A Dynamic Model of Service Usage, Customer Satisfaction, and Retention

Transcription

1 A Dynamic Model of Service Usage, Customer Satisfaction, and Retention Nan Yang Juin-Kuan Chong Department of Marketing, NUS Business School Dec 13, 2016, Melbourne / APIO Conference 1 / 29

2 SATISFACTION, SERVICE USAGE, & CHURN Customer satisfaction always the core of Customer Relationship Management. Measuring satisfaction, the usual practice: costly and sparse surveys, stated preferences. Usage and attrition are informative on satisfaction: conceptual ground for economic identification. 2 / 29

3 SATISFACTION, SERVICE USAGE, & CHURN Customer satisfaction always the core of Customer Relationship Management. Measuring satisfaction, the usual practice: costly and sparse surveys, stated preferences. Usage and attrition are informative on satisfaction: conceptual ground for economic identification. 2 / 29

4 SATISFACTION, SERVICE USAGE, & CHURN Customer satisfaction always the core of Customer Relationship Management. Measuring satisfaction, the usual practice: costly and sparse surveys, stated preferences. Usage and attrition are informative on satisfaction: conceptual ground for economic identification. 2 / 29

5 SATISFACTION, SERVICE USAGE, & CHURN Customer satisfaction always the core of Customer Relationship Management. Measuring satisfaction, the usual practice: costly and sparse surveys, stated preferences. Usage and attrition are informative on satisfaction: conceptual ground for economic identification. 2 / 29

6 THIS PROJECT A dynamic structural model of customer satisfaction, usage, and attrition Observed usage and unobserved satisfaction influence each other s dynamics. Attrition as optimal stopping decision, depending on the realizations and expectations of both processes. Estimated using data from a Massively Multiplayer Online Role Playing Game (MMORPG). 3 / 29

7 THIS PROJECT A dynamic structural model of customer satisfaction, usage, and attrition Observed usage and unobserved satisfaction influence each other s dynamics. Attrition as optimal stopping decision, depending on the realizations and expectations of both processes. Estimated using data from a Massively Multiplayer Online Role Playing Game (MMORPG). 3 / 29

8 WHAT WE CONTRIBUTE LITERATURE: MOSTLY REDUCED-FORM Duration (hazard) model: Bolton (1998) Hidden Markov models: Netzer and Srinivasan (2008), Ascarza and Hardie (2013) CONTRIBUTION Methods: Structural framework based on utility maximization ready for counter-factual analysis. Estimation approach that s quick enough to generate near-real time retention strategies. Context: Empirical analysis of a multi-billion industry. 4 / 29

9 WHAT WE CONTRIBUTE LITERATURE: MOSTLY REDUCED-FORM Duration (hazard) model: Bolton (1998) Hidden Markov models: Netzer and Srinivasan (2008), Ascarza and Hardie (2013) CONTRIBUTION Methods: Structural framework based on utility maximization ready for counter-factual analysis. Estimation approach that s quick enough to generate near-real time retention strategies. Context: Empirical analysis of a multi-billion industry. 4 / 29

10 THIS IS WHAT IT LOOKS LIKE 5 / 29

11 MMORPG A Massively Multiplayer Online Role Playing Game from China. Users log into virtual worlds, assume roles like wizards/warriors, complete quests like slay dragons, buy gears like weapons/armour, advance in levels, and interact with others. A game of continuous play with no obvious ending point. More than 820k users daily activity data (login, play time, quests completed, spending, gear, etc.) spans a full year. 6 / 29

12 WHY CARE ABOUT ATTRITION? Free playing time, revenue from selling gears. Attrition is a big deal: 16% of players quit (without activities for 30 days) every week, and replenished. Serving additional user costs little. Retention means direct revenue: Surviving into a week, 3.4% will spend and 1% will be a first-time spender. Further indirect revenue coming from making movies etc. 7 / 29

13 GENERAL SETUP: PER PERIOD Discrete time in weeks t {0, 1,...}. Individual-level analysis. Start with (s t, Ω t ) Active user plays & gets utility. Observed states and gaming interest updated. Forward looking decision. Go to next period with (s t+1, Ω t+1 ) 8 / 29

14 GENERAL SETUP: PER PERIOD s t [ŝ, š]: unobserved gaming interest (satisfaction); Ω t observed states; both first-order Markovian. Start with (s t, Ω t ) Active user plays & gets utility. Observed states and gaming interest updated. Forward looking decision. Go to next period with (s t+1, Ω t+1 ) 8 / 29

15 GENERAL SETUP: PER PERIOD Static decisions on playing hours h t and spending m t to maximize U(s t, Ω t, h t, m t ) = Λ(s t )ū(s t, Ω t, h t, m t ). Start with (s t, Ω t ) Active user plays & gets utility. Observed states and gaming interest updated. Forward looking decision. Go to next period with (s t+1, Ω t+1 ) 8 / 29

