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[PAXDEV2019] Implementing Behavioral Economics Model into a Game Server

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[PAXDEV2019] Implementing Behavioral Economics Model into a Game Server

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Video game player has diverse motivations; they change as time passes. In this session, Sentience's Research Lead, Hyeyon Kwon, will describe 1) how to parametrize motivation from game log data, 2) build behavioral economics models, and 3) apply the analysis result and implications to the game server. With this approach, at one of the clients' games, the targeted user's retention rate, in-app purchase, and engagement have increased significantly.

Video game player has diverse motivations; they change as time passes. In this session, Sentience's Research Lead, Hyeyon Kwon, will describe 1) how to parametrize motivation from game log data, 2) build behavioral economics models, and 3) apply the analysis result and implications to the game server. With this approach, at one of the clients' games, the targeted user's retention rate, in-app purchase, and engagement have increased significantly.

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[PAXDEV2019] Implementing Behavioral Economics Model into a Game Server

  1. 1. Implementing Behavioral Economics Model into a Game Server
  2. 2. Who we are • Behavioral economics-based AI company • Analyze games and user’s behavior and their motivation- to-play • Develop and service recommendation system based on the user’s motivation-to-play
  3. 3. What I am going to talk about 1. Meta model for user’s motivation-to-play 2. How to measure each motivation based on player’s log data • Analysis cases 3. Integrate the model-driven analysis into the game server 4. The results and use cases 5. Conclusion
  4. 4. What I am going to talk about 1. Meta model for user’s motivation-to-play 2. How to measure each motivation based on player’s log data • Analysis cases 3. Integrate the model-driven analysis into the game server 4. The results and use cases 5. Conclusion
  5. 5. What I am going to talk about 1. Meta model for user’s motivation-to-play 2. How to measure each motivation based on player’s log data • Analysis cases 3. Integrate the model-driven analysis into the game server 4. The results and use cases 5. Conclusion
  6. 6. What I am going to talk about 1. Meta model for user’s motivation-to-play 2. How to measure each motivation based on player’s log data • Analysis cases 3. Integrate the model-driven analysis into the game server 4. The results and use cases 5. Conclusion
  7. 7. Behavioral economics?
  8. 8. Behavioral economics? Behavioral Economics • Integrated from psychological research into economic science • Study of the effect of psychological, emotional, social factors on economic decisions of individuals
  9. 9. Motivation-to-play Motivation Decision & Action It takes too much time to level up. Games are pushing too many pop-ups and ads. My character is not strong enough! There are not enough PvE contents I want! There are not many cute characters. There are not many PvP contents I want.
  10. 10. Motivation-to-play RETENTION Want to be famous To kill times Catch monster Play PvP Collect characters App open rates, times Personal information Device type Love for the character Motivation Behavior Superficial factors
  11. 11. Meta model for motivation-to-play SocialPersonal Intrinsic Extrinsic Personal Satisfaction Social Interaction Personal Rewards Public Recognition • McGuinness M. 2015. Motivation for Creative People: How to Stay Creative While Gaining Money • Rigby, S. and Skinner, T. GDC 2014, The Importance of Player Autonomy: Motivating Sustained Engagement through Volition and Choice • Baron J. GDC 1999, Glory and Shame: Powerful Psychology in Multiplayer Online Games • Ryan, R.M. and Deci, E.L.2000. Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions
  12. 12. Meta model for motivation-to-play SocialPersonal Intrinsic Extrinsic Personal Satisfaction Social Interaction Personal Rewards Public Recognition • McGuinness M. 2015. Motivation for Creative People: How to Stay Creative While Gaining Money • Rigby, S. and Skinner, T. GDC 2014, The Importance of Player Autonomy: Motivating Sustained Engagement through Volition and Choice • Baron J. GDC 1999, Glory and Shame: Powerful Psychology in Multiplayer Online Games • Ryan, R.M. and Deci, E.L.2000. Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions Inherently interesting or enjoyable
  13. 13. Meta model for motivation-to-play SocialPersonal Intrinsic Extrinsic Personal Satisfaction Social Interaction Personal Rewards Public Recognition • McGuinness M. 2015. Motivation for Creative People: How to Stay Creative While Gaining Money • Rigby, S. and Skinner, T. GDC 2014, The Importance of Player Autonomy: Motivating Sustained Engagement through Volition and Choice • Baron J. GDC 1999, Glory and Shame: Powerful Psychology in Multiplayer Online Games • Ryan, R.M. and Deci, E.L.2000. Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions Inherently interesting or enjoyable Leads to a separable outcome
