IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v69y2023i6p3437-3456.html
   My bibliography  Save this article

Optimizing Free-to-Play Multiplayer Games with Premium Subscription

Author

Listed:
  • Yunke Mai

    (Gatton College of Business and Economics, University of Kentucky, Lexington, Kentucky 40506)

  • Bin Hu

    (Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080)

Abstract

We consider the optimal operating policies of a free-to-play multiplayer game with a premium subscription to maximize its lifetime operating profit. Accounting for social comparisons between free and premium players, we model the game attracting or losing players with a hybrid of the Bass diffusion model and the replicator equation in evolutionary game theory. Leveraging optimal control theory, we characterize optimal dynamic pricing and advertising policies and show that the developer should prioritize initial growth through aggressive advertising, while postponing the introduction of a premium subscription. Surprisingly, the optimal subscription price may start high and gradually decrease. We further show that the developer should strengthen social-comparison effects, that payment-based matchmaking can be an effective monetization driver, and that our main findings remain robust when allowing individual in-game item purchases/partial premium subscription. These findings are potentially instructive for game developers adopting the premium subscription model.

Suggested Citation

  • Yunke Mai & Bin Hu, 2023. "Optimizing Free-to-Play Multiplayer Games with Premium Subscription," Management Science, INFORMS, vol. 69(6), pages 3437-3456, June.
    • Handle: RePEc:inm:ormnsc:v:69:y:2023:i:6:p:3437-3456
    DOI: 10.1287/mnsc.2022.4510
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.2022.4510
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.2022.4510?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hummy Song & Anita L. Tucker & Karen L. Murrell & David R. Vinsonc, 2018. "Closing the Productivity Gap: Improving Worker Productivity Through Public Relative Performance Feedback and Validation of Best Practices," Management Science, INFORMS, vol. 64(6), pages 2628-2649, June.
    2. Zijun (June) Shi & Kaifu Zhang & Kannan Srinivasan, 2019. "Freemium as an Optimal Strategy for Market Dominant Firms," Marketing Science, INFORMS, vol. 38(1), pages 150-169, January.
    3. Ningyuan Chen & Adam N. Elmachtoub & Michael L. Hamilton & Xiao Lei, 2021. "Loot Box Pricing and Design," Management Science, INFORMS, vol. 67(8), pages 4809-4825, August.
    4. Qi Feng & Sirong Luo & Dan Zhang, 2014. "Dynamic Inventory–Pricing Control Under Backorder: Demand Estimation and Policy Optimization," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 149-160, February.
    5. Marius F. Niculescu & D. J. Wu, 2014. "Economics of Free Under Perpetual Licensing: Implications for the Software Industry," Information Systems Research, INFORMS, vol. 25(1), pages 173-199, March.
    6. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    7. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    8. Sunil Kumar & Jayashankar M. Swaminathan, 2003. "Diffusion of Innovations Under Supply Constraints," Operations Research, INFORMS, vol. 51(6), pages 866-879, December.
    9. Bin Hu & Zhankun Sun, 2022. "Managing Self-Replicating Innovative Goods," Management Science, INFORMS, vol. 68(1), pages 399-419, January.
    10. Hsi Tse Wang, 2020. "Discussion of the Competitive Strategies of Telecom Operators and Over-the-Top Service Providers from the Perspective of Evolutionary Game Theory," Decision Analysis, INFORMS, vol. 17(3), pages 260-275, September.
    11. Guillaume Roels & Xuanming Su, 2014. "Optimal Design of Social Comparison Effects: Setting Reference Groups and Reference Points," Management Science, INFORMS, vol. 60(3), pages 606-627, March.
    12. Hsing Kenneth Cheng & Yipeng Liu, 2012. "Optimal Software Free Trial Strategy: The Impact of Network Externalities and Consumer Uncertainty," Information Systems Research, INFORMS, vol. 23(2), pages 488-504, June.
