In this study a multiagent model of behaviour of the dispersion of retail prices for petroleum products has been developed, depending on changes of external factors, in particular, sharp changes in wholesale prices. Therefore, there is a need for a model that would not only have the potential to test the existence of a price dispersion as a consequence of the specifics of competition in the market of petroleum products and consumer search strategies, but would have the ability to quantify the price variance as a consequence of the behaviour of individual market agents. The basis of the behaviour of market agents of this model is algorithms of price oligopolistic competition from traders and user price search strategies. Calibration models and verification of historical data of the Kyiv region, where they were previously established empirical data on the dispersion of prices showed a fairly good correspondence between the model and the actual data. In particular, the existence of a price pattern has been established at jump-like changes of wholesale prices. The presence of price strategy of buyers, which are based on the strategy of the base price, is shown. The coincidence of model and real data still needs to be improved.
Despite world trends in reducing the share of hydrocarbons in energy consumption, the petroleum product market remains an extremely important institution for every single economy on any continent. Relatively long history of the functioning of the market shows that the central issue of this market is price behaviour. Governments of all countries must closely monitor changes in prices, especially for their significant increase, which can lead to negative social consequences. The long-established fact, both empirical and theoretical, lies in the fact that prices in this market behave as nonstationary time series. Some features of competition in the market of petroleum products, as well as significant sensitivity of fluctuations in the level of domestic prices from external factors, are the cause of such behaviour. The presence of the so-called price asymmetry is also a characteristic phenomenon, when jumps in prices on the wholesale market are accompanied by a rapid increase in retail prices and a slow decline in retail prices after the reduction of wholesale prices.
However, this is not the only problem in this market. Another characteristic
phenomenon is the presence of price dispersion. This means that for the same product,
at the same time, prices even at neighbouring gas stations are usually different.
Establishing the conditions in which firms choose a range of prices was and remains
the main issue in the theory of prices. Starting from the pioneering work of Stigler [
G. Stigler has a fundamental paper [
Varian has shown that there is no equilibrium in pure strategies, but equilibrium is
achieved in mixed strategies. Diamond’s paradox and Bertrand’s competition are
extreme cases when all consumers are informed or not informed. This paper looks at
the interesting conclusion about increasing the number of companies operating in the
market. When the number of competitors increases, the likelihood that any particular
seller will successfully sell the product to some informed clients is reduced. As a
consequence, in the equilibrium distribution of prices, higher prices increase their share.
But this effect turns out to be positive for informed customers, because the expected
lower price is decreasing. The reason is that more firms compete and well-informed
buyers pay the lowest price. For unskilled clients, the expected price is clearly
increasing. The gasoline market is a good example of a homogeneous, albeit not perfect,
market where price dispersions are observed. Many consumers are only aware of some
prices, and this gives some monopoly power to gas stations. In many cases, consumers
find themselves in a situation where fuel runs out and have no choice other than filling
their petrol tanks at the first-best filling station they are facing, which gives additional
market power for gas stations. Prices change quite often, and to determine which
gasoline station has the cheapest fuel in this market is a non-trivial task. The price
variation in the fuel markets was widely documented in the scientific literature. In
particular, publications on this topic [
The price variation is measured by unexplained price fluctuations, namely, the
square of the residues of the logarithmic regression of market characteristics, including
the density of sellers. It was established that the increase in the number of neighbouring
gas stations is associated with a decrease in the price dispersion. Lewis [
Identification of the role of imperfect information cannot be made by simply
checking the usual comparative static of the dispersion of prices for costs or benefits of
the search, or the number of enterprises on the market. Price dispersion becomes a
nonmonotonic function of these variables if we allow consumers to adjust their
strategies for finding equilibrium. Using a new test of rank spreads and price spreads
between pairs of stations, it has been found that the time dispersion of the prices at the
market level is consistently higher than for stations at one crossroads. This is consistent
with the theory of consumer search, since the dispersion in the latter group is carried
out only through the differentiation of petroleum products. At the same time, the
assumption that the development of modern communication technologies will
automatically eliminate the problem of the variance of prices themselves did not justify.
