# Network formation in repeated interactions: experimental evidence on dynamic behaviour

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## Abstract

Here, we present some experiments of non-cooperative games of network formation based on Bala and Goyal (Econometrica 68:1181–1229, 2000). We have looked at the one-way and the two-way flow models, each for high and low link costs. The models come up with both multiple equilibria and coordination problems. We conducted the experiments under various conditions which allowed for repeated interactions between subjects. We found that coordination on non-empty Strict Nash equilibria was not an easy task to achieve, even in the one-way model where the Strict Nash equilibria are wheels. We found some evidence of convergence to equilibrium networks through learning dynamics, while we found no effect of salient labels to help coordination. The evidence on learning behavior provides support for subjects that were choosing strategies in line with various learning rules, principally Reinforcement and Fictitious Play.

## Keywords

Experiments Networks Behavioral game theory Learning dynamics## Notes

### Acknowledgments

Financial supports from Italian MIUR and from Fondazione Cariplo are gratefully acknowledged.

## References

- Aumann R, Myerson R (1988) Endogenous formation of links between players and coalitions: an application of the Shapley value. In: Roth AE (ed) The Shapley value. Cambridge University Press, New York, pp 175–191CrossRefGoogle Scholar
- Bacharach M (1993) Variable universe games. In: Binmore K, Kirman A, Tani P (eds) Frontiers of game theory. MIT Press, Cambridge, MA, pp 255–275Google Scholar
- Bacharach M, Bernasconi M (1997) The variable frame theory of focal points: an experimental study. Game Econ Behav 19:1–45CrossRefGoogle Scholar
- Bala V, Goyal S (2000) A non-cooperative model of network formation. Econometrica 68:1181–1229CrossRefGoogle Scholar
- Ballester C, Calvò-Armengol A, Zenou Y (2006) Who’s who in networks: wanted the key player. Econometrica 74:1403–1417CrossRefGoogle Scholar
- Barabasi A, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512CrossRefGoogle Scholar
- Bardsley N, Mehta J, Starmer C, Sugden R (2009) Explaining focal points: cognitive hierarchy theory versus team reasoning. Econ J 120:40–79CrossRefGoogle Scholar
- Bernasconi M, Galizzi MM (2005) Coordination in networks formation: experimental evidence on learning and salience. FEEM working paper no. 107Google Scholar
- Berninghaus SK, Ehrhart K-M, Ott M (2006) A network experiment in continuous time: the influence of link costs. Exp Econ 9:237–251CrossRefGoogle Scholar
- Bolton P, Dewatripont M (1994) The firm as a communication network. Q J Econ 109:809–839CrossRefGoogle Scholar
- Bramoullè Y, Kranton R (2007) Public goods in networks. J Econ Theory 135:478–494CrossRefGoogle Scholar
- Breiger RL, Boorman SA, Arabie P (1975) An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling. J Math Psychol 12:328–383CrossRefGoogle Scholar
- Callander S, Plott CR (2005) Principles of network development and evolution: an experimental study. J Public Econ 89:1469–1495CrossRefGoogle Scholar
- Calvó-Armengol A (2001) Bargaining power in communication networks. Math Soc Sci 41:69–87CrossRefGoogle Scholar
- Calvó-Armengol A (2003) A decentralized market with trading links. Math Soc Sci 45:83–103CrossRefGoogle Scholar
- Calvó-Armengol A (2004) Job contact networks. J Econ Theory 115:191–206CrossRefGoogle Scholar
- Calvó-Armengol A, Jackson MO (2007) Networks in labor markets: wage and employment dynamics and inequality. J Econ Theory 132:27–46CrossRefGoogle Scholar
- Camerer C (2003) Behavioural game theory: experiments in strategic interaction. Russel Sage Foundation Princeton University Press, PrincetonGoogle Scholar
- Camerer C, Ho TH (1999) Experienced-weighted attraction learning in normal form games. Econometrica 67:827–874CrossRefGoogle Scholar
- Cheung YW, Friedman D (1997) Individual learning in normal form games. Game Econ Behav 19:46–76CrossRefGoogle Scholar
- Colman AM, Thomas C (2006) Schelling’s psychological decision theory: introduction to a special issue. J Econ Psychol 27:603–608CrossRefGoogle Scholar
- Currarini S, Jackson MO, Pin P (2009) An economic model of friendship: homophily, minorities and segregation. Econometrica 77:1003–1045Google Scholar
- Demange G, Wooders M (2005) Group formation in economics: networks, clubs, and coalitions. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Dutta B, Mutuswami S (1997) Stable networks. J Econ Theory 76:322–344CrossRefGoogle Scholar
- Erdos P, Renyi A (1959) On random graphs. Publ Math 6:290–297Google Scholar
- Erdos P, Renyi A (1961) On the strength of connectedness of a random graph. Acta Math Acad Sci Hung 12:261–267CrossRefGoogle Scholar
- Erev I, Roth AE (1998) Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria. Am Econ Rev 88:848–881Google Scholar