    13. Ruslan Momot & Elena Belavina & Karan Girotra, 2020. "The Use and Value of Social Information in Selective Selling of Exclusive Products," Management Science, INFORMS, vol. 66(6), pages 2610-2627, June.
    14. Jiahua Wu & Mengze Shi & Ming Hu, 2015. "Threshold Effects in Online Group Buying," Management Science, INFORMS, vol. 61(9), pages 2025-2040, September.
    15. Friedman, Daniel & Sinervo, Barry, 2016. "Evolutionary Games in Natural, Social, and Virtual Worlds," OUP Catalogue, Oxford University Press, number 9780199981151, Decembrie.
    16. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    17. Albert Y. Ha, 2000. "Stock Rationing in an M/E k /1 Make-to-Stock Queue," Management Science, INFORMS, vol. 46(1), pages 77-87, January.
    18. Hong Guo & Lin Hao & Tridas Mukhopadhyay & Daewon Sun, 2019. "Selling Virtual Currency in Digital Games: Implications for Gameplay and Social Welfare," Information Systems Research, INFORMS, vol. 30(2), pages 430-446, June.
    19. Ming Hu & Joseph Milner & Jiahua Wu, 2016. "Liking and Following and the Newsvendor: Operations and Marketing Policies Under Social Influence," Management Science, INFORMS, vol. 62(3), pages 867-879, March.
    20. Teck-Hua Ho & Sergei Savin & Christian Terwiesch, 2002. "Managing Demand and Sales Dynamics in New Product Diffusion Under Supply Constraint," Management Science, INFORMS, vol. 48(2), pages 187-206, February.
    21. Qi Feng & Sirong Luo & J. George Shanthikumar, 2020. "Integrating Dynamic Pricing with Inventory Decisions Under Lost Sales," Management Science, INFORMS, vol. 66(5), pages 2232-2247, May.
    22. Xin Chen & Zhan Pang & Limeng Pan, 2014. "Coordinating Inventory Control and Pricing Strategies for Perishable Products," Operations Research, INFORMS, vol. 62(2), pages 284-300, April.
    23. Yuqian Xu & Lingjiong Zhu & Michael Pinedo, 2020. "Operational Risk Management: A Stochastic Control Framework with Preventive and Corrective Controls," Operations Research, INFORMS, vol. 68(6), pages 1804-1825, November.
    24. Yi Yang & Youhua (Frank) Chen & Yun Zhou, 2014. "Coordinating Inventory Control and Pricing Strategies Under Batch Ordering," Operations Research, INFORMS, vol. 62(1), pages 25-37, February.
    25. Albert Y. Ha, 1997. "Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales," Management Science, INFORMS, vol. 43(8), pages 1093-1103, August.
    26. repec:hhs:iuiwop:487 is not listed on IDEAS
    27. Appel, Gil & Libai, Barak & Muller, Eitan & Shachar, Ron, 2020. "On the monetization of mobile apps," International Journal of Research in Marketing, Elsevier, vol. 37(1), pages 93-107.
    28. Albert Y. Ha, 1997. "Optimal Dynamic Scheduling Policy for a Make-To-Stock Production System," Operations Research, INFORMS, vol. 45(1), pages 42-53, February.
    29. Hsing Kenneth Cheng & Shengli Li & Yipeng Liu, 2015. "Optimal Software Free Trial Strategy: Limited Version, Time-locked, or Hybrid?," Production and Operations Management, Production and Operations Management Society, vol. 24(3), pages 504-517, March.
    30. Quan Yuan & Youhua (Frank) Chen & Jian Yang & Yun Zhou, 2018. "Joint Control of Emissions Permit Trading and Production Involving Fixed and Variable Transaction Costs," Production and Operations Management, Production and Operations Management Society, vol. 27(8), pages 1420-1454, August.
    31. Wenjing Shen & Izak Duenyas & Roman Kapuscinski, 2011. "New Product Diffusion Decisions Under Supply Constraints," Management Science, INFORMS, vol. 57(10), pages 1802-1810, October.
    32. Wenjing Shen & Izak Duenyas & Roman Kapuscinski, 2014. "Optimal Pricing, Production, and Inventory for New Product Diffusion Under Supply Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 28-45, February.
    33. Julian Runge, & Stefan Wagner & Jörg Claussen & Daniel Klapper, 2016. "Freemium pricing: Evidence from a large-scale field experiment," ESMT Research Working Papers ESMT-16-06, ESMT European School of Management and Technology.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bin Hu & Zhankun Sun, 2022. "Managing Self-Replicating Innovative Goods," Management Science, INFORMS, vol. 68(1), pages 399-419, January.