  14. 14. Meta model for motivation-to-play SocialPersonal Intrinsic Extrinsic Personal Satisfaction Social Interaction Personal Rewards Public Recognition • McGuinness M. 2015. Motivation for Creative People: How to Stay Creative While Gaining Money • Rigby, S. and Skinner, T. GDC 2014, The Importance of Player Autonomy: Motivating Sustained Engagement through Volition and Choice • Baron J. GDC 1999, Glory and Shame: Powerful Psychology in Multiplayer Online Games • Ryan, R.M. and Deci, E.L.2000. Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions Inherently interesting or enjoyable Leads to a separable outcome Need for self expression
  15. 15. Meta model for motivation-to-play SocialPersonal Intrinsic Extrinsic Personal Satisfaction Social Interaction Personal Rewards Public Recognition • McGuinness M. 2015. Motivation for Creative People: How to Stay Creative While Gaining Money • Rigby, S. and Skinner, T. GDC 2014, The Importance of Player Autonomy: Motivating Sustained Engagement through Volition and Choice • Baron J. GDC 1999, Glory and Shame: Powerful Psychology in Multiplayer Online Games • Ryan, R.M. and Deci, E.L.2000. Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions Inherently interesting or enjoyable Leads to a separable outcome Need for self expression Other people’s opinions matter
  16. 16. Who are social-intrinsic people? SocialPersonal Intrinsic Extrinsic • Harmony • Collaboration • Loyalty • … Personal Satisfaction Social Interaction Personal Rewards Public Recognition
  17. 17. Who are social-intrinsic people?
  18. 18. Who are social-extrinsic people? Personal Satisfaction Social Interaction Personal Rewards Public Recognition SocialPersonal Intrinsic Extrinsic • Recognition • Appreciation • Awards and Prizes • …
  19. 19. Who are social-extrinsic people?
  20. 20. Who are personal-extrinsic people? Personal Satisfaction Social Interaction Personal Rewards Public Recognition SocialPersonal Intrinsic Extrinsic • Money • Privileges • Opportunities • …
  21. 21. Who are personal-extrinsic people?
  22. 22. Who are personal-intrinsic people? Personal Satisfaction Social Interaction Personal Rewards Public Recognition SocialPersonal Intrinsic Extrinsic • Pleasure • Learning • Meaning • …
  23. 23. Who are personal-intrinsic people?
  24. 24. Analysis methodology How to define & parametrize & analyze the motivation model?
  25. 25. Analysis methodology How to define & parametrize & analyze the motivation model? Econometrics Methodology
  26. 26. Analysis methodology How to define & parametrize & analyze the motivation model? Behavioral Economics vs Econometrics • Behavioral economics: Study of the effect of psychological, emotional, social factors on economic decisions of individuals • Econometrics: Statistical methods for empirical analysis
  27. 27. Analysis methodology How to define & parametrize & analyze the motivation model? Behavioral Economics vs Econometrics • Behavioral economics: Study of the effect of psychological, emotional, social factors on economic decisions of individuals • Econometrics: Statistical methods for empirical analysis BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE
  28. 28. Case 1: Play Garden
  29. 29. Case 1: Play Garden Social interaction in the social game (Play Garden) Personal Satisfaction Social Interaction Personal Rewards Public Recognition
  30. 30. Case 1: Play Garden Social interaction in the social game (Play Garden) Shutdown law in South Korea forbidding children under the age of 16 to play online video games between 00:00~06:00
  31. 31. Case 1: Play Garden Social interaction in the social game (Play Garden) Research Question: How shutdown law changed the social interactions among players? Shutdown law in South Korea forbidding children under the age of 16 to play online video games between 00:00~06:00
  32. 32. Case 1: Play Garden Social interaction in the social game (Play Garden) Social interaction Network effect Find social interaction in Play Garden1 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE
  33. 33. Case 1: Play Garden Social interaction in the social game (Play Garden) Social interaction Network effect Find social interaction in Play Garden1 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE As more users use a service, they create more values, and more people join
  34. 34. Case 1: Play Garden Social interaction in the social game (Play Garden) Social interaction Network effect Find social interaction in Play Garden1 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE More users ↔ the number of concurrent users Use a service & create more value ↔ play time
  35. 35. Case 1: Play Garden Social interaction in the social game (Play Garden) Parametrize social interaction The number of concurrent users and their play time Social interaction Network effect 2 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE
