Bounded Budget Connection (BBC) Games or How to make friends and influence people, on a budget
Nikolaos Laoutaris, Laura J. Poplawski, Rajmohan Rajaraman, Ravi, Sundaram, Shang-Hua Teng

TL;DR
This paper introduces and analyzes the Bounded Budget Connection (BBC) game, exploring the existence, structure, and properties of Nash equilibria in network formation under budget constraints, with implications for social and overlay networks.
Contribution
It establishes complexity results, existence conditions, and structural properties of Nash equilibria in BBC games, including uniform and fractional variants, and analyzes stability and fairness.
Findings
NP-hardness of equilibrium existence in general BBC games
Existence of pure Nash equilibrium in fractional BBC games
Stable, fair graphs exist in (n,k)-uniform BBC games
Abstract
Motivated by applications in social networks, peer-to-peer and overlay networks, we define and study the Bounded Budget Connection (BBC) game - we have a collection of n players or nodes each of whom has a budget for purchasing links; each link has a cost as well as a length and each node has a set of preference weights for each of the remaining nodes; the objective of each node is to use its budget to buy a set of outgoing links so as to minimize its sum of preference-weighted distances to the remaining nodes. We study the structural and complexity-theoretic properties of pure Nash equilibria in BBC games. We show that determining the existence of a pure Nash equilibrium in general BBC games is NP-hard. However, in a natural variant, fractional BBC games - where it is permitted to buy fractions of links - a pure Nash equilibrium always exists. A major focus is the study of…
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Taxonomy
TopicsGame Theory and Applications · Auction Theory and Applications · Economic theories and models
