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Potential maximizers and network formation

Author

Listed:
  • Slikker, Marco
  • Dutta, Bhaskar
  • van den Nouweland, Anne
  • Tijs, Stef
Abstract
In this paper we study the formation of cooperation structures in superadditive cooperative TU-games.Cooperation structures are represented by hypergraphs.The formation process is modelled as a game in strategic form, where the payoffs are determined according to a weighted (extended) Myerson value.This class of solution concepts turns out to be the unique class resulting in weighted potential games.The argmax set of the weighted potential predicts the formation of the complete structure and structures payoff-equivalent to the complete structure.As by-products we obtain a representation theorem of weighted potential games in terms of weighted Shapley values and a characterization of the weighted (extended) Myerson values.
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Suggested Citation

  • Slikker, Marco & Dutta, Bhaskar & van den Nouweland, Anne & Tijs, Stef, 2000. "Potential maximizers and network formation," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 55-70, January.
    • Handle: RePEc:eee:matsoc:v:39:y:2000:i:1:p:55-70
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    References listed on IDEAS

    as
    1. Stef Tijs & Anne van den Nouweland & Bhaskar Dutta, 1998. "Link formation in cooperative situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 245-256.
    2. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    3. Slikker, Marco, 2001. "Coalition Formation and Potential Games," Games and Economic Behavior, Elsevier, vol. 37(2), pages 436-448, November.
    4. Slikker, M., 1999. "Coalition Formation and Potential Games," Other publications TiSEM 5d4b7f7b-20a0-440f-a4c2-6, Tilburg University, School of Economics and Management.
    5. Qin, Cheng-Zhong, 1996. "Endogenous Formation of Cooperation Structures," Journal of Economic Theory, Elsevier, vol. 69(1), pages 218-226, April.
    6. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 255-268.
    7. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    9. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    10. Crawford, Vincent P., 1991. "An "evolutionary" interpretation of Van Huyck, Battalio, and Beil's experimental results on coordination," Games and Economic Behavior, Elsevier, vol. 3(1), pages 25-59, February.
    11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    Cited by:

    1. Slikker, M. & Gilles, R.P. & Norde, H.W. & Tijs, S.H., 2000. "Directed Communication Networks," Discussion Paper 2000-84, Tilburg University, Center for Economic Research.
    2. repec:ebl:ecbull:v:3:y:2003:i:12:p:1-11 is not listed on IDEAS
    3. Arnold, Tone & Wooders, Myrna, 2002. "Dynamic Club Formation with Coordination," Economic Research Papers 269414, University of Warwick - Department of Economics.
    4. Rod Garratt & James E. Parco & Cheng-Zhong Qin & Amnon Rapoport, 2005. "Potential Maximization And Coalition Government Formation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 407-429.
    5. Charlson, G., 2021. "Third-Degree Price Discrimination in the Age of Big Data," Janeway Institute Working Papers 2104, Faculty of Economics, University of Cambridge.
    6. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    7. Page Jr., Frank H. & Wooders, Myrna, 2010. "Club networks with multiple memberships and noncooperative stability," Games and Economic Behavior, Elsevier, vol. 70(1), pages 12-20, September.
    8. Slikker, Marco, 2001. "Coalition Formation and Potential Games," Games and Economic Behavior, Elsevier, vol. 37(2), pages 436-448, November.
    9. repec:ebl:ecbull:v:3:y:2003:i:5:p:1-9 is not listed on IDEAS
    10. Roland K. Cheo, 2007. "Adopting Shapley values to address embedding biases in contingent valuation studies," Applied Economics Letters, Taylor & Francis Journals, vol. 14(10), pages 765-768.
    11. Jun, Tackseung & Kim, Jeong-Yoo, 2009. "Hypergraph Formation Game," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 50(2), pages 1-16, December.
    12. Navarro Noemí & Perea Andres, 2013. "A Simple Bargaining Procedure for the Myerson Value," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 131-150, May.
    13. Slikker, M. & Gilles, R.P. & Norde, H.W. & Tijs, S.H., 2000. "Directed Communication Networks," Other publications TiSEM 00f2df6e-3a8e-4ed3-84cf-2, Tilburg University, School of Economics and Management.
    14. Charlson, G., 2021. "Third-Degree Price Discrimination in the Age of Big Data," Cambridge Working Papers in Economics 2159, Faculty of Economics, University of Cambridge.
    15. Slikker, Marco & Gilles, Robert P. & Norde, Henk & Tijs, Stef, 2005. "Directed networks, allocation properties and hierarchy formation," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 55-80, January.
    16. Filippo Vergara Caffarelli, 2009. "Networks with decreasing returns to linking," Temi di discussione (Economic working papers) 734, Bank of Italy, Economic Research and International Relations Area.
    17. Chen, J. & Elliott, M. & Koh, A., 2020. "Capability Accumulation and Conglomeratization in the Information Age," Cambridge Working Papers in Economics 2069, Faculty of Economics, University of Cambridge.

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