Network Pricing: How to Induce Optimal Flows Under Strategic Link Operators

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Private-link tolls can fail to have any pure equilibrium, cycle, or be arbitrarily inefficient; imposing caps below marginal tolls guarantees an equilibrium (indeed a strong Nash) that implements the social optimum. Proof uses convex variational characterizations, a key lemma: raising a toll reduces flow but raises link cost, and a second-order local-optimality bound; a linear program finds caps with provable guarantees (linear latencies give a 2× payment bound, series-parallel graphs achieve optimal payments).

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" chapters (17)

1. 0:00Introduction
2. 0:28Problem setting and model
3. 5:30Defining social cost
4. 7:18Role of tolls
5. 8:46Operator behavior
6. 9:15Nash equilibrium defined
7. 11:06Literature context
8. 11:44Regulatory toll caps
9. 12:36Main theoretical results
10. 15:18Proof sketches
11. 20:48Optimal toll selection
12. 24:32Performance benchmarks
13. 25:32Network complexity
14. 25:52Series-parallel graphs
15. 26:16Solution comparison
16. 27:06Future work
17. 27:22Q&A and conclusion