Polynomially bounded minimization problems that are hard to approximate
Nordic Journal of Computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal marketing strategies over social networks
Proceedings of the 17th international conference on World Wide Web
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
Pricing Strategies for Viral Marketing on Social Networks
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Approximating pure nash equilibrium in cut, party affiliation, and satisfiability games
Proceedings of the 11th ACM conference on Electronic commerce
Optimal iterative pricing over social networks
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Equilibrium pricing with positive externalities
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Optimal auctions with positive network externalities
Proceedings of the 12th ACM conference on Electronic commerce
Mechanisms and allocations with positive network externalities
Proceedings of the 13th ACM Conference on Electronic Commerce
| Hi-index | 0.00 |
We consider the problem of a monopolist seller who wants to sell some items to a set of buyers. The buyers are strategic, unit-demand, and connected by a social network. Furthermore, the utility of a buyer is a decreasing function of the number of neighbors who do not own the item. In other words, they exhibit negative externalities, deriving utility from being unique in their purchases. In this model, any fixed setting of the price induces a sub-game on the buyers. We show that it is an exact potential game which admits multiple pure Nash Equilibria. A natural problem is to compute those pure Nash equilibria that raise the most and least revenue for the seller. These correspond respectively to the most optimistic and most pessimistic revenues that can be raised. We show that the revenues of both the best and worst equilibria are hard to approximate within sub-polynomial factors. Given this hardness, we consider a relaxed notion of pricing, where the price for the same item can vary within a constant factor for different buyers. We show a 4-approximation to the pessimistic revenue when the prices are relaxed by a factor of 4. The interesting aspect of this algorithm is that it uses a linear programming relaxation that only encodes part of the strategic behavior of the buyers in its constraints, and rounds this relaxation to obtain a starting configuration for performing relaxed Nash dynamics. Finally, for the maximum revenue Nash equilibrium, we show a 2-approximation for bipartite graphs (without price relaxation), and complement this result by showing that the problem is NP-Hard even on trees.