So, on the data of Italian motorways [
The above results of outstanding researchers have proved not only the existence of
a dispersion of prices in the market of petroleum products as a consequence of the
search behavior of buyers, but also allowed to find quantitative dependence of price
characteristics on the infrastructure parameters of the market and the behavior of market
actors. However, many questions remain unclear. One of the difficult problems is the
estimation of the change in the variance of retail prices in the case of spin-off changes
in wholesale prices. As already noted, in such cases there is a phenomenon of price
asymmetry caused by the behavior of participants in the oligopolistic market of
petroleum products. This phenomenon was not studied by the classical theory, but in
recent decades, by the efforts of many researchers, this gap has largely been overcome,
but only with the assumption of a hypothesis of a single price. The question of how the
variation in retail prices in wholesale jumps has attracted the attention of researchers
recently, in particular Noel [
In this paper we study of the level of dispersion and its dynamics at the data on gasoline prices in the retail market of petroleum products of Ukraine for separate filling stations were provided by the Scientific-Technical Centre “Psychea”. The choice of gasoline, as a fuel, is explained by the higher homogeneity of consumers, compared with consumers of diesel fuel. However, despite the homogeneity of the market of petroleum products, in particular the gasoline market, the product market boundaries were clearly limited to cover the most homogeneous product: ─ Only non-branded gasoline, which falls under the state standard of quality, is involved in the consideration. ─ Gasoline of the brand А-95 is considered, because this type of fuel has the most homogeneity of consumers.
A comparative analysis of regional petroleum products markets in Ukraine showed existent of a daily dispersion of prices for gas stations belonging to different owners, as well as a significant difference in the level of price dispersion between individual regions of the country (Fig. 1, 2). Although there is a certain correlation between the level of retail prices and the level of dispersion, the market concentration may also affect the level of dispersion. Therefore, the study of the phenomenon of price dispersion is advisable to do for individual regions, and not for the whole country as a whole, because it will distort the results. Therefore, a sample of historical data of retail prices for A-95 gasoline of the Kyiv region for the period 2012-2017 was selected for the study.
The analysis behaviour gasoline prices for years 2012-2017 showed that most developments in the petroleum product market characterized by unique dispersion, but for intermittent changes in retail prices, to some extent, can assert the presence of the characteristic pattern of behaviour dispersion. In Fig. 3 shows a typical pattern of dispersion behaviour at a jump in retail prices caused by fluctuations in world oil prices. A characteristic feature of the dispersion is a significantly higher level of dispersion in the course of price growth and its return to the initial level during a decline.
There are many models of behavior of retail prices in the market of petroleum products. The overwhelming majority, including those that quantify the price dispersion phenomenon in the fuel market, are based on econometric approaches. However, for the study of the influence of the behavior of individual market agents on the behavior of market prices, the multi-agent approach seems more relevant. The bottom line is that multi-agent model of petroleum product markets can more flexibly take into account the different structure and rules for the functioning of national markets and the behavior of market agents.
The model of [
It should also be noted that an improved multi-agent model takes into account the basic means of state regulation of the pricing of retail networks. In particular, unlike petroleum products markets in some countries, where the change in retail prices is not forbidden for one day, the model takes into account the rule that operates in the Ukrainian petroleum product market, where retail networks can only change prices once a day. In the multi-agent petroleum market model there are the following agents: retail chain, gas station, consumer and trader. According to the model, the daily activities of petroleum products trading consist of the following actions: consumers purchase fuel, retail networks collect statistics from gas stations, gas stations if necessary, order a new consignment of fuel from the trader, interaction between the gas station and the trader, retail networks analysing all available information, set prices for the next day. The software model is represented by the following class diagram (Fig. 4).
The base class of each agent is MAgent, which is followed by agents of the gas station (MAzs class), retail network (MAzsNet class) and trader (class MTrader). For abstraction of a separate modeling, there is the MSimulation class, which manages the whole model and provides a set of tools for working with the model. The MInformSystem class is an interface for agent communication and information support. It should be noted that in the absence of a dedicated state agent, his functions in this model are assigned to this class, namely: to provide information on the list of taxes paid by retail networks and their current rates. The dynamics of the interaction between the flows of agents is shown in Fig. 5. In the proposed multi-agent model, the algorithm for retail network behaviour is based on states. The model outlines the following agent states retail network: market followup (S1), strategy changes (S2), trade stop (S3), return to market (S4). State S1 implements the behaviour of the agent in the presence of profits during periods of decline in prices and for their minor fluctuations during periods of high margins. State S2 realizes the agent's response to a sharp change in the market situation: a leap of prices, a sharp decline in demand, and so on. The states S3 and S4 implement market exit strategies if it is impossible to get the profit and return to the market in the event of such an opportunity. Fig. 6 shows a diagram of states of the mechanism of decisionmaking by the agent “Network”.