  36. 36. Case 1: Play Garden Social interaction in the social game (Play Garden) Social interaction Network effect Find social interaction in Play Garden1 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE • The number of concurrent users • Total play time • Other variables that may affect the players: • Level, gold
  37. 37. Case 1: Play Garden Social interaction in the social game (Play Garden) Build a model measuring social interaction and the effect of shutdown policy 3 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE
  38. 38. Case 1: Play Garden Social interaction in the social game (Play Garden) The number of concurrent users The number of concurrent users The user’s play time - The user’s level - Gold - Weekend - School vacations - Demographics BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kwon and Suh (2013)
  39. 39. Case 1: Play Garden Social interaction in the social game (Play Garden) The number of concurrent users The number of concurrent users The user’s play time - The user’s level - Gold - Weekend - School vacations - Demographics BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kwon and Suh (2013) Shutdown Law
  40. 40. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE 2SLS Select the right methodology and analyze 4 Chow Test Source: Kwon and Suh (2013)
  41. 41. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE 2SLS A methodology for analyzing the effect of independent variables on the dependent variable when there are feedback loops in the model Select the right methodology and analyze 4 Chow Test A methodology for testing the presence of a structural break at a specific event in time series data Source: Kwon and Suh (2013)
  42. 42. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Select the right methodology and analyze 4 Source: Kwon and Suh (2013) The number of concurrent users The number of concurrent users The user’s play time - The user’s level - Gold - Weekend - School vacations - Demographics Shutdown Law
  43. 43. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE 2SLS A methodology for analyzing the effect of independent variables on the dependent variable when there are feedback loops in the model Select the right methodology and analyze 4 Chow Test A methodology for testing the presence of a structural break at a specific event in time series data Source: Kwon and Suh (2013)
  44. 44. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Select the right methodology and analyze 4 Source: Kwon and Suh (2013) The number of concurrent users The number of concurrent users The user’s play time - The user’s level - Gold - Weekend - School vacations - Demographics Shutdown Law
  45. 45. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kwon and Suh (2013) The number of concurrent users The number of concurrent users The user’s play time - The user’s level - Gold - Weekend - School vacations - Demographics Result: Before shutdown law No network effect
  46. 46. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kwon and Suh (2013) Result: After shutdown law Network Effect & Reverse Network Effect The number of concurrent users The number of concurrent users The user’s play time - The user’s level - Gold - Weekend - School vacations - Demographics Shutdown Law
  47. 47. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kwon and Suh (2013) Result: After shutdown law Network Effect & Reverse Network Effect More concurrent users Play time Fewer concurrent users
  48. 48. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kwon and Suh (2013) Result: After shutdown law Network Effect & Reverse Network Effect More concurrent users Play time Fewer concurrent users Reverse network effect
  49. 49. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kwon and Suh (2013) Result: After shutdown law Network Effect & Reverse Network Effect More concurrent users Play time Fewer concurrent users Network effect
  50. 50. Case 1: Play Garden Social interaction in the social game (Play Garden) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kwon and Suh (2013) Result: After shutdown law Network Effect & Reverse Network Effect More concurrent users Play time Fewer concurrent users Network effect Social Intrinsic
  51. 51. Case 2: Ever Planet
  52. 52. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Personal Satisfaction Social Interaction Personal Rewards Public Recognition
  53. 53. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Social distance is the gap between different groups; social class, race, gender, or sexuality. In the virtual world, social distance is the level difference between existing users and new users.
  54. 54. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Social distance is the gap between different groups; social class, race, gender, or sexuality. In the virtual world, social distance is the level difference between existing users and new users. Research Question: Does social distance influences the player’s behavior in games?
  55. 55. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Public recognition Social distance Find public recognition in Ever Planet1 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE The gap of levels among users; mostly between existing users and new users.
