed bandit problem. The innovation here is to endogenize the cost of experimentation by allowing for price competition between the sellers. Prices determine the intertemporal costs and benefits of learning for buyer and sellers. All Markov perfect equilibria are efficient. Prices below marginal cost sustain experimentation. Intertemporal exchange of the gains of learning is necessary to support efficient experimentation. Copyright 1996 by The Econometric Society.

The Dynamic Pivot Mechanism

We consider truthful implementation of the socially efficient allocation in an independent private-value environment in which agents receive private information over time. We propose a suitable generalization of the pivot mechanism, based on the marginal contribution of each agent. In the dynamic pivot mechanism, the ex-post incentive and ex-post participation constraints are satisfied for all agents after all histories. In an environment with diverse preferences it is the unique mechanism satisfying ex-post incentive, ex-post participation and efficient exit conditions. We develop the dynamic pivot mechanism in detail for a repeated auction of a single object in which each bidder learns over time her true valuation of the object. We show that the dynamic pivot mechanism is equivalent to a modified second price auction.

Experimentation in Markets

We present a model of entry and exit with Bayesian learning and price competition. A new product of initially unknown quality is introduced in the market, and purchases of the product yield information on its true quality. We assume that the performance of the new product is publicly observable. As agents learn from the experiments of others, informational externalities arise. We determine the Markov Perfect Equilibrium prices and allocations. In a single market, the combination of the informational externalities among the buyers and the strategic pricing by the sellers results in excessive experimentation. If the new product is launched in many distinct markets, the path of sales converges to the efficient path in the limit as the number of markets grows.

Dynamic Pricing of New Experience Goods

We develop a dynamic model of experience goods pricing with independent private valuations. We show that the optimal paths of sales and prices can be described in terms of a simple dichotomy. In a mass market, prices are declining over time. In a niche market, the optimal prices are initially low followed by higher prices that extract surplus from the buyers with a high willingness to pay. We consider extensions of the model to integrate elements of social rather than private learning and turnover among buyers.

Information in Mechanism Design

We survey the recent literature on the role of information in mechanism design. First, we discuss an emerging literature on the role of endogenous payoff and strategic information for the design and the efficiency of the mechanism. We specifically consider information management in the form of acquisition of new information or disclosure of existing information. Second, we argue that in the presence of endogenous information, the robustness of the mechanism to the type space and higher order beliefs becomes a natural desideratum. We discuss recent approaches to robust mechanism design and robust implementation.

Dynamic Common Agency

We consider a general model of dynamic common agency with symmetric information. We focus on Markov perfect equilibria and characterize the equilibrium set for a refinement of the Markov perfect equilibria. Particular attention is given to the existence of a marginal contribution equilibrium where each principal receives her contribution to the coalition of agent and remaining principals. The structure of the intertemporal payoffs is analyzed in terms of the flow marginal contribution. As a byproduct, new results for the static common agency game are obtained. The general characterization results are then applied to two dynamic bidding games for a common agent: (i) multi-task allocation and (ii) job matching under uncertainty.

Market Diffusion with Two-Sided Learning

The diffusion of a new product of uncertain value is analyzed in a duopolistic market in continuous time. The two sides of the market, buyers and sellers, learn the true value of the new product over time as a result of experimentation. Buyers have heterogeneous preferences over the products and sellers compete in prices. The pricing policies and market shares of the sellers in the unique Markov perfect equilibrium are obtained explicitly. The dynamics of the equilibrium market shares display excessive sales of the new product relative to the social optimum in early stages and too low sales later on. The dynamic resolution of uncertainty implies ex post differentiation and hence both sellers value information positively. As information is generated only by experiments with the new product, this relaxes the price competition in the dynamic setting. Finally, the diffusion path of a successful product is shown to be S-shaped.

Efficient Dynamic Auctions

We consider the truthful implementation of the socially efficient allocation in a dynamic private value environment in which agents receive private information over time. We show that a suitable generalization of the Vickrey-Clark-Groves mechanism, based on the marginal contribution of each agent, leads to truthtelling in every period. A leading example of a dynamic allocation model is the sequential auction of a single good in which the current winner of the object receives additional information about her valuation. We show that a modified sequential second price auction in which only the current winner makes a positive payment leads to truthtelling. In general allocation problems, the marginal contribution mechanism continues to induce truthtelling in every period but may now include positive transfers for many agents.

Dynamic Price Competition

We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption characterize Markovian equilibria for finite and infinite horizon versions of the model and show that the stationary infinite horizon version of the model possesses an equilibrium where all the sellers receive an equilibrium payoff equal to their marginal contribution to the social welfare.