- Falk A, Kosfeld M (2003) It’s all about connections: evidence on network formation. Institute for empirical research in economics. Zurich IEER working paper no. 152Google Scholar
- Fischbacher U (2007) z-Tree: Zurich toolbox for ready-made economic experiments. Exp Econ 10:171–178CrossRefGoogle Scholar
- Frank O, Strauss D (1986) Markov graphs. J Am Stat Assoc 81:832–842CrossRefGoogle Scholar
- Fudenberg D, Levine D (1998) The theory of learning in games. MIT Press, CambridgeGoogle Scholar
- Goeree JK, Riedl A, Ule A (2009) In search of stars: network formation among heterogeneous agents. Game Econ Behav 67:445–466CrossRefGoogle Scholar
- Goodreau SM, Kitts JA, Morris M (2009) Birds of a feather, or friend of a friend? Using exponential random graph models to investigate adolescent social networks. Demography 46:103–125CrossRefGoogle Scholar
- Goyal S, Joshi S (2003) Networks of collaboration in oligopoly. Game Econ Behav 43:57–85CrossRefGoogle Scholar
- Goyal S, Moraga Gonzalez JL (2001) R&D networks. Rand J Econ 32:686-707CrossRefGoogle Scholar
- Goya S (2005) Learning in networks: a survey. In: Demange G, Wooders M (eds) Group formation in economics: networks, clubs, and coalitions. Cambridge University Press, CambridgeGoogle Scholar
- Granovetter M (1973) The strength of weak ties. Am J Sociol 78:1360–1380CrossRefGoogle Scholar
- Granovetter M (1985) Economic action and social structure: the problem of embeddedness. Am J Sociol 91:481–510CrossRefGoogle Scholar
- Granovetter M (1995) Getting a job: a study of contacts and careers (2nd edn). University Chicago Press, ChicagoGoogle Scholar
- Janssen MCW (2001) Rationalizing focal points. Theor Decis 50:119–148CrossRefGoogle Scholar
- Jackson MO, Wolinsky A (1996) A strategic model of economic and social networks. J Econ Theory 71:44–74CrossRefGoogle Scholar
- Jackson MO (2004) A survey of models of network formation: stability and efficiency. In: Demange G, Wooders M (eds) Group formation in economics: networks, clubs, and coalitions. Cambridge University Press, CambridgeGoogle Scholar
- Jackson MO (2010) An overview of social networks and economic applications. In: Benhabib J, Bisin A, Jackson MO (eds) The handbook of social economics. Elsevier Press, Amsterdam (Forthcoming)Google Scholar
- Kosfeld M (2004) Economic networks in the laboratory: a survey. Rev Netw Econ 3:20–41CrossRefGoogle Scholar
- Lazarsfeld P, Merton RK (1954) Friendship as a social process: a substantive and methodological analysis. In: Morroe B, Abel T, Page CH (eds) Freedom and control in modern society. Van Nostrand, New YorkGoogle Scholar
- Mehta J, Starmer C, Sugden R (1994) The nature of salience: an experimental investigation of pure coordination games. Am Econ Rev 84:658–673Google Scholar
- Mookherjee D, Sopher B (1994) Learning behaviour in an experimental matching pennies game. Game Econ Behav 7:62–91CrossRefGoogle Scholar
- Mookherjee D, Sopher B (1997) Learning and decision costs in experimental constant sum games. Game Econ Behav 19:97–132CrossRefGoogle Scholar
- Morris S (2000) Contagion. Rev Econ Stud 67:57–78CrossRefGoogle Scholar
- Radner R (1993) The organization of decentralized information processing. Econometrica 61:1110–1147CrossRefGoogle Scholar
- Rauch JE, Hamilton GG (2001) Networks and markets: concepts for bridging disciplines. In: Rauch JE, Casella A (eds) Networks and markets. Russel Sage Foundation, Princeton University Press, PrincetonGoogle Scholar
- Roth AE, Erev I (1995) Learning in extensive-form games: experimental data and simple dynamic models in the intermediate term. Game Econ Behav 8:164–212CrossRefGoogle Scholar
- Salmon TC (2001) An evaluation of econometric models of adaptive learning. Econometrica 69:1597–1628CrossRefGoogle Scholar
- Schelling T (1960) The strategy of conflict. Harvard University Press, BostonGoogle Scholar
- Schweitzer F, Fagiolo G, Sornette D, Vega-Redondo F, Vespigiani A, White DR (2009a) Economics networks: the new challenges. Science 325:422–425Google Scholar
- Schweitzer F, Fagiolo G, Sornette D, Vega-Redondo F, White DR (2009b) Economics networks: what do we know and what do we need to know? Adv Complex Syst 12:407–422CrossRefGoogle Scholar
- Sugden R (1995) A theory of focal points. Econ J 105:533–550CrossRefGoogle Scholar
- Van Huyck JB, Battalio RC, Rankin FW (1997) On the origin of convention: evidence from coordination games. Econ J 107:576–596CrossRefGoogle Scholar
- Vega Redondo F (2003) Economics and the theory of games. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Vega Redondo F (2007) Complex social networks. Econometric society monograph. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Watts DJ, Strogatz S (1998) Collective dynamics of small-world networks. Nature 393:440–442CrossRefGoogle Scholar
- Wellman B, Berkowitz SD (1988) Social structures: A network approach. Cambridge University Press, CambridgeGoogle Scholar