On a Conjecture for Dynamic Priority Queues and Nash Equilibrium for Quality of Service Sensitive Markets

TL;DR

This paper models the strategic interaction between service providers and customers in QoS-sensitive markets using a game-theoretic approach, proving the existence of multiple Nash equilibria and identifying revenue-maximizing strategies.

Contribution

It settles a key conjecture in a joint pricing and scheduling model, demonstrating the existence of a continuum of Nash equilibria and providing a method to compute the revenue-maximizing equilibrium.

Findings

Existence of a continuum of Nash equilibria in QoS-sensitive markets.

A finite step algorithm to identify revenue-maximizing equilibrium.

Both service providers and customers can benefit from strategic operational decisions.

Abstract

Many economic transactions, including those of online markets, have a time lag between the start and end times of transactions. Customers need to wait for completion of their transaction (order fulfillment) and hence are also interested in their waiting time as a Quality of Service (QoS) attribute. So, they factor this QoS in the demand they offer to the firm (service-provider) and some customers (user-set) would be willing to pay for shorter waiting times. On the other hand, such waiting times depend on the demand user-set offers to the service-provider. We model the above economic-QoS strategic interaction between service-provider and user-set under a fairly generic scheduling framework as a non-cooperative constrained game. We use an existing joint pricing and scheduling model. An optimal solution to this joint pricing and scheduling problem was guaranteed by a finite step algorithm subject to a conjecture. We first settle this conjecture based on queuing and optimization arguments and discuss its implications on the above game. We show that a continuum of Nash equilibria (NE) exists and it can be computed easily using constrained best response dynamics. Revenue maximal NE is identified by above finite step algorithm. We illustrate how both players can benefit at such revenue maximal NE by identifying suitable operational decisions, i.e., by choosing an appropriate game along the theme of pricing and revenue management.