Chapter Outline for Algorithmic Game Theory Book

The focus will be on settings in which agents are connected by an underlying network, and new “behaviors” spread through this network from neighbor to neighbor. Consider, for example, the way in which people come to believe a rumor if they hear it from enough of their friends; or the way in which people adopt some new piece of technology if enough of their friends have already done so. The study of such processes is often termed the diffusion of innovation [11], and it is a central area of research in the social sciences, with a significant fraction of the contributions coming from the economics literature. It is also a topic where one can identify a number of forward-looking computing applications, in keeping with the theme for the part of the book in which this chapter is appearing. The chapter will be organized as follows. In the first section, I plan to introduce the basic notions and definitions, discuss two of the earliest mathematical models in this style — Granovetter’s threshold model [4] and Schelling’s segregation model [12] — and consider generalizations of these models. In the second section, I plan to discuss how such processes can be viewed in terms of network coordination games [2, 9, 13]: we have a graph G, and on every edge (v, w) the nodes v and w are playing a 2-strategy coordination game — strategy 2 is to adopt the new behavior, and strategy 1 is to keep the old behavior. The fact that we have a coordination game means that nodes have an incentive to be like their neighbors; so this forms a game-theoretic basis for models in which a node will switch from strategy 1 to 2 (non-adopting to adopting) if enough of its network neighbors have done so. In the third and fourth sections, I plan to discuss three computing applications of these ideas.