Game-theoretical model of service quality indicators choice:
Mobile service market
Margarita A. Gladkova and Nikolay A. Zenkevich
Graduate School of Management, St. Petersburg State University,
Volkhovsky Per. 3 St. Petersburg, 199004, Russia
zenkevich@gsom.pu.ru
gladkova@gsom.pu.ru
Keywords: quality evaluation, quality measurement, consumer's taste for quality, quality choice,
two-stage game, Nash equilibrium, Stakelberg equilibrium, Pareto-optimal solution, optimal
quality differentiation, index of consumers’ satisfaction.
In the paper a game-theoretical model of quality choice under competition is suggested.
The game-theoretical model is presented as a two-stage game where companies compete on an
industrial market and consumer's taste to quality is non-uniformly distributed. From a practical
perspective, the aim of the paper is to check the validity of the suggested game-theoretical
model.
Thus, two firms are assumed to produce homogeneous service differentiated by quality
on some industrial market. The game consists of the following two stages:
1. At the first stage companies simultaneously define quality level;
2. At the second stage they choose service prices. At this stage both simultaneous and
sequential choices are analyzed.
Each consumer buys at most one unit of the service. Consumers differ in their willingness
to pay for quality level s, which is described by the parameter   0, b. This parameter is called
“taste for quality”. The utility of a consumer with a willingness to pay for quality  when buying
a service of quality s at a price p is equal to:
s  p,
U  ( p)  
 0,
p  s
p  s .
The investigated industrial market is considered to be partially covered. Besides, in our
model the case when taste for quality parameter is non-uniformly distributed over the interval
0, b, namely the triangular distribution is investigated.
The payoff function of the firm i which produces the service of quality s i ,
where si [s, s] , is the following:
Ri ( p1 , p2 , s1 , s 2 )  pi ( s1 , s 2 ) Di ( p1 , p2 , s1 , s 2 ) , i  1,2 ,
where Di ( p1 , p 2 , s1 , s 2 )  the demand function for the service of quality s i , which is specified.
The Nash equilibrium in the investigated game was obtained in the explicit form which
allowed us to evaluate prices, companies’ demand and revenues in the equilibrium.
The paper includes a case study for the market of mobile operators in Saint-Petersburg
which was used to approve the suggested game-theoretical approach to quality choice.
Processing an empirical data which was obtained from consumer survey let us evaluate mobile
service quality and using the model we can show the ways of performance improvement to
production companies.
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