Classroom Companion: Business

 
Chapter 18 · Digital Market Modeling

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players (P), or quitters (Q) as a function of time. Observe that the sum of these 
categories of individuals is always 100%. At t = 0, there are only potential players 
and no players or quitters (i.e., B = 100% and P = Q = 0%). As time increases, more 
and more potential players become players, who, after some time, leave the game 
and become quitters. However, quitters may rejoin the game and become players 
again. Eventually (in the figure, for t > 90), all individuals are either players or 
quitters.
From the form of the differential equations, important conclusions can be 
drawn without solving the equations:
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If there are no innovators among the potential players, the time it takes for the 
game to reach sufficient popularity may be long in the same way as in the Bass 
model with only imitators. The game may then be prematurely withdrawn from 
the market.
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To prolong the lifetime of the game, quitters must be stimulated to rejoin the 
game. This requires frequently updating of the game with interesting new features.
Time (in months)
Share of total population
0
0
10
20
30
40
50
60
70
80
90
100
20
40
60
80
100
120
B
P
Q
. Fig. 18.7 Plot of the BPQ model. (Authors’ own figure)
18.4 · Models for Massive Multiplayer Online Games

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Updating of the game may also stimulate current players to continue to play, 
thereby reducing the rate by which payers are leaving the game.