Routing-Proofness in Congestion-Prone Networks

We consider the problem of sharing the cost of connecting a large number of atomless agents in a network. The centralized agency elicits the target nodes that agents want to connect, and charges agents based on their demands. We look for a cost-sharing mechanism that satisfies three desirable properties: efficiency which charges agents based on the minimum total cost of connecting them in a network, stand-alone core stability which requires charging agents not more than the cost of connecting by themselves directly, and limit routing-proofness which prevents agents from profitable reporting as several agents connecting from A to C to B instead of A to B. We show that these three properties are not always compatible for any set of cost functions and demands. However, when these properties are compatible, a new egalitarian mechanism is shown to satisfy them. When the properties are not compatible, we find a rule that meets stand-alone core stability, limit routing-proofness and minimizes the budget deficit.

[1]  E. Melo.  CONGESTION PRICING AND LEARNING IN TRAFFIC NETWORK GAMES , 2011 .

[2]  Rajnish Kumar,et al.  Secure implementation in production economies , 2013, Math. Soc. Sci..

[3]  Tim Roughgarden.  The price of anarchy is independent of the network topology , 2003, J. Comput. Syst. Sci..

[4]  Ruben Juarez,et al.  Free intermediation in resource transmission , 2018, Games Econ. Behav..

[5]  J. Benassy,et al.  The economics of market disequilibrium , 1982 .

[6]  Jens Leth Hougaard,et al.  Minimum cost connection networks: Truth-telling and implementation , 2015, J. Econ. Theory.

[7]  Hervé Moulin,et al.  Pricing traffic in a spanning network , 2009, ACM Conference on Economics and Computation.

[8]  Andreas S. Schulz,et al.  The Complexity of Congestion Games , 2008 .

[9]  Harold W. Lewis,et al.  A New Optimization Algorithm For Combinatorial Problems , 2013 .

[10]  Ruben Juarez,et al.  Sharing sequential values in a network , 2016, J. Econ. Theory.

[11]  Debasis Mishra,et al.  Minimum cost arborescences , 2012, Games Econ. Behav..

[12]  Hervé Moulin,et al.  Cost Sharing in Networks: some Open Questions , 2013, IGTR.

[13]  Aranyak Mehta,et al.  Fairness and optimality in congestion games , 2005, EC '05.

[14]  Paul G. Spirakis,et al.  Cost-Balancing Tolls for Atomic Network Congestion Games , 2008 .

[15]  Jens Leth Hougaard,et al.  Truth-telling and Nash equilibria in minimum cost spanning tree models , 2012, Eur. J. Oper. Res..

[16]  Ron Holzman,et al.  Sharing the Cost of a Capacity Network , 2010, Math. Oper. Res..

[17]  Jung S. You,et al.  Optimality of the uniform rule under single-peaked preferences , 2019 .

[18]  Jens Leth Hougaard,et al.  An Introduction to Allocation Rules , 2009 .

[19]  Hervé Moulin,et al.  Traffic Based Cost Allocation in Network , 1996 .

[20]  Hervé Moulin,et al.  Equal-need sharing of a network under connectivity constraints , 2011, Games Econ. Behav..

[21]  Yves Sprumont.  The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule , 1991 .

[22]  Baomin Dong,et al.  Highway Toll Pricing , 2009 .

[23]  Ruben Juarez,et al.  Group strategyproof cost sharing: The role of indifferences , 2013, Games Econ. Behav..

[24]  Juan D. Moreno-Ternero,et al.  Sharing the Proceeds from a Hierarchical Venture , 2015, Games Econ. Behav..

[25]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[26]  Rajnish Kumar,et al.  Implementing efficient graphs in connection networks , 2011, EC '11.