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Pricing Virtual Goods: Using Intervention Analysis and Products’ Usage Data Pricing Virtual Goods: Using Intervention Analysis and Products’ Usage Data by Lin Yang A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Applied Science in Management Sciences Waterloo, Ontario, Canada, 2014 © Lin Yang 2014 AUTHOR'S DECLARATION I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract The rapid growth of online games enables firms to charge players for virtual goods they sell for use within their online game environments. Determining prices for such virtual goods is inherently challenging due to the absence of explicit supply curve as the marginal cost of producing additional virtual goods is negligible. Utilizing sales data, we study daily revenue of a firm operating a virtual world and selling cards. Explicitly, we analyze the impact of new product releases on revenue using ARIMA with intervention model. We show that during initial days after a new product release, the firm's daily revenue significantly increases. Using a quality measure, based on the Elo rating method, we can determine the relative good prices based on good usage. Applying this method we show that the rating of a product can be a good proxy for units sold. We conclude that our quality-based measure can be adopted for pricing other virtual goods. iii Acknowledgements I am deeply indebted to Dr. Benny Mantin and Dr. Stanko Dimitrov for their guidance and constant supervision. Their positive attitude and encouragement helped me immensely to achieve my goal. I will always remember the time Dr. Stanko Dimitrov spent to help me develop an academic and professional thinking in research. I am equally grateful to Dr. Benny Mantin for his meticulous attention to detail and his critical thinking when doing research. This dissertation would not be complete without the support of my two supervisors. I would like to thank Dmytro Korol who dedicated invaluable inputs to our project during his co-op term. We had really intensive and meaningful discussions during the progress. I benefited greatly from his passion for research. My gratitude towards our industry partner who was providing necessary data information, and all of the individuals at the organization that supported and helped us throughout the process. It is my pleasure to thank Amy E. Greene who offered her time and shared experiences to help me with improving writing skills almost everyday when I started writing my thesis. I owe all my achievements to my family. I am grateful to my parents, Chuanfeng Yang and Yuzhi Wang, and my brother, Mu Yang. Their unswerving support has helped me overcome difficult times. I have drawn strength and inspiration from them and am fortunate to find my role models so close to me in life. Finally, I would like to thank Dr. Brian Cozzarin and Dr. Selcuk Onay for their careful reviewing and constructive criticism of this thesis. iv Table of Contents AUTHOR'S DECLARATION ............................................................................................................... ii Abstract .................................................................................................................................................. iii Acknowledgements ................................................................................................................................ iv Table of Contents .................................................................................................................................... v List of Figures ........................................................................................................................................ vi List of Tables ........................................................................................................................................ vii Chapter 1 Introduction ............................................................................................................................ 1 Chapter 2 Virtual Worlds: Background .................................................................................................. 3 Chapter 3 Gameplay Background ........................................................................................................... 5 Chapter 4 Exploring Daily Revenue Spikes Through Time-series Analysis ......................................... 7 4.1 The fundamentals of the ARIMA model ...................................................................................... 7 4.2 ARIMA modeling with intervention analysis ............................................................................... 9 4.3 Results of intervention analysis .................................................................................................. 11 4.4 The duration and magnitude of each intervention ...................................................................... 12 Chapter 5 Initial Pricing of Cards: an Elo Rating Approach ................................................................ 15 5.1 The Elo ratings specifics ............................................................................................................. 15 5.2 Set-based Elo rating method ....................................................................................................... 16 5.3 Comparing head-to-head Elo ratings to set-based Elo ratings .................................................... 18 5.4 Implementing the rating system .................................................................................................. 21 5.5 Using Spearman’s and Pearson’s correlations to measure performance .................................... 22 Chapter 6 Concluding Remarks ............................................................................................................ 27 Appendix ............................................................................................................................................... 29 Bibliography ......................................................................................................................................... 35 v List of Figures Figure 1: Daily total revenue and timing of new card releases and other external events ..................... 6 Figure 2: Intervention analysis process ................................................................................................ 10 Figure 3: The ratings from set-based Elo method, uniformly choosing 1 to 4 cards within 5 cards, and the head-to-head Elo method, randomly choosing any two cards, with different observations ........... 19 Figure 4: Correlation tracked with number of observations ................................................................ 21 Figure 5: Spearman's rank correlation between prices and revenue, and between Elo ratings and revenue .................................................................................................................................................. 23 Figure 6: Pearson's correlation between prices and revenue, and between modified Elo and revenue ............................................................................................................................................................... 23 Figure 7: Spearman's rank correlation between prices and units sold, and between Elo ratings and units sold ............................................................................................................................................... 24 Figure 8: Pearson's correlation between prices and units sold, and between modified Elo and units sold ........................................................................................................................................................ 25 Figure A- 1: Proportion of total revenue from cards ............................................................................ 30 vi List of Tables Table 1: The estimation results ............................................................................................................ 12 Table 2: Days to decay for each event and ratio of revenue from average intervention day over nominal day .......................................................................................................................................... 13 Table A- 1: Expected utility of Pack A with respect to D and r. The values of utility are normalized and rounded. The r values were selected based on Taylor (2013). Shaded cells reflect preference for individual card; otherwise the player prefers a pack. ........................................................................... 33 vii Chapter 1 Introduction The inception of the Internet allowed entrepreneurs to create new economies based on goods that have no physical properties besides some bits on a hard drive or network, commonly referred to as digital goods. In this work we focus on a subset of digital goods called virtual goods, goods that are exchanged and used only within online virtual environments. Pricing virtual goods is of great interest to companies operating virtual environments; the standard supply curve is no longer applicable as it can be set by the manufacturer at little to no additional cost. Working with an industry partner who sells virtual goods, we investigate how virtual goods can be priced in order to increase revenue. We characterize the impact of marketing externalities
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