Network Perception in Network Games

Ruiz Palazuelos, Sofía (2021): Network Perception in Network Games.

Abstract

People form cognitive maps about their networks from the information they have −mental representations of who is connected with whom in the network they are embedded in (Krackhardt, 1987). The aim of this paper is twofold. First, we develop a model of how people form mental representations about the network from the (incomplete) information they have. We relate them with notions of equivalence among nodes and identify a cognitive bias towards asymmetric network structures. We then explore the incidence that players’ network perception has on their equilibrium behavior and payoffs in the induced Bayesian Games. A general condition for equilibrium existence under different setups of incomplete network information is derived. Such a condition uncovers the relevance of the order of the automorphism group of the cognitive networks as a main driver of behavior and welfare.

• Item Type: MPRA Paper
• Language: English
• Keywords: Network Games, Graphical Games, Network Cognition, Incomplete Information, Structural Equivalence, Automorphic Equivalence
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; D - Microeconomics > D0 - General; D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D85 - Network Formation and Analysis: Theory

References

[1] Backstrom, L., Boldi, P., Rosa, M., Ugander, J., Vigna, S. (2012, June). "Four degrees of separation". In Proceedings of the 4th Annual ACM Web Science Conference (pp. 33-42). [2] Bala, V. and Goyal, S. (1998). "Learning from neighbours". The Review of Economic Studies, 65(3), 595- 621. [3] Ball, F. and Geyer-Schulz, A. (2018a). "How symmetric are real-world graphs? A large-scale study". Symmetry, 10(1), 29. [4] Ball, F. and Geyer-Schulz, A. (2018b). "The impact of graph symmetry on clustering". Arch. Data Sci., A, 5(1), 1-19. [5] Ballester, C., Calvó-Armengol, A. and Zenou, Y. (2006). "Who’s who in networks. Wanted: the key player". Econometrica, 74(5), 1403-1417. [6] Boorman, S. A. and White, H. C. (1976). "Social structure from multiple networks. II. Role structures". American Journal of Sociology, 81(6), 1384-1446.. [7] Borgatti, S. P., Everett, M. G. (1992). "Notions of position in social network analysis". Sociological methodology, 1-35. [8] Bourlès, R., Bramoullé, Y. and Perez-Richet, E. (2017). "Altruism in networks". Econometrica, 85(2), 675-689. [9] Bourlès, R., Bramoullé, Y., Perez-Richet, E. (2021). "Altruism and risk sharing in networks". Journal of the European Economic Association, 19(3), 1488-1521. [10] Brashears, M. E. (2013). "Humans use compression heuristics to improve the recall of social networks". Scientific Reports, 3(1), 1-7. [11] Brashears, M. E., Hoagland, E., Quintane, E. (2016). "Sex and network recall accuracy". Social Networks, 44, 74-84. [12] Brashears, M. E., Quintane, E. (2015). "The microstructures of network recall: How social networks are encoded and represented in human memory". Social Networks, 41, 113-126. [13] Bramoullé, Y., Djebbari, H., Fortin, B. (2020). "Peer effects in networks: A survey". Annual Review of Economics, 12, 603-629. [14] Bramoullé, Y. and Kranton, R. (2007). "Public goods in networks". Journal of Economic Theory, 135(1), 478-494. [15] Bramoullé, Y., Kranton, R. and D’Amours, M. (2014). "Strategic interaction and networks". American Economic Review, 104(3), 898-930. [16] Brands, R. A. (2013). "Cognitive social structures in social network research: A review". Journal of Organizational Behavior, 34(S1), S82-S103. [17] Brewer, D. D. (2011). "Biases in perceiving one’s own social position and social ties as evolved psychological mechanisms". Available at SSRN 1879624. [18] Burt, R. S. (1976). "Positions in networks". Social Forces, 55(1), 93-122. [19] Burt, R. S. (1977). "Positions in multiple network systems, part one: a general conception of stratification and prestige in a system of actors cast as a social topology". Social Forces, 56(1), 106-131. [20] Burt, R. S. (1978a). "Cohesion versus structural equivalence as a basis for network subgroups". Sociological Methods and Research, 7(2), 189-212. [21] Burt, R. S. (1978b). "A structural theory of interlocking corporate directorates". Social Networks, 1(4), 415-435. [22] Burt, R. S. (1987). "Social contagion and