# Algorithmic Game Theory for Network Bottlenecks

### by Dr. Costas Busch

- When: Friday, 09/18/2020, between 1pm and 2pm, EDT
- Where: Zoom; Outside guests please RSVP by emailing Harley Eades
- YouTube Recording: https://youtu.be/zAxA-JT8mp8

#### Abstract

Game theory studies interactions of selfish players, where each player attempts to improve its own utility function without considering the impact on others. Nash equilibria are states where all players are in a locally optimal state from which no player wishes to deviate. Algorithmic game theory studies how fast Nash equilibria can be computed (if they exist) and also how the quality of equilibria compare to globally optimal states (i.e. Price of Stability). Here, we consider communication network games where packets to be routed are modeled as players that interact with each other. Each packet is routed along a chosen path in the network. The communication links may be used simultaneously by multiple packet paths which causes network congestion. To avoid congestion, packets prefer to be routed along lowest utilized links. The congestion on a link can be simply measured as the number of packet paths that use the link. The packet cost function is proportional to the congestion of the links on the chosen path. To improve its cost, each packet picks a path will the lowest congestion possible. However, in doing so a packet may increase the congestion of other packets. Thus, selfish acts of packets can destabilize the current state of other packets in the network. A natural question is whether a global stable state (Nash equilibrium) can be reached. Hence, we can formulate network congestion games.

Congestion games have been thoroughly studied in the literature for the player (packet) cost function which is the sum of link congestions in the chosen path. Such a cost function is not suitable to express some critical performance attributes of the network, as for example congestion bottlenecks and lifetime in battery operated wireless networks. Here, we consider an alternative player cost function which is the congestion of the bottleneck link in the chosen path, namely, the maximum congestion of any link in the playerâ€™s path. Bottleneck congestion is an interesting metric because it directly relates to the time it takes to transfer all the packets in the network. Moreover, the bottleneck congestion is particularly appropriate for wireless networks because it relates to the energy used along the adjacent nodes of the bottleneck link. It is known that Nash equilibria exist for bottleneck congestion games. However, computing such equilibria is a PLS-complete problem. Here, we present the first polynomial time algorithm that finds a poly-log factor approximation of a bottleneck Nash equilibrium. The resulting equilibrium has also near optimal global bottleneck congestion. Thus, our work answers to the positive a long standing open question of whether we can efficiently compute Nash equilibria for bottleneck games.

#### Author Bio

Costas Busch obtained a B.Sc. degree in 1992 and an M.Sc. degree in 1995 both in computer science from the University of Crete, Greece. He received a Ph.D. degree in computer science from Brown University in 2000. He is a professor at the School of Computer and Cyber Sciences at Augusta University. His research interests are in the areas of distributed algorithms and data structures, design and analysis of communication algorithms, algorithmic game theory, and blockchains. He has publications in several prominent venues in algorithms and distributed computing. His research has been supported by the National Science Foundation.