Monotonicity in sharing the revenues from broadcasting sports leagues

Bergantiños, Gustavo and Moreno-Ternero, Juan D. (2021): Monotonicity in sharing the revenues from broadcasting sports leagues.

Abstract

We explore the implications of the principle of monotonicity in the problem of sharing the revenues from broadcasting sports leagues. We formalize different forms of this principle as several axioms for sharing rules. We show that, combined with two other basic axioms (equal treatment of equals and additivity), they provide axiomatic characterizations of focal rules for this problem, as well as families of rules compromising among them.

• Item Type: MPRA Paper
• Language: English
• Keywords: resource allocation, broadcasting, axioms, monotonicity, additivity.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

References

Algaba E., Fragnelli, V., Llorca, N., Sánchez-Soriano, J., 2019. Horizontal cooperation in a multimodal public transport system: The profit allocation problem. European Journal of Operational Research 275, 659-665.

Arlegi, R., Dimitrov, D., 2020. Fair elimination-type competitions, European Journal of Operational Research 287, 528-535.

Bergantiños, G., Gomez-Rua, M., Llorca, N., Pulido, M., Sanchez-Soriano, J., 2020. Allocating costs in set covering problems, European Journal of Operational Research 284, 1074-1087.

Bergantiños, G., Moreno-Ternero, J.D., 2015. The axiomatic approach to the problem of sharing the revenue from museum passes. Games and Economic Behavior 89, 78-92.

Bergantiños, G., Moreno-Ternero, J.D., 2020a. Sharing the revenues from broadcasting sport events. Management Science 66 (6), 2417-2431.

Bergantiños, G., Moreno-Ternero, J.D., 2020b. Allocating extra revenues from broadcasting sports leagues. Journal of Mathematical Economics 90, 65-73.

Bergantiños, G., Moreno-Ternero, J.D., 2020c. On the axiomatic approach to sharing the revenues from broadcasting sports leagues. Mimeo Repec.

Bergantiños, G., Moreno-Ternero, J.D., 2020d. Broadcasting La Liga. Mimeo, Repec.

Bergantiños, G., Moreno-Ternero, J.D., 2021. Compromising to share the revenues from broadcasting sports leagues. Journal of Economic Behavior and Organization 183, 57-74.

Bergantiños, G., Vidal-Puga, J., 2007. A fair rule in minimum cost spanning tree problems. Journal of Economic Theory 137, 326-352.

van den Brink, R., 2007. Null or nullifying players: The difference between the Shapley value and equal division solutions. Journal of Economic Theory 136, 767-775.

van den Brink, R. Funaki, Y., Ju, Y., 2013. Reconciling marginalism with egalitarism: consistency, monotonicity, and implementation of egalitarian Shapley values. Social Choice and Welfare 40, 693-714.

van Bulck, D., Goossens, D., Schonberger, J., Guajardo, M., 2020. RobinX: A three-field classification and unified data format for round-robin sports timetabling, European Journal of Operational Research 280, 568-580.

Calleja, P., Llerena F., 2017. Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results. Social Choice and Welfare 48, 197-220.

Calleja, P., Llerena F., Sudholter, P., 2021. Constrained welfare egalitarianism in surplus-sharing problems. Mathematical Social Sciences 109, 45-51.

Casajus, A., Huettner, F., 2013. Null players, solidarity, and the egalitarian Shapley values, Journal of Mathematical Economics 49, 58-61.

Casajus, A., Huettner, F., 2014. Weakly monotonic solutions for cooperative games, Journal of Economic Theory 154, 162-172.

Chun, Y., Thomson, W., 1988. Monotonicity properties of bargaining solutions when applied to economics, Mathematical Social Sciences 15, 11-27.

Csato, L., Petroczy, D., 2021. On the monotonicity of the eigenvector method, European Journal of Operational Research. Forthcoming.

Elitzur, R., 2020. Data analytics effects in major league baseball. Omega 90, 102001

Gaertner W., Xu, Y., Loss sharing: Characterizing a new class of rules. Mathematical Social Sciences 107, 37-40.

Ginsburgh, V., Zang, I., 2003. The museum pass game and its value. Games and Economic Behavior 43, 322-325.

Goller, D., Krumer, A., 2020. Let's meet as usual: Do games played on non-frequent days differ? Evidence from top European soccer leagues, European Journal of Operational Research 286, 740-754.

Kalai, E., 1977. Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45, 1623-1630.

Kalai, E., Smorodinsky, M., 1975. Other solutions to Nash's bargaining problem. Econometrica 43, 513-518.

Littlechild, S., Owen. G., 1973, A simple expression for the Shapley value in a special case. Management Science 20, 370-372.

van den Nouweland, A., Borm, P., van Golstein Brouwers, W., Groot Bruinderink, R., Tijs, S., 1996. A Game Theoretic Approach to Problems in Telecommunication. Management Science 42, 294-303.

Li, Y., Wang, L., Li, F., 2021. A data-driven prediction approach for sports team performance and its application to National Basketball Association. Omega 98, 102123.

Meggido, N., 1994. On the non-monotonicity of the bargaining set, the kernel, and the nucleolus of a game, SIAM Journal of Applied Mathematics 27, 355-358.

Moreno-Ternero, J., Vidal-Puga, J., 2021. Aggregator operators for dynamic rationing. European Journal of Operations Research 288, 682-691.

Moulin, H., Thomson, W., 1988. Can everyone benefit from growth? Two difficulties, Journal of Mathematical Economics 17, 339-345.

O'Neill, B., 1982. A problem of rights arbitration from the Talmud. Mathematical Social Sciences 2, 345-371.

Peeters, T., Salaga, S., Juravich, M., 2020. Matching and Winning? The Impact of Upper and Middle Managers on Firm Performance in Major League Baseball, Management Science 66, 2735-2751.

Roemer, 1986. Equality of resources implies equality of welfare, Quarterly Journal of Economics 101, 751-784.

Song, K., Shi, J., 2020. A gamma process based in-play prediction model for National Basketball Association games, European Journal of Operational Research 283, 706-713.

Thomson W., 1999. Options-monotonic allocation rules. Mimeo. University of Rochester.

Thomson W., 2019. How to divide when there isn't enough: from Aristotle, the Talmud, and Maimonides to the axiomatics of resource allocation, Econometric Society Monograph. Cambridge University Press

homson, W., Myerson, R., 1980. Monotonicity and independence axioms, International Journal of Game Theory 9, 37-49.

Tijs, S., Branzei, R., Moretti, S., and Norde, H., 2006. Obligation rules for minimum cost spanning tree situations and their monotonicity properties. European Journal of Operational Research 175, 121-134.

Young, H.P. , 1985. Monotonic solutions of cooperative games. International Journal of Game Theory 14, 65-72.

Young H.P., (1987) On dividing an amount according to individual claims or liabilities, Mathematics of Operations Research 12, 398-414.

Young H.P., 1988. Distributive justice in taxation. Journal of Economic Theory 43, 321-335.

Yi, X., Goossens, D., Nobibon, F.T., 2020, Proactive and reactive strategies for football league timetabling. European Journal of Operational Research 282, 772-785.