innovation: Cohesion versus structural equivalence". American Journal of Sociology, 92(6), 1287-1335. [23] Burt, R. S. (1990). "Detecting role equivalence". Social Networks, 12(1), 83-97. [24] Carley, K. (1986). "An approach for relating social structure to cognitive structure". Journal of Mathematical Sociology, 12(2), 137-189. [25] Casciaro, T. (1998). "Seeing things clearly: Social structure, personality, and accuracy in social network perception". Social Networks, 20(4), 331-351. [26] Casse, J. I., Shelton, C. R., and Hanneman, R. A. (2013). "A new criterion function for exploratory blockmodeling for structural and regular equivalence". Social Networks, 35(1), 31-50. [27] Chartrand, G., Lesniak, L. and Zhang, P. (2010). Graphs and Digraphs (Vol. 39). CRC press. [28] Cvetkovíc, D.M., Doob, M. and Sachs, H. (1979). Spectra of graphs: Theory and applications. Academic Press, New York. [29] Dehmer, M., Chen, Z., Emmert-Streib, F., Mowshowitz, A., Varmuza, K., Feng, L., Jodlbauer, H., Shi, Y. and Tao, J. (2020). "The Orbit-Polynomial: A Novel Measure of Symmetry in Networks". IEEE Access, 8, 36100-36112. [30] Dessi, R., Gallo, E. and Goyal, S. (2016). "Network cognition". Journal of Economic Behavior and Organization, 123, 78-96. [31] Dodds, P. S., Muhamad, R., Watts, D. J. (2003). "An experimental study of search in global social networks". Science, 301(5634), 827-829. [32] Doreian, P., Batagelj, V. and Ferligoj, A. (2005). Generalized blockmodeling. Cambridge University Press. [33] Easley, D. and Kleinberg, J. (2010). Networks, crowds, and markets. Cambridge: Cambridge University Press. [34] Erdös, P., Renyi, A. (1963). "Asymmetric graphs". Acta Math. Acad. Sci. Hungar, 14(295-315), 3. [35] Erwin, D. and Harary, F. (2006). "Destroying automorphisms by fixing nodes". Discrete Mathematics, 306(24), 3244-3252. [36] Espinosa, MP., KovárÃk, J., Ruiz-Palazuelos, S. (2020). "Are close-knit communities good for employment?", mimeo, University of the Basque Country. [37] Everett, M. G. (1985). "Role similarity and complexity in social networks". Social Networks, 7(4), 353- 359. [38] Everett, M. G., Boyd, J. P., Borgatti, S. P. (1990). "Egocentered and local roles: A graph theoretic approach". Journal of Mathematical Sociology, 15(3-4), 163-172. [39] Faust, K. (1988)."Comparison of methods for positional analysis: Structural and general equivalences". Social networks, 10(4), 313-341. [40] Feri, F., Pin, P. (2020). "Externalities aggregation in network games". International Economic Review, 61(4), 1635-1658. [41] Freeman, L. C. (1992). "Filling in the blanks: A theory of cognitive categories and the structure of social affiliation". Social Psychology Quarterly, 118-127. [42] Friedkin, N. E., Johnsen, E. C. (1997). "Social positions in influence networks". Social Networks, 19(3), 209-222. [43] Galeotti, A. Goyal, S., Jackson, M. O., Vega-Redondo, F., and Yariv, L. (2010). "Network games". The Review of Economic Studies, 77(1), 218-244. [44] Goyal, S. and Moraga-Gonzalez, J. L. (2001). "RD networks". Rand Journal of Economics, 686-707. [45] Golubitsky, M. and Stewart, I. (2003). The symmetry perspective: from equilibrium to chaos in phase space and physical space (Vol. 200). Springer Science and Business Media. [46] Hanneman, R. A. and Riddle, M. (2005). Introduction to social network methods. 2005. University of California, Riverside. [47] Jackson, M. O. (2010). Social and economic networks. Princeton university press. [48] Jackson, M. O., Rogers, B. W. and Zenou, Y. (2017). "The economic consequences of social-network structure". Journal of Economic Literature, 55(1): 49-95. [49] Jackson, M. O. and Yariv, L. (2005). "Diffusion on social networks". In Economie Publique. [50] Jackson, M. O. and Yariv, L. (2007). "Diffusion of behavior and equilibrium properties in network games". American Economic Review, 97(2), 92-98. [51] Janicik, G. A., Larrick, R. P. (2005). "Social network schemas and the learning of incomplete networks". Journal of personality and Social Psychology, 88(2), 348. [52] Johnson, J. C. and Orbach, M. K. (2002). "Perceiving the political landscape: ego biases in cognitive political networks". Social Networks, 24(3), 291-310. [53] Jin, R., Lee, V. E. and Li, L. (2014). "Scalable and axiomatic ranking of network role similarity". ACM Transactions on Knowledge Discovery