The uniqueness of dynamic Groves mechanisms on restricted domains

TL;DR

This paper investigates the conditions under which dynamic Groves mechanisms are unique on restricted valuation domains, extending static results to dynamic settings through a novel valuation function approach.

Contribution

It introduces a dynamic valuation function to extend static Groves mechanism results, establishing necessary and sufficient conditions for their uniqueness in dynamic contexts.

Findings

Characterizes conditions for dynamic Groves mechanism uniqueness

Defines a dynamic valuation function as a discounted sum of period valuations

Extends static mechanism results to dynamic settings

Abstract

This paper examines necessary and sufficient conditions for the uniqueness of dynamic Groves mechanisms when the domain of valuations is restricted. Our approach is to appropriately define the total valuation function, which is the expected discounted sum of each period's valuation function from the allocation and thus a dynamic counterpart of the static valuation function, and then to port the results for static Groves mechanisms to the dynamic setting.