International Journal of Game Theory

, Volume 45, Issue 3, pp 497–509 | Cite as

Strategic complementarities, network games and endogenous network formation

Article

Abstract

This paper investigates the role of strategic complementarities in the context of network games and network formation models. In the general model of static games on networks, we characterize conditions on the utility function that ensure the existence and uniqueness of a pure-strategy Nash equilibrium, regardless of the network structure. By applying the game to empirically-relevant networks that feature nestedness—Nested Split Graphs—we show that equilibrium strategies are non-decreasing in the degree. We extend the framework into a dynamic setting, comprising a game stage and a formation stage, and provide general conditions for the network process to converge to a Nested Split Graph with probability one, and for this class of networks to be an absorbing state. The general framework presented in the paper can be applied to models of games on networks, models of network formation, and combinations of the two.

Keywords

Social networks Network formation Social interaction 

References

  1. Bala V, Goyal S (2000) A non-cooperative model of network formation. Econometrica 68(5):1181–1230CrossRefGoogle Scholar
  2. Ballester C, Calvò-Armengol A, Zenou Y (2006) Who’s who in networks. Wanted: the key player. Econometrica 74(5):1403–1417CrossRefGoogle Scholar
  3. Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512CrossRefGoogle Scholar
  4. Berman A, Plemmons RJ (1994) Nonnegative matrices in the mathematical sciences. SIAM, PhiladelphiaCrossRefGoogle Scholar
  5. Bramoullè Y, Lopez D, Goyal S, Vega-Redondo F (2004) Social interaction in anti-coordination games. Int J Game Theory 33:1–19CrossRefGoogle Scholar
  6. Bramoullè Y, Kranton R, D’Amours M (2014) Strategic interaction and networks. Am Econ Rev 104(3):898–930Google Scholar
  7. Case AC, Katz LF (1991) The company you keep: the effects of family and neighborhood on disadvantaged youths. NBER Working Paper No. 3705Google Scholar
  8. Cabrales A, Calvò-Armengol A, Zenou Y (2010) Social interactions and spillovers. Games Econ Behav 72:339–360CrossRefGoogle Scholar
  9. Calvó-Armengol A, Patacchini E, Zenou Y (2009) Peer effects and social networks in education. Rev Econ Stud 76(4):1239–1267CrossRefGoogle Scholar
  10. Durlauf SN (2004) Neighborhood effects. In: Henderson V, Thisse JF (eds) Handbook of regional and urban economics, vol 4. Elsevier, Amsterdam, pp 2173–2242Google Scholar
  11. Dutta B, Ghosal S, Ray D (2005) Farsighted network formation. J Econ Theory 122:143–164CrossRefGoogle Scholar
  12. Foster AD, Rosenzweig M (1995) Learning by doing and learning from others: human capital and technical change in agriculture. J Political Econ 103(6):1176–1209CrossRefGoogle Scholar
  13. Galeotti A, Goyal S (2010) The law of the few. Am Econ Rev 100(4):1468–1492CrossRefGoogle Scholar
  14. Galeotti A, Goyal S, Jackson MO, Vega-Redondo F, Yariv L (2010) Network games. Rev Econ Stud 77(1):218–244CrossRefGoogle Scholar
  15. Goyal S (2007) Connections: an introduction to the economics of networks. Princeton University Press, PrincetonGoogle Scholar
  16. Goyal S, Joshi S (2003) Networks in collaboration in oligopoly. Games Econ Behav 43:57–85CrossRefGoogle Scholar
  17. Granovetter M (1994) Getting a job: a study of contacts and careers. Northwestern University Press, EvanstonGoogle Scholar
  18. Jackson MO (2008) Social and economic networks. Princeton University Press, PrincetonGoogle Scholar
  19. Jackson MO, Rogers BW (2007) Meeting strangers and friends of friends: how random are socially generated networks? Am Econ Rev 97(3):890–915CrossRefGoogle Scholar
  20. Jackson MO, Watts A (2002) On the formation of interaction networks in social coordination games. Games Econ Behav 41(2):265–291CrossRefGoogle Scholar
  21. Jackson MO, Wolinsky A (1996) A strategic model of social and economic network networks. J Econ Theory 71:44–74CrossRefGoogle Scholar
  22. Karamardian S (1969a) The nonlinear complementarity problem with applications, part 1. J Optim Theory Appl 4(1):87–98CrossRefGoogle Scholar
  23. Karamardian S (1969b) The nonlinear complementarity problem with applications, part 2. J Optim Theory Appl 4(3):167–181CrossRefGoogle Scholar
  24. König MD, Tessone CJ, Zenou Y (2014) Nestedness in networks: a theoretical model and some applications. Econ Theory 9:695–752CrossRefGoogle Scholar
  25. Lin N (1982) Social resources and instrumental action. In: Marsden PV, Lin N (eds) Social structure and network analysis. Sage Focus Editions, Beverly Hills, pp 131–145Google Scholar
  26. Lin N (1990) Social resources and social mobility: a structural theory of status attainment. In: Breiger RL (ed) Social mobility and social structure. Cambridge University Press, Cambridge, pp 237–271Google Scholar
  27. Lin N (1999) Social networks and status attainment. Annu Rev Sociol 25:467–487CrossRefGoogle Scholar
  28. Mahadev NVR, Peled UN (1995) Threshold graphs and related topics, annals of discrete mathematics, 1st edn. Elsevier, AmsterdamGoogle Scholar
  29. Milgrom P, Roberts DJ (1990) Rationalizability, learning, and equilibrium in games with strategic complements. Econometrica 58(6):1255–1277CrossRefGoogle Scholar
  30. Moré JJ (1974) Coercivity conditions in nonlinear complementarity problems. SIAM Rev 16(1):1–16CrossRefGoogle Scholar
  31. Rosen JB (1965) Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33(3):520–534CrossRefGoogle Scholar
  32. Tamir A (1974) Minimality and complementarity properties associated with z-functions and m-functions. Math Program 7:17–31CrossRefGoogle Scholar
  33. Watts DJ, Strogatz SH (1998) Collective dynamics of small-world networks. Nature 393:440–442CrossRefGoogle Scholar
  34. Watts A (2001) A dynamic model of network formation. Games Econ Behav 34:331–341CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsStockholm UniversityStockholmSweden
  2. 2.Department of EconomicsUniversity of TorontoTorontoCanada
  3. 3.The Research Institute for Industrial EconomicsStockholmSweden

Personalised recommendations