16 GENERAL SETUP: PER PERIOD According to joint distribution f (s t+1, Ω t+1 s t, Ω t ). Start with (s t, Ω t ) Active user plays & gets utility. Observed states and gaming interest updated. Forward looking decision. Go to next period with (s t+1, Ω t+1 ) 8 / 29

17 GENERAL SETUP: PER PERIOD Maximize expected future utility flow. Outside option logistic shock. Start with (s t, Ω t ) Active user plays & gets utility. Observed states and gaming interest updated. Forward looking decision. Go to next period with (s t+1, Ω t+1 ) 8 / 29

18 GENERAL SETUP: PER PERIOD Future utilities discounted with factor β. Start with (s t, Ω t ) Active user plays & gets utility. Observed states and gaming interest updated. Forward looking decision. Go to next period with (s t+1, Ω t+1 ) 8 / 29

19 DIMENSIONALITY: COMPUTATIONAL HURDLE Ω is a high dimensional state variable. Solution: similar to inclusive value approach (Hendel and Nevo 2006, Gowrisankaran and Rysman 2012) U(s t, Ω t, h t, m t ) Λ(s t )ū(s t, Ω t, h t, m t ). ū t measures usage activity. ADDITIONAL ASSUMPTIONS (LOOSELY STATED) (s t, ū t ) are sufficient statistics for (s t, Ω t, h t, m t ). (Implied) Dynamic decision only depends on the (s t, ū t ) processes. ū t and s t evolves sequentially. 9 / 29

20 DIMENSIONALITY: COMPUTATIONAL HURDLE Ω is a high dimensional state variable. Solution: similar to inclusive value approach (Hendel and Nevo 2006, Gowrisankaran and Rysman 2012) U(s t, Ω t, h t, m t ) Λ(s t )ū(s t, Ω t, h t, m t ). ū t measures usage activity. ADDITIONAL ASSUMPTIONS (LOOSELY STATED) (s t, ū t ) are sufficient statistics for (s t, Ω t, h t, m t ). (Implied) Dynamic decision only depends on the (s t, ū t ) processes. ū t and s t evolves sequentially. 9 / 29

21 DIMENSIONALITY: COMPUTATIONAL HURDLE Ω is a high dimensional state variable. Solution: similar to inclusive value approach (Hendel and Nevo 2006, Gowrisankaran and Rysman 2012) U(s t, Ω t, h t, m t ) Λ(s t )ū(s t, Ω t, h t, m t ). ū t measures usage activity. ADDITIONAL ASSUMPTIONS (LOOSELY STATED) (s t, ū t ) are sufficient statistics for (s t, Ω t, h t, m t ). (Implied) Dynamic decision only depends on the (s t, ū t ) processes. ū t and s t evolves sequentially. 9 / 29

22 DIMENSIONALITY: COMPUTATIONAL HURDLE Ω is a high dimensional state variable. Solution: similar to inclusive value approach (Hendel and Nevo 2006, Gowrisankaran and Rysman 2012) U(s t, Ω t, h t, m t ) Λ(s t )ū(s t, Ω t, h t, m t ). ū t measures usage activity. ADDITIONAL ASSUMPTIONS (LOOSELY STATED) (s t, ū t ) are sufficient statistics for (s t, Ω t, h t, m t ). (Implied) Dynamic decision only depends on the (s t, ū t ) processes. ū t and s t evolves sequentially. 9 / 29

23 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

24 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

25 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

26 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

27 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

28 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

29 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

30 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

31 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

32 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

33 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

34 USAGE AND INTERESTS Usage ū 0 ū 1 ū 2 ū 3... Interests s 1 s 2 s 3 s 4 Week 1 Week 2 Week 3 Initial usage determines initial interest Usage and interest determine attrition Previous usage and interest determine current usage Current usage and previous interest determine current interest The payoff relevant states for in week t are (s t+1, ū t ) 10 / 29

35 TWO-STEP PROCEDURE 1 Static choice on usage: Reduced-form estimation using functional form assumptions. 2 Dynamic choice on stopping: Full information MLE. 11 / 29

36 STEP 1: ESTIMATING ū. Cobb-Douglas production function with time and money as inputs. Constant return to scale. User n week t: Budget constraint U(s nt, Ω nt, h nt, m nt ) Λ(s nt )h α(ω nt ) nt m 1 α(ω nt ) nt. h nt p nht + m nt p nmt = B(s nt ), Restriction: s nt doesn t affect the input ratio. 12 / 29