  56. 56. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kim and Lee (2013) Social distance ↔ the difference between the user's level and the average level of all users.
  57. 57. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Parametrize public recognition the difference between the user's level and the average level of all users. Public recognition Social distance 2 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kim and Lee (2013)
  58. 58. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kim and Lee (2013) • The difference between the user's level and the average level of all users. • Total play time • Accumulated play time • The number of players
  59. 59. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Build a model measuring public recognition and its effect on the player’s behavior 3 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kim and Lee (2013)
  60. 60. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kim and Lee (2013) Social distance The number of concurrent users The user’s play time - Accumulated playtime - Number of days passed - Weekend - School vacations
  61. 61. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE A methodology for analyzing panel data when group means are fixed for each group. Select the right methodology and analyze 4 Source: Kim and Lee (2013) Fixed Effect
  62. 62. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Select the right methodology and analyze 4 Source: Kim and Lee (2013) Social distance The number of concurrent users The user’s play time - Accumulated playtime - Number of days passed - Weekend - School vacations
  63. 63. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kim and Lee (2013) Result: As users have been playing more, they play the less today (-) Social distance The number of concurrent users The user’s play time - Accumulated playtime - Number of days passed - Weekend - School vacations
  64. 64. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Kim and Lee (2013) Result: But the social distance makes people behave differently; the higher level, the longer they play The user’s play time - Accumulated playtime - Number of days passed - Weekend - School vacations Social distance (higher level) The number of concurrent users (+)
  65. 65. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Source: Kim and Lee (2013) How to manage the social distance?
  66. 66. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Source: Kim and Lee (2013) How to manage the social distance? The example of Divisions and Tiers systems in online / offline sports
  67. 67. Case 2: Ever Planet Public recognition in MMORPG (Ever Planet) Source: Kim and Lee (2013) How to manage the social distance? # of players Agent-Based Model A computational model for simulating the actions and interactions of autonomous agents
  68. 68. Case 3: Mobile Personal Health Record Personal satisfaction in mPHR (My Chart in My Hand)
  69. 69. Case 3: Mobile Personal Health Record Personal satisfaction in mPHR (My Chart in My Hand) Research Question: Which feature makes people to have higher retention rates?
  70. 70. Case 3: Mobile Personal Health Record Personal satisfaction in mPHR (My Chart in My Hand) Personal satisfaction Self-monitoring Find personal satisfaction in mPHR1 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Tracking and updating the user’s health information Personal Satisfaction Social Interaction Personal Rewards Public Recognition
  71. 71. Case 3: Mobile Personal Health Record Personal satisfaction in mPHR (My Chart in My Hand) Parametrize personal satisfaction & other features The average and the frequency of usage 2 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Lee et al. (2018) Personal satisfaction Self-monitoring • 𝐴𝑉𝐺_𝑆𝑀𝑖: Average usage of self-monitoring function by patient i • 𝑆𝑇𝐷_𝑆𝑀𝑖: Standard deviation of usage of self- monitoring function by patient i
  72. 72. Case 3: Mobile Personal Health Record Personal satisfaction in mPHR (My Chart in My Hand) Build a model measuring each feature’s effect on user retention 3 BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Lee et al. (2018) The average usage of self-monitoring function The standard deviation of self- monitoring function usage User retention - Demographics - The level of illness) The average usage of other functions The standard deviation of other function usages
  73. 73. Case 3: Mobile Personal Health Record Personal satisfaction in mPHR (My Chart in My Hand) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Cox proportional hazard A methodology for analyzing the expected time until an event of interest happens Select the right methodology and analyze 4 Source: Lee et al. (2018)
  74. 74. Case 3: Mobile Personal Health Record Personal satisfaction in mPHR (My Chart in My Hand) BUILD A MODELQUANTIFY PARAMETRIZE ANALYZE Source: Lee et al. (2018) Result: People with personal satisfaction have higher retention rates. The average usage of self- monitoring function The standard deviation of self- monitoring function usage User retention - Demographics - The level of illness The average usage of other functions The standard deviation of other function usages (+) (-)
