Dynamic Mechanism Design with Interdependent Valuations

TL;DR

This paper develops a novel dynamic mechanism design framework for interdependent valuations with Markovian type evolution, achieving efficiency and strict ex-post incentive compatibility in an infinite horizon setting.

Contribution

It introduces the first dynamic mechanism that is efficient, strictly ex-post incentive compatible, and individually rational in interdependent valuation environments with Markovian types.

Findings

Designed a dynamic mechanism satisfying the desired properties.

Achieved strict ex-post incentive compatibility in a complex setting.

Extended the static interdependent valuation results to a dynamic, infinite horizon context.

Abstract

We consider an infinite horizon dynamic mechanism design problem with interdependent valuations. In this setting the type of each agent is assumed to be evolving according to a first order Markov process and is independent of the types of other agents. However, the valuation of an agent can depend on the types of other agents, which makes the problem fall into an interdependent valuation setting. Designing truthful mechanisms in this setting is non-trivial in view of an impossibility result which says that for interdependent valuations, any efficient and ex-post incentive compatible mechanism must be a constant mechanism, even in a static setting. Mezzetti (2004) circumvents this problem by splitting the decisions of allocation and payment into two stages. However, Mezzetti's result is limited to a static setting and moreover in the second stage of that mechanism, agents are weakly indifferent about reporting their valuations truthfully. This paper provides a first attempt at designing a dynamic mechanism which is efficient, `strict' ex-post incentive compatible and ex-post individually rational in a setting with interdependent values and Markovian type evolution.