# American Institute of Mathematical Sciences

July  2019, 6(3): 211-219. doi: 10.3934/jdg.2019015

## Social networks and global transactions

 School of Management, Yasuda Women's University, 6-13-1 Yasuhigashi, Hiroshima, 731-0153, Japan

* Corresponding author: Yuki Kumagai

Received  March 2019 Published  July 2019

In the repeated prisoner's dilemma with private monitoring, Bhaskar and Obara [2] construct a belief-based mixed trigger strategy which may be modified to approximate full cooperation when a public randomisation device is available. By modifying their assumption about trading relationships, this paper generalises the model and demonstrates that without introducing public randomisations, long-run cooperation may be approximately sustained by mixed trigger strategies with delayed communication. By applying our model, we investigate when efficient trade is attainable in a nonmarket trading system of social networks by looking into a role of communication in long-run community enforcement of efficient trade.

Citation: Yuki Kumagai. Social networks and global transactions. Journal of Dynamics and Games, 2019, 6 (3) : 211-219. doi: 10.3934/jdg.2019015
##### References:
 [1] D. Abreu, P. Milgrom and D. Pearce, Information and timing in repeated partnerships, Econometrica, 59 (1991), 1713-1733.  doi: 10.2307/2938286. [2] V. Bhaskar and I. Obara, Belief-based equilibria in the repeated prisoners' dilemma with private monitoring, Journal of Economic Theory, 102 (2002), 40-69.  doi: 10.1006/jeth.2001.2878. [3] G. Ellison, Cooperation in the prisoner's dilemma with anonymous random matching, Review of Economic Studies, 61 (1994), 567-588.  doi: 10.2307/2297904. [4] D. Fudenberg, D. Levine and E. Maskin, The folk theorem with imperfect public information, Econometrica, 62 (1994), 997-1039.  doi: 10.2307/2951505. [5] A. Greif, Institutions and the Path to the Modern Economy: Lessons from Medieval trade, Cambridge University Press, Cambridge and New York, 2006.  doi: 10.1017/CBO9780511791307. [6] M. Kandori, Social norms and community enforcement, Review of Economic Studies, 59 (1992), 63-80. [7] M. Kandori, Repeated games played by overlapping generations of players, Review of Economic Studies, 59 (1992), 81-92.  doi: 10.2307/2297926. [8] R. Radner, R. Myerson and E. Maskin, An example of a repeated partnership game with discounting and with uniformly inefficient equilibria, Review of Economic Studies, 53 (1986), 59-69.  doi: 10.2307/2297591. [9] J. Rauch and V. Trindade, Ethnic Chinese networks in international trade, Review of Economics and Statistics, 84 (2002), 116-130.

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##### References:
 [1] D. Abreu, P. Milgrom and D. Pearce, Information and timing in repeated partnerships, Econometrica, 59 (1991), 1713-1733.  doi: 10.2307/2938286. [2] V. Bhaskar and I. Obara, Belief-based equilibria in the repeated prisoners' dilemma with private monitoring, Journal of Economic Theory, 102 (2002), 40-69.  doi: 10.1006/jeth.2001.2878. [3] G. Ellison, Cooperation in the prisoner's dilemma with anonymous random matching, Review of Economic Studies, 61 (1994), 567-588.  doi: 10.2307/2297904. [4] D. Fudenberg, D. Levine and E. Maskin, The folk theorem with imperfect public information, Econometrica, 62 (1994), 997-1039.  doi: 10.2307/2951505. [5] A. Greif, Institutions and the Path to the Modern Economy: Lessons from Medieval trade, Cambridge University Press, Cambridge and New York, 2006.  doi: 10.1017/CBO9780511791307. [6] M. Kandori, Social norms and community enforcement, Review of Economic Studies, 59 (1992), 63-80. [7] M. Kandori, Repeated games played by overlapping generations of players, Review of Economic Studies, 59 (1992), 81-92.  doi: 10.2307/2297926. [8] R. Radner, R. Myerson and E. Maskin, An example of a repeated partnership game with discounting and with uniformly inefficient equilibria, Review of Economic Studies, 53 (1986), 59-69.  doi: 10.2307/2297591. [9] J. Rauch and V. Trindade, Ethnic Chinese networks in international trade, Review of Economics and Statistics, 84 (2002), 116-130.
The stage-game payoffs
 $e$ $s$ $e$ $1, 1$ $-l, 1+g$ $s$ $1+g, - l$ $0$, $0$
 $e$ $s$ $e$ $1, 1$ $-l, 1+g$ $s$ $1+g, - l$ $0$, $0$

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