Long-Term Contracting with Markovian Agents

Princeton University, Princeton NJ

Investigators

Abstract

Advances in information processing and new management strategies have made long-term, non-anonymous relations between buyers and sellers feasible in an increasing number of markets. Retailers now can -- and do -- store large databases on consumers' choices. Marketing experts are increasingly advising firms to use these data to make pricing decisions. Of course, this creates an incentive for consumers to make their own decisions knowing that the retailer may try to exploit the resulting data. This research project will study long-term, non anonymous contracts between economic players to answer the question of whether and how these contracts can achieve effecient economic outcomes. The PI will investigate the conditions under which these outcomes are efficient; whenever the outcomes are inefficient, the nature of the inefficiencies; and the policy measures that would correct these inefficiencies. The research will use mathematical modeling to develop a general framework to study the optimal contract between an uninformed principal and an agent with private information on some economically relevant variable (e.g. his/her preferences, a coefficient of technological productivity, etc.). The model captures the fact that the economic fundamentals may evolve over time in an unpredictable way by assuming that the type of the agent evolves over time following a stochastic process. Because types may be persistent across periods, however, the agent's past behavior may be important to predict future behavior. The analysis of this model has two parts. First, the PI will characterize the optimal contract between the principal and the agent when the principal can credibly commit to a contract. It is well known that in a static environment, asymmetric information causes the allocation in this type of contracts to be inefficient. When the interaction is repeated, non-anonymous and types are persistent, the principal can mitigate the problem of asymmetric information by using the agent's choices to forecast future behavior. However, as a result, agents are more reluctant to reveal private information which affects their consumption decisions: their strategic reaction may limit or even eliminate the benefits for the principal. Among other things, this project will characterize the conditions under which the optimal contract for the principal converges over time to an efficient contract. The second part of the analysis studies the case when the principal cannot commit to a contract. The research will characterize when the best allocation with commitment is attainable even with this renegotiation-proofness requirement; and when this is not attainable, we will characterize the optimal contract which respects the renegotiation-proofness constraint. This research project has direct implications for the design of more efficient public policies. Understanding optimal pricing decisions in dynamic environments is essential to an improvement in the regulation of markets and can help guide antitrust policy. The model, however, does not only provide insights into the interaction between a seller and a buyer: the findings of this research may contribute to the design of a better taxation system that can take advantage of data collected from the agent's past income levels to mitigate future asymmetric information. The project also provides new insights into the optimal ownership structure of a production technology: this may be important for the regulation of new patents or of other types of property rights.