Agent Based Simulation of Customers Behavior for the Purpose of Price Distribution Estimation Marek Zachara and Cezary Piskor-Ignatowicz AGH University of Science and Technology, Krakow, Poland
[email protected],
[email protected]
Abstract. Price dispersion is an observed variation of price of the same (or similar) product among different vendors. This paper provides a possible explanation of the observed shape of the dispersion, proven by simulations of an agent based client-vendor environment. Proposed models for client and vendor representation are included. It turns out that the observed shape is achieved when some key environmental elements are taken into account; i.e. communication between clients, a limited memory of a client and the cost of crossing the distance between agents. As a benefit of the proposed model, it allows for speculation on how the future commerce may look like - in an Internet world where distances matter little. Keywords: price dispersion, clients behavior, simulation
1
Introduction
Price is a key element of virtually any economic activity. Even though its not always explicitly mentioned, its always present - often as a property of cost (e.g. cost of the alternative, cost of supplies, etc.). Price in general is considered to be a ratio of exchange between two types of goods, usually expressed in certain monetary units [3]. Thorough this article two types of price will be used: a transactional price (i.e. a price at which transaction between a supplier and a purchaser is carried out) and an offered price (i.e. a price that one side of the transaction is willing to accept, but the other might not always do so - in which case the transaction is not concluded). The transactional price can be determined in various ways. Probably most common is a free market scenario, where suppliers and buyers freely negotiate the price until they come to the point when they are both willing to perform the transaction - or they abandon the negotiations. Another major option is a fixed price scenario, where the price is set (usually by the authorities) and all transactions can be performed only at this set price. The later usually leads however to under/over supply of the traded commodity, or development of an illegal (black) market where the transactions are performed at free market prices [5]. As mentioned above, price is a central issue of economic activities. Economics, like other sciences, strives to build theories that would allow to predict an outcome of conditions not observed before. Yet it lacks the primary scientific tool;
2
Marek Zachara and Cezary Piskor-Ignatowicz
i.e. a controlled experiment. For obvious reasons, it is not possible to lock large groups of humans in a controlled environment for extended periods of time to test scientific theories on them. As a result, Economics relies mainly on postfactum data analysis, with modeling and simulation added to the portfolio of tools in recent years. Certainly, all of us are subject to economic experiments - as the authorities continuously try to adjust the environmental conditions of individuals, groups and nations. Yet, this does not meet scientific criteria (controlled variables, stable environment, defined observables), so in reality is useful only for the ’post-factum’ analysis. It is necessary to mention that all Economics’ theories are based on sets of data collected through observation of the real world. Modeling and simulation offer some advantage over the traditional analysis of such data in terms of observability, they are however still subject to insufficient input and unproven assumptions.
2
Price Evaluation and Price Dispersion
In a free market economy, the price is usually set by sellers based on the feedback they receive from buyers. For a client, the following model of perceived attractiveness of a certain seller’s offer is proposed: A = aVq + bVs − cS − dCr .
(1)
Where: – A is the perceived attractiveness – Vq is the assumed value of the considered item. It is a property of each specific item and may include physical quality, brand value among peers, etc. – Vs is the expected quality of service from the seller – S is the transactional price – Cr is the cost of purchase (e.g. time needed to reach the shop) – a, b, c, d are factors denoting personal preferences If the client decides to purchase a particular type of item or service, he or she will choose a seller with the greatest perceived attractiveness, which in turn depends on the offered price (S), but also on other, less easy to measure factors. Sellers try to maximize the overall profit by adjusting their offer. The profit earned can be defined as: P = n (S − Cp (n)) − Cs (n) − Cc . Where: – P is the total profit for the defined period of time – S is the transactional price
(2)
Simulation of Customers Behavior for Price Distribution Estimation
– – – –
3
Cp (n) is the cost of purchasing or producing the item being sold Cs (n) is the cost of sales (e.g. staff, packaging) Cc is the constant operating costs (e.g. rent) n is the number of transaction during the defined period (e.g. a month)
To maximize the overall profit, sellers can adjust several factors of their equation: – Adjust their product portfolio. This will change the Cp component of equation (2), but will also affect the Vq of the client’s equation (1) – Adjust the offered price. This directly changes the profit generated and perceived offer attractiveness. – Adjust their quality of the service. That will affect the Cs component of seller’s equation (2) and Vs component of the client’s equation (1) – Relocating the shop. This changes the Cc component and also changes Cr component of ALL of the potential customers.
