Abstract
Social networks play an important role in life. We interact with our friends, neighbors and business partners, who in turn also interact with people who are not part of the community we directly interact with. How people form and maintain networks and how networks impact their behaviors raises behavioral questions that have been addressed by sociologists, economists, physicists, computer scientists and anthropologists.
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Notes
- 1.
This result is even stronger in similar experiments based on the minimum-pay-off function rather than the average-pay-off function in Keser et al. (1998).
- 2.
Bala and Goyal (2000) introduce a network in the two-way flow model as a non-directed graph. This makes sense when an edge between two players denotes the two-way flow. In our model we emphasize the aspect of opening connections. We are interested in finding out which players initiate links with other players. For example, when both players i and j open a link with each other they are connected in the corresponding directed graph via two adversely oriented edges.
- 3.
For example, if g ij = 0, but g ji = 1 holds.
- 4.
This assumption contrasts with the framework of Bala and Goyal in which a player receives a payoff of a even if he is isolated in the network.
- 5.
In labor markets, for example, social networks play a significant role in getting a job. The empirical investigation of Granovetter (1995) concentrates on jobs found via social contacts. It reveals that the main part of the people, who got their job via social contacts, had heard about it from their friends, relatives or acquaintances (39.1% of the cases), or from acquaintances of those (45.3 %). That is, from a network point of view the person who is looking for a job has access to the information of his “neighbors” who are at the most two “steps” away.
- 6.
A periphery-sponsored star is a graph where all n−1 players in I− { i } have an active connection with i, no other connections exist.
- 7.
Two networks have the same architecture if one network can be obtained from the other by permuting the labels of agents. For example for n = 6 players the ps-star architecture has 6 configurations, i.e. the ps-stars are 6 of (25)6 = 1.073.741.824 possible networks or 1 of 1.540.944 possible architectures.
- 8.
It is easy to see that the strategic problem for a single player in treatment IV is rather simple. The empty network is the only strict Nash network, no other network has the Nash property.
- 9.
In a population of n = 6 players we find 6 essentially different ps-stars that are obtained by interchanging the center players.
- 10.
Note that we distinguish in this model only active and passive neighbors. In contrast to the model of network formation in the previous section we assume that players do not play a base game with indirect neighbors.
- 11.
Concerning continuous time experiments we refer to the results in the section “Strategic network formation.”
- 12.
A detailed report on these experiments can be found in Berninghaus et al. (2010).
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Appendix
Appendix
Experimental Results of Coordination on Networks: Graphical Illustration
Percentage of X-decisions in AVG2GROUP and AVG2CIRCLE
Percentage of X-decisions in AVG2CIRCLE and AVG4CIRCLE
Percentage of X-decisions in AVG4CIRCLE and AVG4LATTICE
Experimental Results of the Network Formation Game: Graphical Illustrations
Observed ps-stars in groups 1–8 (treatment I)
Observed ps-stars in groups 1–8 (treatment II)
Observed ps-stars in groups 1–8 (treatment III)
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Berninghaus, S.K., Keser, C., Vogt, B. (2010). Strategy Choice and Network Effects. In: Sadrieh, A., Ockenfels, A. (eds) The Selten School of Behavioral Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13983-3_8
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