  75. 75. 3 Steps for implementing motivation model into games RECOMMENDDEFINE FIND (1) Define and parametrize the motivation you want to find Personal Satisfaction Social Interaction Personal Rewards Public Recognition
  76. 76. 3 Steps for implementing motivation model into games (2) Find each player’s motivation based on the player’s log data RECOMMENDDEFINE FIND
  77. 77. 3 Steps for implementing motivation model into games (3) Send recommendation message based on the motivation RECOMMENDDEFINE FIND THE PERFECTIONISTS THE COLLECTORS FRIENDSHIPS
  78. 78. Automate the 3 Steps of implementing motivation model into games (3) Send recommendation message based on the motivation RECOMMENDDEFINE FIND THE PERFECTIONISTS THE COLLECTORS FRIENDSHIPS (1) Define and parametrize the motivation you want to find (2) Find each player’s motivation based on the player’s log data
  79. 79. Implementation Integrating the model-driven analysis into the game server Gameplay Log Data Features Preprocessed Data Motivation Model Analysis Result Data In-game recommendation message Game Player
  80. 80. Implementation Integrating the model-driven analysis into the game server Gameplay Log Data Features Preprocessed Data Motivation Model Analysis Result Data In-game recommendation message Game Player 1 Preprocessing • Data connector • Batch with dependency • Generate features
  81. 81. Implementation Integrating the model-driven analysis into the game server Gameplay Log Data Features Preprocessed Data Motivation Model Analysis Result Data In-game recommendation message Game Player 1 Preprocessing • Data connector • Batch with dependency • Generate features 2 Analysis and Segmentation • Motivation analysis with the preprocessed data • Segment players with a specific motivation
  82. 82. Implementation Integrating the model-driven analysis into the game server Gameplay Log Data Features Preprocessed Data Motivation Model Analysis Result Data In-game recommendation message Game Player 1 Preprocessing • Data connector • Batch with dependency • Generate features 2 Analysis and Segmentation • Motivation analysis with the preprocessed data • Segment players with a specific motivation 2 Send recommendation message to the player
  83. 83. The result of automizing the three steps: Retention rate increased by 13% User engagement increased by 45% In-app purchase increased by 8% Real case example: Result of applying motivation-based recommendation system in mobile game
  84. 84. Wrap up • Define and find the motivation of players in games • Personal Satisfaction • Social Interaction • Personal Rewards • Public Recognition • Find the players with analysis methodology • Recommend items and contents based on the motivation
  85. 85. References • McGuinness M. 2015. Motivation for Creative People: How to Stay Creative While Gaining Money • Rigby, S. and Skinner, T. GDC 2014, The Importance of Player Autonomy: Motivating Sustained Engagement through Volition and Choice • Baron J. GDC 1999, Glory and Shame: Powerful Psychology in Multiplayer Online Games • Ryan, R.M. and Deci, E.L.2000. Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions, Contemporary Educational Psychology 25, 54–67 • Kwon, H., Suh, C. 2013, The Effect of the Shutdown System on Social Games, Business Administration Research 6, 1-12 • Kim, M., Lee, B. 2013, Are There Too Many Superheroes? Analysis of the Social Distance in Massive Multiplayer Online Role Playing Game, https://ssrn.com/abstract=2330090 • Lee K, Kwon H, Lee B, Lee G, Lee JH, Park YR, et al. (2018) Effect of self- monitoring on long-term patient engagement with mobile health applications. PLoS ONE 13(7): e0201166. https:// doi.org/10.1371/journal.pone.0201166
  86. 86. Thank you. Homepage: www.sentience.rocks Hyeyon Kwon: h.kwon@sentience.rocks

Editor's Notes

  • What is behavioral economics?
  • What is behavioral economics?
  • Why finding motivation is important?
  • Why finding motivation is important?
    Because when you find factors that lead to high purchase probability, or high retention rates, you don’t know it is because the player originally has high probability of purchase or high probability of playing games longer
  • First of all, to find social interaction in Play Garden, we quantified "social interaction" as network effect.
  • In this case, because it is  massive multiplayer online role playing game, we focused on finding players with social extrinsic motivation, who seek public recognition like high rankings.
  • So in video games, the social distance is the difference between the user's level and the average level of all users.
  • So we parametrize social distance
  • But social distance makes that effect weaker.
    People with larger social distance, players with high level compared to average users, play longer.

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