37 STEP 1: ESTIMATING ū. Cobb-Douglas production function with time and money as inputs. Constant return to scale. User n week t: Budget constraint U(s nt, Ω nt, h nt, m nt ) Λ(s nt )h α(ω nt ) nt m 1 α(ω nt ) nt. h nt p nht + m nt p nmt = B(s nt ), Restriction: s nt doesn t affect the input ratio. 12 / 29

38 STEP 1: ESTIMATING ū. Optimal ratio satisfies: log ( hnt m nt ) = log ( α(ωnt ) 1 α(ω nt ) ) + log(p mnt ) log(p hnt ). Ratio Elasticity Price of money Price of time Observed Function of Ω nt Assumed Constant Assumed i.i.d. Regressing time/money ratio on observables (level, guild affiliation, role, gear etc.) recovers elasticity α and hence ū nt. 13 / 29

39 STEP 1: ESTIMATING ū. Optimal ratio satisfies: log ( hnt m nt ) = log ( α(ωnt ) 1 α(ω nt ) ) + log(p mnt ) log(p hnt ). Ratio Elasticity Price of money Price of time Observed Function of Ω nt Assumed Constant Assumed i.i.d. Regressing time/money ratio on observables (level, guild affiliation, role, gear etc.) recovers elasticity α and hence ū nt. 13 / 29

40 STEP 1: ESTIMATING ū. Optimal ratio satisfies: log ( hnt m nt ) = log ( α(ωnt ) 1 α(ω nt ) ) + log(p mnt ) log(p hnt ). Ratio Elasticity Price of money Price of time Observed Function of Ω nt Assumed Constant Assumed i.i.d. Regressing time/money ratio on observables (level, guild affiliation, role, gear etc.) recovers elasticity α and hence ū nt. 13 / 29

41 STEP 1: ESTIMATING ū. Optimal ratio satisfies: log ( hnt m nt ) = log ( α(ωnt ) 1 α(ω nt ) ) + log(p mnt ) log(p hnt ). Ratio Elasticity Price of money Price of time Observed Function of Ω nt Assumed Constant Assumed i.i.d. Regressing time/money ratio on observables (level, guild affiliation, role, gear etc.) recovers elasticity α and hence ū nt. 13 / 29

42 STEP 1: RESULTS. OLS model, easy to estimate (random-effect model rejected). Flexible function form of a large set of Ω used. Including t and its higher orders to account for non-stationarity. What you would expect: A user who is a member of an in-game guild, joins the game for longer, and has more balance in the in-game currency account is more inclined to invest money in substitution for time. Further discretize ū unto an equidistant grid of 30 points. 14 / 29

43 . Effects with Respect to RESULTS Average Marginal Effects with 95% CIs fmem fposmax noroles levelmax levelagg logres week weeksq weekfmem weekfposmax weeknoroles weeklvmax weeklvagg weeklogres Effects on Linear Prediction 15 / 29

44 . ū CAPTURES USAGE WELL ubar hours spending / 29

45 .... BUT CAN T EXPLAIN CHURN ALONE 16 #104 Last week ubar 2.5 #106 Regular week ubar / 29

46 STEP 2: NON-PARAMETRIC IDENTIFICATION HU & SHUM (2013) The Markov law of motion f (s t+1, ū t+1 s t, ū t ) can be identified from four periods of observations ū t+2, ū t+1, ū t, ū t 1. Intuition: Conditional on ū t, ū t 1 is an excluded variable which affects ū t+1 only via the unobserved s t+1. Identification paper: No operationalization recipe. High-level assumptions that are not directly testable. 18 / 29

47 STEP 2: NON-PARAMETRIC IDENTIFICATION HU & SHUM (2013) The Markov law of motion f (s t+1, ū t+1 s t, ū t ) can be identified from four periods of observations ū t+2, ū t+1, ū t, ū t 1. Intuition: Conditional on ū t, ū t 1 is an excluded variable which affects ū t+1 only via the unobserved s t+1. Identification paper: No operationalization recipe. High-level assumptions that are not directly testable. 18 / 29

48 OPERATIONALIZATION 1 Logistic shock: Maximum likelihood of /continuation. 2 Discretize interest on a 21-point equidistant grid [ 10, 10]. 3 Parametrize initial distribution of s 1. 4 Parametrize transition densities as AR(1) with mean approximated by polynomials. 5 Parametrize Λ(s) with polynomials. 6 Recursive construction of likelihood from week 1 till : integrating out unobserved gaming interest. 7 CCP-based EM-algorithm (Arcidiacono and Miller, 2011) v.s. NXFP? 19 / 29