    2. A. Negahban & J.S. Smith, 2016. "The effect of supply and demand uncertainties on the optimal production and sales plans for new products," International Journal of Production Research, Taylor & Francis Journals, vol. 54(13), pages 3852-3869, July.
    3. Vahideh Manshadi & Sidhant Misra & Scott Rodilitz, 2020. "Diffusion in Random Networks: Impact of Degree Distribution," Operations Research, INFORMS, vol. 68(6), pages 1722-1741, November.
    4. Xiting Gong & Youhua (Frank) Chen & Quan Yuan, 2022. "Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 511-528, February.
    5. Nan Yang & Renyu Zhang, 2022. "Dynamic pricing and inventory management in the presence of online reviews," Production and Operations Management, Production and Operations Management Society, vol. 31(8), pages 3180-3197, August.
    6. Schwarz, Justus Arne & Tan, Barış, 2021. "Optimal sales and production rollover strategies under capacity constraints," European Journal of Operational Research, Elsevier, vol. 294(2), pages 507-524.
    7. Ashkan Negahban & Jeffrey S. Smith, 2018. "A joint analysis of production and seeding strategies for new products: an agent-based simulation approach," Annals of Operations Research, Springer, vol. 268(1), pages 41-62, September.
    8. Hong, Zhaofu & Li, Mengfan & Han, Xiaoya & He, Xuhuai, 2020. "Innovative green product diffusion through word of mouth," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    9. ElHafsi, Mohsen & Fang, Jianxin & Hamouda, Essia, 2021. "Optimal production and inventory control of multi-class mixed backorder and lost sales demand class models," European Journal of Operational Research, Elsevier, vol. 291(1), pages 147-161.
    10. Wenjing Shen & Izak Duenyas & Roman Kapuscinski, 2014. "Optimal Pricing, Production, and Inventory for New Product Diffusion Under Supply Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 28-45, February.
    11. Eryn Juan He & Joel Goh, 2022. "Profit or Growth? Dynamic Order Allocation in a Hybrid Workforce," Management Science, INFORMS, vol. 68(8), pages 5891-5906, August.
    12. Apurva Jain & Swapnil Rayal, 2023. "Managing medical equipment capacity with early spread of infection in a region," Production and Operations Management, Production and Operations Management Society, vol. 32(5), pages 1415-1432, May.
    13. Hongmin Li & Dieter Armbruster & Karl G. Kempf, 2013. "A Population-Growth Model for Multiple Generations of Technology Products," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 343-360, July.
    14. Il-Horn Hann & JooHee Oh, 2017. "Combating Prerelease Piracy: Modeling the Effects of Antipiracy Measures in P2P Networks," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 92-107, February.
    15. Negahban, Ashkan & Smith, Jeffrey S., 2018. "Optimal production-sales policies and entry time for successive generations of new products," International Journal of Production Economics, Elsevier, vol. 199(C), pages 220-232.
    16. Zhang, Mingyang & Zhang, Juliang & Cheng, T.C.E. & Hua, Guowei, 2018. "Why and how do branders sell new products on flash sale platforms?," European Journal of Operational Research, Elsevier, vol. 270(1), pages 337-351.
    17. Krishnan, Trichy V. & Feng, Shanfei & Jain, Dipak C., 2023. "Peak sales time prediction in new product sales: Can a product manager rely on it?," Journal of Business Research, Elsevier, vol. 165(C).
    18. Peters, Kay & Albers, Sönke & Kumar, V., 2008. "Is there more to international Diffusion than Culture? An investigation on the Role of Marketing and Industry Variables," EconStor Preprints 27678, ZBW - Leibniz Information Centre for Economics.
    19. Abedi, Vahideh Sadat, 2019. "Compartmental diffusion modeling: Describing customer heterogeneity & communication network to support decisions for new product introductions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    20. Kartik Hosanagar & Peng Han & Yong Tan, 2010. "Diffusion Models for Peer-to-Peer (P2P) Media Distribution: On the Impact of Decentralized, Constrained Supply," Information Systems Research, INFORMS, vol. 21(2), pages 271-287, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:69:y:2023:i:6:p:3437-3456. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.