The paper presents empirical models based on game theory for assessing the car market concentration. The analysis of games with simultaneous moves is carried out, the specifications of econometric models of discrete games are developed. Binary probit models with external and internal factors that determine the activity of auto dealers are formalized. Points of break-even demand for monopoly and duopoly are defined. The experimental sample accounted for 81 markets with a population from 5 thousand to 150 thousand people, 55 of which are monopolistic, and 26 consist of two dealers. As a result of the analysis the best model was chosen, the factors influencing the dealers entry into the market were revealed. It was found that the choice of auto dealers is mostly influenced by the number of people in the isolated market and the level of average per capita income. The model with internal factors turned out inadequate, which indicates a low quality of the information provided by companies to accountancy statistics agencies.
The entrance to the car market is associated with significant costs. This is due to
the presence of entry barriers from competitors and specific features of the
commercial environment, which include the concentration of consumers, the volume
of the market, infrastructure, etc. That accounts for the need for the tools for
assessing the consequences of entering the market of auto dealers. Bresnahan and
Reiss [
When assessing situations of alternatives, binary choice models, formalizing
two decision-making strategies of whether to enter into the market or not, are
traditionally used [
In practical application of the game-theoretic concept Bresnahan and Reiss
[
This study of the activity of auto dealers in domestic markets is based on
the methods proposed by Bresnahan and Reiss [
The economic basis for computer modeling the market entry for an equilibrium
number of firms has the following features. In the car market, winnings depend on
the number of operating firms. Most consumers buy new cars in local dealerships.
Dealers work independently of the manufacturer, although manufacturers spend
significant amounts on the organization and location choices of car dealers. Both
manufacturers and dealers argue that the success of the dealership is critically
dependent on the number of closest dealers [
The empirical basis was made up by the following provisions. Winnings depend on the number of firms on the market. Entering the market is equivalent to the activity of a certain number of firms on the market. The state of equilibrium is described by the ratio of winnings for market participants: m(nm) 0; m(nm + 1) < 0; where m stands for the winnings of m-th firm; nm is number of firms in market. The winning function is determined by the formula: (1) (2) (3) (4) Taking into account the random components, we have m(n) = Vm(n)
Fm(n) = sm m(n)
Fm(n): m(n) = sm(xm (n)) (xfm + (n) + "m); where Vm is the income of the m-th firm; Fm is expenses of the m-th firm; sm is the market volume; xm stands for the characteristics of the market; (n), (n), "m are residues of regression that go up as the number of firms increases. The break-even point, according to formula (1), is calculated by the formula: S(n) =
f xm xm + (n) (n) : 3
We use the economic and empirical bases for researching the retail car market in Russia. The data for 2010–2015 were used. Since it is not possible to clearly define the boundaries of the market in urban areas, data on dealers in isolated areas were collected. In each constituent entity of the Russian Federation, we defined cities or stand-alone centers of population concentration. They met the following criteria: the absence of another city with a population of more than 20,000 people within a distance of 50 km from the core city; the absence of a large city within 50 km with more than two dealers. The study identified 81 markets or cities with a population from 5 thousand to 150 thousand people. Since the residents of core cities have to overcome more than 50 km to reach the next city, the dealers have a considerable market power. Due to data gaps, the sample size has significantly decreased (from 150 to 81). The study showed that 55 out of the 81 markets have one dealer (i.e., represent monopolies), and 26 have two dealers (represent duopolies). For example, in the Krasnodar Territory, two monopoly markets and four duopoly markets were identified, corresponding to the above conditions.
As an evaluation tool, a sample of indicators characterizing isolated markets
was used. These are external indicators that characterize the business
environment of companies: the population density of the region, the population density
of a certain settlement (the factors affect the revenue side), the distance between
the given settlement and another one whose population is more than 20,000
people, per capita income of the population, the share of farmland (factors affect the
expenditure side). The resulting indicator of the model is a second dealer’s
market entry or their absence on the market. The description of the environmental
data is presented in Table 1.
Various specifications of binary probit models with external and internal factors
of enterprises were evaluated. The criteria for assessing the adequacy of the
models selection were the McFadden coefficient of determination (the higher
the value, the better the quality of the model), the information criteria (the
lower the value of the criteria, the higher the relative quality of the model) and
the value of the logarithm of the maximum likelihood function (the higher the
value, the higher the quality of the model). The results of the assessment of
the model with internal factors (data for 5 years from the financial statements
of companies) proved inadequate. This is due to the low quality of information
provided by companies, with numerous missing or erroneous data [
Based on the research findings, the following conclusions can be made. The best model is (1), since the value of the logarithm of the maximum likelihood function for it is minimal. The marginal effects on the specifications were calculated on the basis of Table 2 and are presented in Table 3. The marginal effect of per capita income of the population turned out to be 0.033, and the marginal effect of the population of the region is 0.054. This means that with an increase , and indicate the parameter estimates are significant at the 1%, 5% and 10% levels, respectively in per capita income of the population by 1%, the probability of a second dealer entering the market, i.е. the probability of a duopoly increases by 3.3%. With an increase in the population by 1%, the probability of a duopoly increases by 5.4%. For model (2), with an average rise of the regional population density by 1%, the probability of a duopoly in the region increases by 5.4%. A growth of average per capita income of the population by 1% leads to an increase in the likelihood of a second dealer entering the market by 2.7%. Marginal effects for the indicators of the distance from the nearest settlement with a population of more than 20,000 people and the share of farmland are insignificant.
The level of break-even demand calculated for model (2) is presented in Table 4. The data were obtained from formula (2) from the ratio of costs and incomes for monopolies and duopolies. The demand for a duopoly products is about 2 times higher than the demand for monopoly products. To interpret this value, let us represent it in the form of the ratio of the incomes of a monopoly and a duopoly. This ratio determines the amount by which the company’s profit falls when a second dealer enters the market. When duopolists sell the same products, the ratio of incomes is less than or equal to 0.5. This ratio is equal to 0.5, when the duopolists conspire and evenly divide the profits. If the firms do not agree, the ratio falls below 0.5. Finally, if the products of the companies differ significantly, this value will exceed 0.5. In this case, it can be assumed that most companies collude and the differentiation of products increases the profit of the duopoly, while competition reduces it. The third ratio shows that the costs of a second dealer are almost 2 times higher than the monopoly costs, this is explained by the entry barriers.
Let’s compare the ratio of breakeven points, incomes and expenditure of US
firms (according to the data proposed by Bresnahan and Reiss [