49 OPERATIONALIZATION 1 Logistic shock: Maximum likelihood of /continuation. 2 Discretize interest on a 21-point equidistant grid [ 10, 10]. 3 Parametrize initial distribution of s 1. 4 Parametrize transition densities as AR(1) with mean approximated by polynomials. 5 Parametrize Λ(s) with polynomials. 6 Recursive construction of likelihood from week 1 till : integrating out unobserved gaming interest. 7 CCP-based EM-algorithm (Arcidiacono and Miller, 2011) v.s. NXFP? 19 / 29

50 OPERATIONALIZATION 1 Logistic shock: Maximum likelihood of /continuation. 2 Discretize interest on a 21-point equidistant grid [ 10, 10]. 3 Parametrize initial distribution of s 1. 4 Parametrize transition densities as AR(1) with mean approximated by polynomials. 5 Parametrize Λ(s) with polynomials. 6 Recursive construction of likelihood from week 1 till : integrating out unobserved gaming interest. 7 CCP-based EM-algorithm (Arcidiacono and Miller, 2011) v.s. NXFP? 19 / 29

51 OPERATIONALIZATION 1 Logistic shock: Maximum likelihood of /continuation. 2 Discretize interest on a 21-point equidistant grid [ 10, 10]. 3 Parametrize initial distribution of s 1. 4 Parametrize transition densities as AR(1) with mean approximated by polynomials. 5 Parametrize Λ(s) with polynomials. 6 Recursive construction of likelihood from week 1 till : integrating out unobserved gaming interest. 7 CCP-based EM-algorithm (Arcidiacono and Miller, 2011) v.s. NXFP? 19 / 29

52 OPERATIONALIZATION 1 Logistic shock: Maximum likelihood of /continuation. 2 Discretize interest on a 21-point equidistant grid [ 10, 10]. 3 Parametrize initial distribution of s 1. 4 Parametrize transition densities as AR(1) with mean approximated by polynomials. 5 Parametrize Λ(s) with polynomials. 6 Recursive construction of likelihood from week 1 till : integrating out unobserved gaming interest. 7 CCP-based EM-algorithm (Arcidiacono and Miller, 2011) v.s. NXFP? 19 / 29

53 OPERATIONALIZATION 1 Logistic shock: Maximum likelihood of /continuation. 2 Discretize interest on a 21-point equidistant grid [ 10, 10]. 3 Parametrize initial distribution of s 1. 4 Parametrize transition densities as AR(1) with mean approximated by polynomials. 5 Parametrize Λ(s) with polynomials. 6 Recursive construction of likelihood from week 1 till : integrating out unobserved gaming interest. 7 CCP-based EM-algorithm (Arcidiacono and Miller, 2011) v.s. NXFP? 19 / 29

54 OPERATIONALIZATION 1 Logistic shock: Maximum likelihood of /continuation. 2 Discretize interest on a 21-point equidistant grid [ 10, 10]. 3 Parametrize initial distribution of s 1. 4 Parametrize transition densities as AR(1) with mean approximated by polynomials. 5 Parametrize Λ(s) with polynomials. 6 Recursive construction of likelihood from week 1 till : integrating out unobserved gaming interest. 7 CCP-based EM-algorithm (Arcidiacono and Miller, 2011) v.s. NXFP? 19 / 29

55 RESULTS: TRANSITION OF INTEREST FIGURE: Low usage: Low interests to low, medium to medium, high to low 20 / 29

56 RESULTS: TRANSITION OF INTEREST FIGURE: medium usage: Low interests to low/medium, medium to medium, high to low/medium 21 / 29

57 RESULTS: TRANSITION OF INTEREST FIGURE: High usage: Low interests to medium, medium to medium/high, high to low/medium 22 / 29

58 RESULTS: TRANSITION OF USAGE FIGURE: Low interest: Low/medium usage to low, high to low/medium 23 / 29

59 RESULTS: TRANSITION OF USAGE FIGURE: medium interest: Low usage to low, medium/high to maintain 24 / 29

60 RESULTS: TRANSITION OF USAGE FIGURE: High interest: Low usage to low, medium/high to increase 25 / 29

61 OBSERVATIONS ON TRANSITIONS Usage inter-temporal complement, enhanced by interest Interest has gravity, alleviated by usage High interest leads to high usage, which leads to quick reversion to low interest Low interest, low usage states repeat themselves. 26 / 29

62 RESULTS: SURVIVAL FIGURE: Low Survival Prob. When Both Usage & Interest Are High: Interest Will Decline Fast Low Option Value 27 / 29

63 SKELETON(S) IN THE CLOSET Reduced-form modelling of usage restricts the scope of counterfactual. Unobserved interest only affects level but not ratio of inputs. All user heterogeneity loaded on the unobserved interest. 28 / 29

64 TO-DO LIST Richer modelling of initial conditions and outside options. Richer state space Counter-factual analysis: the impact of restricting playing hour Actionable and real-time managerial recommendations on Big-Data applications. 29 / 29