Cost Sharing
Stub. Cooperative cost-sharing games, the core, group-strategyproof cross-monotonic cost-sharing schemes, the primal-dual schema for constructing them, their limitations, and the Shapley value / Nash bargaining solution. (AGT ch. 15)
How to split the cost of a jointly-used resource (e.g. a Steiner tree) fairly and strategyproofly: cooperative game theory’s core as the fairness notion, cross-monotonic cost-sharing schemes as the mechanism-design tool for group-strategyproofness, a primal-dual method for building them, known limitations, and the Shapley value / Nash bargaining solution as alternative allocation rules.
Outline (TODO — flesh out each)
- Cooperative games and cost sharing
- The core of cost-sharing games
- Group-strategyproof mechanisms and cross-monotonic cost-sharing schemes
- Cost sharing via the primal-dual schema
- Limitations of cross-monotonic cost-sharing schemes
- The Shapley value and the Nash bargaining solution