from Data (TKDD), 8(1), 1-37. [54] Kocay, W. L. (2007). "Groups and graphs - software for graphs, digraphs, and their automorphism groups". Match, 58(2), 431-443. [55] Krackhardt, D. (1987). "Cognitive social structures". Social Networks, 9(2), 109-134. [56] Kilduff, M., Crossland, C., Tsai, W. and Krackhardt, D. (2008). "Organizational network perceptions versus reality: A small world after all?". Organizational Behavior and Human Decision Processes, 107: 15-28. [57] Kilduff, M., Tsai, W. (2003). Social networks and organizations. Sage. [58] Kumbasar, E., Rommey, A. K. and Batchelder, W. H. (1994). "Systematic biases in social perception". American Journal of Sociology, 100(2), 477-505.. [59] Leicht, E. A., Holme, P. and Newman, M. E. (2006). "Vertex similarity in networks". Physical Review E, 73(2), 026120. [60] Lorrain, F., White, H. C. (1971). "Structural equivalence of individuals in social networks". The Journal of Mathematical Sociology, 1(1), 49-80. [61] MacArthur, B. D., Anderson, J. W. (2006). "Symmetry and self-organization in complex systems". arXiv preprint cond-mat/0609274. [62] MacArthur, B. D., Sánchez-García, R. J. and Anderson, J. W. (2008). "Symmetry in complex networks". Discrete Applied Mathematics, 156(18), 3525-3531. [63] Milgram, S. (1967). "The small world problem". Psychology today, 2(1), 60-67. [64] Michaelson, A. and Contractor, N. S. (1992). "Structural position and perceived similarity". Social Psychology Quarterly, 300-310. [65] Müller, J. and Brandes, U. (2022). "The evolution of roles". Social Networks, 68, 195-208. [66] Newman, M. E. (2004). "Detecting community structure in networks". The European Physical Journal B, 38(2), 321-330. [67] Prota, L. and Doreian, P. (2016). "Finding roles in sparse economic hierarchies: Going beyond regular equivalence". Social Networks, 45, 1-17. [68] Rossi, R. A. and Ahmed, N. K. (2014). "Role discovery in networks". IEEE Transactions on Knowledge and Data Engineering, 27(4), 1112-1131. [69] Ruiz-Palazuelos, S. (2021). "Clustering in network games". Economics Letters, 205, 109922. [70] Sailer, L. D. (1978). "Structural equivalence: Meaning and definition, computation and application". Social Networks, 1(1), 73-90.. [71] Simpson, B., Markovsky, B., Steketee, M. (2011). "Power and the perception of social networks". Social Networks, 33(2), 166-171. [72] Smith, E. B., Brands, R. A., Brashears, M. E., Kleinbaum, A. M. (2020). "Social networks and cognition". Annual Review of Sociology, 46, 159-174. [73] Sundararajan, A. (2008). "Local network effects and complex network structure". The BE Journal of Theoretical Economics, 7(1). [74] Soicher, (2004). Topics in Algebraic Graph Theory. Cambridge University Press. [75] Travers, J., Milgram, S. (1977). "An experimental study of the small world problem". In Social networks (pp. 179-197). Academic Press. [76] Vega-Redondo, F. (2007). Complex social networks (No. 44). Cambridge University Press. [77] Wang, H., Yan, G. and Xiao, Y. (2009). "Symmetry in world trade network". Journal of Systems Science and Complexity, 22(2), 280-290. [78] Wasserman, S. and Faust, K. (1994). "Social network analysis: Methods and applications". Cambridge university press. [79] Weinstein, J. and Yildiz, M. (2007). "A structure theorem for rationalizability with application to robust predictions of refinements". Econometrica, 75(2), 365-400. [80] White, H. C., Boorman, S. A. and Breiger, R. L. (1976). "Social structure from multiple networks. I. Blockmodels of roles and positions". American journal of sociology, 81(4), 730-780. [81] Winship, C., Mandel, M. (1983). "Roles and positions: A critique and extension of the blockmodeling approach". Sociological methodology, 14, 314-344. [82] Winship, C. (1988) "Thoughts about roles and relations: an old document revisited". Social Networks, 10(3), 209-231. [83] Xiao, Y., MacArthur, B. D.,Wang, H., Xiong, M. andWang, W. (2008a). "Network quotients: Structural skeletons of complex systems". Physical Review E, 78(4), 046102. [84] Xiao, Y., Xiong, M., Wang, W. and Wang, H. (2008b). "Emergence of symmetry in complex networks". Physical Review E, 77(6), 066108. [85] Xiao, Y. H.,Wu, W. T.,Wang, H., Xiong, M. andWang, W. (2008c). "Symmetry-based structure entropy of complex networks". Physica A: Statistical Mechanics and its Applications, 387(11), 2611-2619.