the the the the
Sellers have a number of factors under their control, yet all of them affect both their profit per transaction as well as the perceived attractiveness by customers. Maximizing the profit is therefore a non trivial and non-linear task. Since many of the factors in the equations are unknown (especially in respect to clients’ personal preferences), the sellers in real word often probe the market by adjusting their offer parameters and getting the feedback in terms of transactions number increase or decrease. With the adoption of Internet and on-line transactions, the seller-buyer relation has been altered. Until then, the location of the shop was one of the most important factor, as long distance travel to make a purchase was in most cases unjustified. Thus the competition was limited. At the same time premium location rent was a major cost for the sellers. Internet sales affect the Cs and Cc components of the equation (2) but also the Cr part of the client’s equation (1). The later is affected in two ways. First, the cost of a trip to the shop is flattened for all suppliers to the level of parcel’s delivery cost. On the other hand, a cost of dissatisfaction is added as the customer must wait for the transaction to complete. Finally, there is a social and knowledge context of each client’s decision. Every client can only choose to buy from a seller he or she is aware of. Even if a client has an extremely cheap and high quality shop just ’around the corner’, which in every aspect is best for him, he can only go there if he is aware of its presence. Therefore the clients’ knowledge about available sellers and their offer heavily influences their decisions. Also, the social groups a client belongs to may additionally favor or disapprove certain products or sellers. Considering all the factors involved, its understandable that with many clients and sellers in the market, their personal preferences and locations, even in a completely free market environment, there will be no single optimal price that the whole market will adopt. This is known as a price dispersion and is a well known effect in a free market [1], [6], with good mathematical analysis performed in [2]. Traditional analysis of the price dispersion leads to a conclusion that in most cases the the distribution of prices is Gaussian-like [6]. However, when Internet
4
Marek Zachara and Cezary Piskor-Ignatowicz
trade is considered, especially if substitutes are taken into consideration, the distribution becomes more asymmetrical (see Fig. 1) as has been demonstrated in [7].
0.15
0.1
0.05
0 2000
4000
6000
8000
10000
Fig. 1. Example of price dispersion for on-line shops, data gathered from pricecomparison sites by authors. The X axis represents price offered for tv-sets by online shops, while the Y axis represent the estimated relative number of transactions. Methodology for the estimation is presented in [7].
3
Simulation Model
The simulation environment used for simulating clients’ behavior and price distribution consists of two distinguishable types of agents [4] interacting with each other. Their initial placement in the defined space is random, as well as their initial properties. 3.1
The Vendors
A Vendor is represented be a quadruple: V {L, S, Z, Q} .
(3)
Where: – – – –
L is the location of the vendor S is the price of offered product Z is the product offered (represented by a certain abstract quality value) Qs is the quality of the service offered by the vendor
Vendors are focused on one single goal - to maximize their profit generated for each defined period of time (counted in simulation cycles). To achieve this goal,
Simulation of Customers Behavior for Price Distribution Estimation
5
they keep history of profit and price changes made during the recent periods - and adjust their offered price S. The amount of price change is random but limited in value, the direction of price change is however determined by the outcome of previous decisions. If decrease (or increase) in price resulted in increased profit (calculated as per equation (2)) for the evaluation period, the decrease (increase) will be continued. If however, the decrease lowered the profit, the offered price will be increased. 3.2
The Clients
Similarly, a model of Client consists of a number of properties: C {L, K, R, A, E} .
(4)
Where: – – – – –
L is the location of the client K is the knowledge possessed by the client R is the relationships they have with other clients A is their current assets (owned items) E is their personality
For the purpose of identifying properties thorough this paper a convention known from object-oriented programming will be used. A hierarchical access to class properties is represented by a ’.’ (dot) - so C.E means the personality of some client C, while C.E.F means certain aspect of this personality Some of these properties may require further explanation: Knowledge Possessed by a Client. This is limited to knowledge about available vendors, with each piece of knowledge consisting of: vendor location (K.L), their product and its price (K.Z, K.S), and (optionally) the service quality (K.Qs ). Each piece of knowledge has certain strength of memory imprint (K.B) and can fade with passing time. K = {V, L, S, Z, Qs , B} .
(5)
Relationships with other Clients. Relationships are of type ’acquaintance’ (i.e. certain client knows another client). A client can form new relationships as well as break existing ones (see “Agents’ interactions”) Personality of a Client. It consists of several factors that affect each clients behavior. These are: friendliness (E.F ), price sensitivity (E.S) and product adoption (E.Z) that denotes how quickly a client gets bored of a newly bought product and starts looking for a new one. E = {F, S, Z} .
(6)
6
Marek Zachara and Cezary Piskor-Ignatowicz
3.3
Clients’ Actions and Interactions
As it has been described earlier in this section, vendors’ behavior is limited to adjusting the offer price to maximize the profit generated. The clients on the other hand have much wider variety of actions available: Relation Evolvement. With each simulation cycle, each client has a chance to ’meet’ another client and develop a relation. A probability of meeting (Pm ) depends on the euclidean distance (d(C1 , C2 )) and its importance (X.Rd ) between the clients. X.Rc is a constant simulation factor (thorough the rest of the article, simulation parameters will be prefixed with ’X’): Pm =
X.Rc . 1 + X.Rd ∗ d(C1 , C2 )
(7)
If two clients meet, the chance of developing a relation (Pr ) depends on the friendliness of each one (Cn .E.F ) and their current number of friends (Cn .count(R)) Pr =
X.Re ∗ (C1 .E.F + C2 .E.F ) . (1 + X.Rf (C1 .count(R))) ∗ (1 + X.Rf (C2 .count(R)))
(8)
A newly created relation has an initial default strength of 30%, although this value will be subject to change as simulation progresses. This is because with each simulation cycle every relation is tested against the condition: X.Rd ∗ rand()