Agent’s behavioral algorithm Network in state S1 has the following appearance:
END
END ELSE
IF price_c > 0 AND current_trader_price_c < 0 AND competitors_prrice_c < 0 AND competitors_prrice - price < -0.5 THEN
delta = (competitors_prrice – price)*Pd; ELSE
IF price_c > 0 AND price_c < Pd AND current_trader_price_c < 0.1 THEN
delta = (optimal_price - price) * PrM * last_buy_prrice_c * 0.75 + 0.25 * competitors_prrice_c * Ck;
ELSE
delta = 0;
END
END END price = price + delta; To analyse the current situation, each agent has a statistical module that, with the help of the Ordinary Least Squares method, linearly defines the trajectory of the main indicators. Variables with suffixes “_c” denote the coefficient of the linear equation with the corresponding variable. Analysis of real data showed that retail networks mostly do not adjust the prices daily for a small value, and make a change in prices at least a certain value (usually it is 0.1 – 0.3 UAH / litre). Therefore, for the formation of the correct dispersion dynamics, the rules for the formation of threshold price changes by each network are additionally prescribed. In addition, in the price change algorithm, 3 main drivers are allocated, which form the necessary level of prices in the usual situation: ─ The behaviour of wholesale (current_trader_price) prices with respect to the prices of last fuel purchases (last_by_price). ─ Price behaviour of competing networks (competitors_prrice). ─ Optimal price that maximizes profit (optimal_price).
We determine the optimum price as maximizing the profit of the retail network, taking into account current demand: profit D(P,Pavg )P Tax Costs max
Pc P 1.4Pacg (1) (2) where D P, Pavg a0 a1 P Pavg – function of estimating the volume of sales of fuel
Pavg at the gas station; Pavg – average fuel price within a radius of K km from the location of the gas station; P – the fuel price of the agent, the variable for which the optimization takes place; Tax – Tax Component; Costs – Costs; Pc – the price of fuel purchases. The demand function coefficients (α0 and α1) are automatically evaluated for each agent individually and specified at each step of the model during simulation. It should be noted that the establishment of both the upper and lower bounds of this indicator is dictated by both insufficiently studied demand function and consumer behaviour. The formation of the initial level of dispersion is achieved by setting variables and constant costs for each network based on real estimates of these indicators with some correction on the assumption of model and the stability of the initial state of the model. 4.2
Algorithms of Consumer Behaviour As the results of previous studies have shown, consumer strategy with the search for a base price can generate asymmetric behaviour of retail prices. Therefore, based on the basic algorithm of consumer behaviour, the search for the base price is chosen: the consumer searches until he finds a price not higher than the price of the previous purchase. At the same time, as you know, consumers are not homogeneous, and among them there are groups with other patterns of behaviour: consumer orientation at the price and random selection of gas stations.
The algorithm of consumer behaviour with the search for the base price is presented in Fig. 7. The consumer makes several attempts to find a price lower than the price of the last purchase of fuel. In the basic version of the model, the number of attempts to search is 5. The behaviour of consumers without a search is equivalent to a uniform distribution of demand for all filling stations. The scheme of the algorithm is shown in Fig. 8.
The behavior of price-oriented consumers is carried out by the construction by each consumer of distribution at the gas station in accordance with the price level at the gas station. The basis of such a distribution is an exponential distribution with modifications based on the following empirical assumptions: the consumer is guided by the relative price level when selecting a gas station, the lower the price, the greater the probability of choosing this gas station. Given the complexity of estimating the additional distribution parameters it is assumed that the mathematical expectation is equal to 1, and the density function has the following form as follows: prob = 1 e( pricemin( price)) k (3) where price – price at the gas station, min(price) – the minimum price among all the gas stations in the field of consumer’s vision, k – the coefficient of normalization of distribution density: where M – amount of fuel station that in field of consumer’s vision. This list of observed gas stations prepared for each consumer using empirical assumption that maximum distance from consumer location to station must not exceed 7 km. This value was determined on the basis of a survey of drivers in the region of Kyiv and has a preliminary assessment character, which requires a separate study. However, in order of magnitude it coincides with the values of the authors in the literature cited above.
