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The Tennis Coach Problem: A Game-Theoretic and Experimental Study

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  • Arad Ayala

    (Tel Aviv University)

Abstract

The paper introduces a new allocation game, related to Blotto games: each tennis coach assigns his four different skilled players to four positions, and then each team plays all other teams in the tournament. The winning team is the one with the highest total score.The set of equilibria is characterized and experimental behavior in variants of the game is analyzed in light of an adapted level-k model which is based on an appealing specification of the starting point (Level-0). The results exhibit a systematic pattern- a majority of the subjects used a small number of strategies. However, although level-k thinking is naturally specified in this context, only a limited use of (low) level-k thinking was found. These findings differ from those obtained in previous studies, which found high frequencies of level-k reasoning among subjects in various games. Thus, the results illuminate some bounds of the level-k approach.

Suggested Citation

  • Arad Ayala, 2012. "The Tennis Coach Problem: A Game-Theoretic and Experimental Study," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-43, April.
    • Handle: RePEc:bpj:bejtec:v:12:y:2012:i:1:n:10
    DOI: 10.1515/1935-1704.1738
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    2. Subhasish M Chowdhury & Dan Kovenock & David Rojo Arjona & Nathaniel T Wilcox, 2021. "Focality and Asymmetry in Multi-Battle Contests," The Economic Journal, Royal Economic Society, vol. 131(636), pages 1593-1619.
    3. Dan Kovenock & Brian Roberson & Roman M. Sheremeta, 2019. "The attack and defense of weakest-link networks," Public Choice, Springer, vol. 179(3), pages 175-194, June.
    4. Deck, Cary & Sheremeta, Roman M., 2019. "The tug-of-war in the laboratory," European Journal of Political Economy, Elsevier, vol. 60(C).
    5. Shakun D. Mago & Roman M. Sheremeta, 2019. "New Hampshire Effect: behavior in sequential and simultaneous multi-battle contests," Experimental Economics, Springer;Economic Science Association, vol. 22(2), pages 325-349, June.
    6. Ayala Arad & Ariel Rubinstein, 2013. "Strategic Tournaments," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 31-54, November.
    7. Shane Sanders & Justin Ehrlich & James Boudreau, 2017. "Cycles in Team Tennis and Other Paired-Element Contests," Games, MDPI, vol. 8(3), pages 1-14, June.
    8. Shakun D. Mago & Roman M. Sheremeta, 2017. "Multi‐battle Contests: An Experimental Study," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 407-425, October.
    9. Zeynep B. Irfanoglu & Shakun D. Mago & Roman M. Sheremeta, 2014. "The New Hampshire Effect: Behavior in Sequential and Simultaneous Election Contests," Working Papers 14-15, Chapman University, Economic Science Institute.
    10. Cubel, María & Sanchez-Pages, Santiago, 2022. "Gender differences in equilibrium play and strategic sophistication variability," Journal of Economic Behavior & Organization, Elsevier, vol. 194(C), pages 287-299.
    11. Daniel Rehsmann, 2023. "The Sumo coach problem," Review of Economic Design, Springer;Society for Economic Design, vol. 27(3), pages 669-700, September.
    12. Ayala Arad & Benjamin Bachi & Amnon Maltz, 2023. "On the relevance of irrelevant strategies," Experimental Economics, Springer;Economic Science Association, vol. 26(5), pages 1142-1184, November.
    13. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    14. Arad, Ayala & Rubinstein, Ariel, 2012. "Multi-dimensional iterative reasoning in action: The case of the Colonel Blotto game," Journal of Economic Behavior & Organization, Elsevier, vol. 84(2), pages 571-585.
    15. Deck, Cary & Hao, Li & Porter, David, 2015. "Do prediction markets aid defenders in a weak-link contest?," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 248-258.

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