A study of Nash equilibrium in contribution games for peer-to-peer networks

We consider a stylized model of content contribution in a peer-to-peer network. The model is appealing because it allows for linear-quadratic payoff functions and for very general interaction patterns among agents. Furthermore, when the model has a unique Nash equilibrium (NE) we find that it is defined by a network centrality measure (Bonacich 1987), with L1 and L2 norms of the Bonacich index vector providing aggregate contribution and social welfare. Furthermore, we find that NE are always (even when they are non-unique) computable by solving a linear complementarity problem. We study the network designer's problem of engineering the most efficient equilibrium outcome, proving that maximizing aggregate contribution can be reconciled with maximizing aggregate welfare. We also provide a partial characterization of optimal NE graphs and suggest different approaches for how a network designer can promote more efficient graph structures.

[1]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[2]  Yves Zenou,et al.  Who's Who in Crime Network. Wanted the Key Player , 2004 .

[3]  Penna.  Traveling salesman problem and Tsallis statistics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  S. Durlauf.  Chapter 50 – Neighborhood Effects , 2004 .

[5]  Béla Bollobás,et al.  Robustness and Vulnerability of Scale-Free Random Graphs , 2004, Internet Math..

[6]  G. Debreu,et al.  Nonnegative Square Matrices , 1953 .

[7]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[8]  Panayotis Antoniadis,et al.  Comparing economic incentives in peer-to-peer networks , 2004, Comput. Networks.

[9]  Sanjeev Goyal,et al.  Networks of collaboration in oligopoly , 2000, Games Econ. Behav..

[10]  Benny Sudakov,et al.  The Largest Eigenvalue of Sparse Random Graphs , 2001, Combinatorics, Probability and Computing.

[11]  P. Bonacich.  Power and Centrality: A Family of Measures , 1987, American Journal of Sociology.

[12]  M. Jackson.  A Survey of Models of Network Formation: Stability and Efficiency , 2003 .

[13]  Kathleen M. Carley,et al.  Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers , 2004 .

[14]  Dragan Stevanovic,et al.  The largest eigenvalue of nonregular graphs , 2004, J. Comb. Theory, Ser. B.

[15]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[16]  S. Borgatti.  The Key Player Problem , 2002 .

[17]  Tamara D. Madensen,et al.  Neighborhood Effects , 2021, Encyclopedia of Evolutionary Psychological Science.

[18]  Tim Roughgarden,et al.  The price of stability for network design with fair cost allocation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[19]  Edwin R. Hancock,et al.  Eigenspaces for Graphs , 2002, Int. J. Image Graph..

[20]  Michael L. Littman,et al.  Graphical Models for Game Theory , 2001, UAI.

[21]  D. Cvetkovic,et al.  The largest eigenvalue of a graph: A survey , 1990 .

[22]  Gabrielle Demange,et al.  A Survey of Network Formation Models: Stability and Efficiency , 2005 .

[23]  C. Tsallis,et al.  Generalized simulated annealing , 1995, cond-mat/9501047.

[24]  Alexandre Arenas,et al.  Optimal network topologies for local search with congestion , 2002, Physical review letters.