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Interconnected Contests

Author

Listed:
  • Marcin Dziubi'nski
  • Sanjeev Goyal
  • Junjie Zhou

Abstract

We study a two-player model of conflict with multiple battlefields -- the novel element is that each of the players has their own network of spillovers so that resources allocated to one battle can be utilized in winning neighboring battles. There exists a unique equilibrium in which the relative probability of a player winning a battle is the product of the ratio of the centrality of the battlefield in the two respective competing networks and the ratio of the relative cost of efforts of the two players. We study the design of networks and characterize networks that maximize total efforts and maximize total utility. Finally, we characterize the equilibrium of a game in which players choose both networks and efforts in the battles.

Suggested Citation

  • Marcin Dziubi'nski & Sanjeev Goyal & Junjie Zhou, 2025. "Interconnected Contests," Papers 2510.11452, arXiv.org.
    • Handle: RePEc:arx:papers:2510.11452
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    References listed on IDEAS

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    1. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    2. Yann Bramoull? & Rachel Kranton & Martin D'Amours, 2014. "Strategic Interaction and Networks," American Economic Review, American Economic Association, vol. 104(3), pages 898-930, March.
    3. Brams, Steven J. & Davis, Morton D., 1974. "The 3/2's Rule in Presidential Campaigning," American Political Science Review, Cambridge University Press, vol. 68(1), pages 113-134, March.
    4. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    5. Olszewski, Wojciech & Siegel, Ron, 2020. "Performance-maximizing large contests," Theoretical Economics, Econometric Society, vol. 15(1), January.
    6. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    7. Kenan Huremović, 2021. "A noncooperative model of contest network formation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 275-317, April.
    8. Christian Ewerhart, 2015. "Mixed equilibria in Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 59-71, September.
    9. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    10. Ewerhart, Christian, 2017. "Revenue ranking of optimally biased contests: The case of two players," Economics Letters, Elsevier, vol. 157(C), pages 167-170.
    11. Avinash Dixit, 2008. "Strategic Behavior in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 431-438, Springer.
    12. Dan Kovenock & Brian Roberson, 2018. "The Optimal Defense Of Networks Of Targets," Economic Inquiry, Western Economic Association International, vol. 56(4), pages 2195-2211, October.
    13. repec:oup:restud:v:81:y:2014:i:4:p:1518-1542. is not listed on IDEAS
    14. Michael D. König & Dominic Rohner & Mathias Thoenig & Fabrizio Zilibotti, 2017. "Networks in Conflict: Theory and Evidence From the Great War of Africa," Econometrica, Econometric Society, vol. 85, pages 1093-1132, July.
    15. Itay P. Fainmesser & Andrea Galeotti, 2020. "Pricing Network Effects: Competition," American Economic Journal: Microeconomics, American Economic Association, vol. 12(3), pages 1-32, August.
    16. Sanjeev Goyal & Adrien Vigier, 2014. "Attack, Defence, and Contagion in Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1518-1542.
    17. Dasgupta, Partha & Stiglitz, Joseph, 1980. "Industrial Structure and the Nature of Innovative Activity," Economic Journal, Royal Economic Society, vol. 90(358), pages 266-293, June.
    18. Xu, Jin & Zenou, Yves & Zhou, Junjie, 2022. "Equilibrium characterization and shock propagation in conflict networks," Journal of Economic Theory, Elsevier, vol. 206(C).
    19. Itay P. Fainmesser & Andrea Galeotti, 2016. "Pricing Network Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(1), pages 165-198.
    20. Marina Halac & Navin Kartik & Qingmin Liu, 2017. "Contests for Experimentation," Journal of Political Economy, University of Chicago Press, vol. 125(5), pages 1523-1569.
    21. Dziubiński, Marcin & Goyal, Sanjeev, 2013. "Network design and defence," Games and Economic Behavior, Elsevier, vol. 79(C), pages 30-43.
    22. Snyder, James M, 1989. "Election Goals and the Allocation of Campaign Resources," Econometrica, Econometric Society, vol. 57(3), pages 637-660, May.
    23. Dawei Fang & Thomas Noe & Philipp Strack, 2020. "Turning Up the Heat: The Discouraging Effect of Competition in Contests," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1940-1975.
    24. Fu, Qiang & Wu, Zenan, 2020. "On the optimal design of biased contests," Theoretical Economics, Econometric Society, vol. 15(4), November.
    25. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    26. Garfinkel, Michelle R. & Skaperdas, Stergios (ed.), 2012. "The Oxford Handbook of the Economics of Peace and Conflict," OUP Catalogue, Oxford University Press, number 9780195392777.
    27. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    28. Lawrence Friedman, 1958. "Game-Theory Models in the Allocation of Advertising Expenditures," Operations Research, INFORMS, vol. 6(5), pages 699-709, October.
    29. Hinnosaar, Toomas, 2024. "Optimal sequential contests," Theoretical Economics, Econometric Society, vol. 19(1), January.
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