Due to the lack of reliable data on consumer preferences in the choice of gas stations, the basic algorithm of consumer behaviour will be considered the algorithm for finding the base price. However, for comparison, all types of consumer behaviour algorithms were used. Nelder-Mead method was used to calibrate the model. The criterion of optimality was the sum of absolute deviations of average retail prices in the model from their real values. In total, 130 steps were taken to select the optimal model parameters. These parameters are the following parameters (the notation corresponds to the variables in algorithm above): ─ PrM (with value 7.1195) – optimal price correction coefficient, which determines the effect of the deviation of the calculated optimal price from the current price at the gas station; ─ Pd (with value 0.05) – a coefficient that determines the magnitude of the impact of competitors prices absolute value on the price of gas stations; ─ Ck (with value -2.8899) – coefficient, which determines the influence of the price trend of competitors to the price of gas stations; ─ Trk (with value 1.0292) – coefficient, which determines the effect of wholesale prices change on the price at the gas station; ─ Pd2 (with value -16.861) – the threshold of competitors average price delta, which is used to switch the pricing approach in the algorithm.
As a result of the selection of parameters, it was possible to achieve qualitative detection of the dynamics of retail prices (Fig. 9), while the dynamics of dispersion repeats the actual trends (Fig. 10). That is, the multi-agent model identifies a pattern of price dynamics and dynamics of price dispersion. It should be noted that in general, some discrepancy between the finite level of the real and the model dispersion can be dictated by the local peculiarity of the jump. A slightly lower dispersion level of 75-90 model days is caused by the early reaction of retail networks of the lower price segment. Such an early reaction to the rise in prices in these networks is due to the existence of a single algorithm of behaviour as retail networks operating on both purchased fuel and selfproduced fuel. Therefore, in some cases, the decision to change prices in such networks may occur somewhat later than other networks in connection with the monthly schedule of processing capacity. Along with the calibration of the model of the dynamics of the dispersion of retail prices with the use of the algorithm for searching the base price for consumers, the possibility of forming adequate dispersion estimation for other types of consumer behaviour was also checked. In Fig. 11 shows a comparison of the dynamics of retail price dispersion by various consumer behaviour algorithms. Other patterns of consumer behaviour have a fundamentally different dynamics of dispersion. In cases of search and price targeting, almost the same growth of dispersion is observed during the growth of retail prices. However, in the case of price-targeting, the dispersion, and somewhat lowered while finding retail prices for the “plateau”, began to increase again after falling prices. On the one hand, this testifies to the discrepancy of such behaviour with real situations. However, on the other hand, there may be a simple non-compliance of the rules of retail networks with a similar behaviour of consumers. It should be noted that the re-training of the model with the use of the algorithm of targeting the price was not carried out, because the replacement of the algorithm has a small effect on the dynamics of average prices. The dynamics of dispersion in the use of consumers without a search showed that such a type of consumers cannot be dominant in the market given the significant difference in dispersion from the real. This paper proposes a multiagent model of the phenomenon of dispersion of prices in the market of petroleum products. The conducted research showed that the multiagent model of oil products market as an oligopolistic competitive environment, in which fuel consumers are guided by the strategy of price search, generates the phenomenon of the price variance regardless of the initial conditions of the variance values. The agents’ interaction was based on oligopolistic competition rules and consumer price search strategies. This model was tested on the price data for gasoline in the Kyiv region of the Ukrainian oil market. The choice of data for this region and the choice of gasoline as a commodity were dictated by the desire to identify the effect of dispersion due to the existence of a search strategy for consumers on a market with a homogeneous product. At the same time, the existence of a dispersion of retail prices in the market of petroleum products has been shown as a result of oligopolistic competition of traders and price search behavior of buyers, as well as the growth of price dispersion at price jumps of wholesale prices. It is shown well enough to predict the appearance of this pattern at price jumps. It has been established that the best approach to real data, both in terms of price and dispersion, has been shown by the consumer strategy with the search for the base price. The availability of other search strategies has not been confirmed. Comparison of model calculations and real data showed a fairly satisfactory coincidence, which, however, needs to be improved. However, to do this, there is need to conduct additional research in mixed search strategies for different categories of users.