A Game Theoretic Model for Network Upgrade Decisions

We develop a game theoretic model for studying when interconnected Internet Service Providers (ISP)s will decide to upgrade their networks. We are in particular interested in network upgrades to better accommodate real-time applications like voice over IP, but our game model is applicable to other types of upgrade. Achieving the full benefit from network upgrades requires that enough ISPs upgrade so that the users’ traffic encounters only upgraded ISPs as it traverses the Internet. This situation gives rise to two important effects. One effect is that providers are reluctant to be first to invest in an upgrade when the full benefit of the upgrade cannot be achieved until their peers do the same. The second effect is that when a provider upgrades, the quality of the Internet as a whole increases, increasing demand, and thereby increasing revenue for all ISPs – including those who have not invested in the upgrade. This “free-rider” effect gives providers a temptation to not upgrade and instead enjoy the benefits of their peers upgrading. Our game model takes into account both effects, and finds sufficient conditions for it to be a Nash equilibrium the ISPs involved in the game to decide to upgrade. There are a large number of other equilibria for this game, so we also find stronger conditions under which the Nash equilibrium in which all providers upgrade is the unique Nash equilibrium. Another important feature of network upgrade costs is that they are declining as technology improves. We extend our original game model for upgrades to take into account declining upgrade costs and study what effects this has on the game’s outcome. I. MOTIVATION AND BACKGROUND Today’s Internet is so successful in large part due to the simplicity of its service model. However, this simplicity is also the root one of its biggest failures: the failure to offer differentiated service quality to real time applications. Indeed, the research community has long recognized the utility of designing a network with differentiated classes of services in order to better serve applications that have different requirements for delay, throughput, and other quality of service metrics. For example when traffic from delay sensitive applications like voice over IP share a congested network with a large amount of TCP traffic coming from applications like web browsing, the effect could be that the quality of service seen by the voice users becomes unacceptably bad. A network with the same link capacities, but with mechanisms in place to protect the voice traffic from the congestion of the web traffic, could greatly increase the welfare of the voice users at a modest cost in welfare to voice users. Thus differentiated services have the potential to Research supported in part by NSF Grant ANI-0331659. J. Musacchio and S. Wu are with the Technology and Information Management Program, University of California, Santa Cruz, Santa Cruz, CA 95064, USA {johnm,swu}@soe.ucsc.com J. Warand is with the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA 94720, USA [email protected] increase the social welfare of the network, without increasing its capacity. Work on technical architectures for differentiated services includes [1], [2]. Researchers have also recognized that in order to keep the higher classes of service from becoming just as congested as the lower classes of service, a network with differentiated classes of service needs to charge higher prices for its higher service classes. Work on pricing of differentiated services includes [3], [4], [5], [6], [7]. Another important effect of differentiated pricing is that it can increase the revenue of the provider. Equivalently, differentiated pricing allows the provider to capture more of the increase in social welfare that occurs as a result of upgrading to a differentiated service model. As an upgrade to a differentiated service model would require investments in equipment and software, this increase in provider revenue is essential in giving the providers a sufficient incentive to make the upgrade. While there has been a large amount of research activity in recent years addressing differentiated services and prices, recent trends have suddenly made these ideas of vital commercial importance. Voice over IP has been available for some time, but it can be argued that voice over IP has finally reached a “tipping point” and is now well on its way to becoming adopted by a significant fraction of the public [8]. Interest in IP television has also grown sharply in the past year. The recent explosion in use of the Internet for realtime or high bit rate applications has made the problem of addressing the Internet’s service model shortcomings all the more urgent. Indeed the issue is now receiving attention by the large commercial providers, the popular press, and even the U.S. Congress [9], [10]. We argue that the principal obstacle to deployment of more advanced service models is that the network is owned by different providers, and that the full benefit of upgrading the network can only come when enough providers have upgraded so that when users make a connection across the network, all providers along the way are upgraded. There are two perverse effects these facts give rise to. One is that a provider does not want to upgrade to a differentiated services model if he cannot be sure that the neighboring providers will upgrade, and without his neighbors participating in the upgrade the effect of the upgrade will be reduced. The second effect is a “free-rider” effect. A provider that does not bother to upgrade still earns some benefit from his neighbors upgrading, because the upgrades of other providers improve the network as a whole, which should increase demand in general. For such a provider, it is not enough that the absolute benefit from upgrading exceed the costs; it is necessary that the marginal benefit of upgrading over free-riding exceed the Forty-Fourth Annual Allerton Conference Allerton House, UIUC, Illinois, USA Sept 27-29, 2006 WID.160