MEQU (Market Effects of Quality Uncertainty)
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WHAT IS IT?
MEQU (Market Effects of Quality Uncertainty) is a model designed to study the effects of quality uncertainty and incomplete information on market dynamics. The main assumption in this model is that buyers form quality expectations about products based on their own past experiences and on the experiences of people they know.
This model is based on buyers' expected behaviour, in contrast with classical models of quality uncertainty, which, in addition to quality variability, tend to assume asymmetric information and are based on the phenomenon of adverse selection. MEQU shows that asymmetric information is not necessary for quality variability to damage (or even destroy) a market. It also shows how sharing information, or making aggregate information available, can mitigate the damaging effects of quality variability.
- Set up the model by selecting values for the following parameters:
Press the setup button.
- num-sellers: Number of sellers in the market.
- num-buyers: Number of buyers in the market.
- individual-weight: Sensitivity of each buyer's quality expectations
to her own individual quality experiences.
- social-weight: Sensitivity of each buyer's quality expectations
to her neighbours' quality experiences.
- network-structure: Type of network structure that connects pairs
of buyers through directed links. There are four network structures implemented:
random, preferential attachment, double ring, and star.
If the network structure chosen is random, the value of the parameter num-links
will determine the number of random links to be created. If the network structure selected is
preferential attachment, each buyer will join the network linking to pref-attachment-links
other buyers. Network structures double ring and star do not require any further parameterisation.
- quality-distribution: Statistical distribution for the quality
of the items.
- quality-variance: Variance for the quality distribution (if
The social network (buyers and links) will be represented on the screen. If
the show-network-formation switch is on you will see
the dynamics of the network formation.
Press go-once to see the results after just one trading session, or
press go to start a series of trading sessions. Press go
again to halt the model.
HOW IT WORKS
Buyers can be connected, forming a social network. Thus, each buyer
may link to none, one, or several buyers; this (potentially empty) set of neighbours
defines the buyer's social neighbourhood.
If the network-structure is random, then it is created by establishing a certain
number (num-links) of directed links between randomly selected pairs of buyers.
If the network-structure is preferential attachment, buyers are sequentially
added to the network; every buyer who joins the network selects pref-attachment-links
other buyers to link to, who are selected with probability proportional to their
number of existing (incoming and outgoing) links. At the beginning of the creation
of this network, while the number of buyers is less than pref-attachment-links,
each new buyer links to all existing buyers. This is Barabási and Albert's
preferential attachment model of network growth (See Newman 2003,
If the network-structure is double ring, all buyers are randomly placed
in a ring (randomly "seated" at a round table) and each buyer links
to the one on her right and to the one on her left.
If the network-structure is star, one buyer is randomly selected and
bidirectional links between her and each one of all the other buyers are created.
The supply function is constant. There are num-sellers sellers
indexed in i (i = 1,..., num-sellers) with minimum
selling price for seller i being mspi = i.
A seller i is willing to sell her product if price p >= mspi.
This creates a supply function such that the number of items offered at price
p (p >= 0) is the integer part of p (with the additional
restriction that the number of items offered must always be less than, or equal
The demand function in every session is formed by summing up buyers' individual reservation prices. The reservation price of buyer i in session n is equal to her initial reservation price multiplied by her current expected quality (qexpi,n) for the product.
At any trading session n, the num-buyers individual reservation prices can be sorted out as follows:
- Initial reservation price: Each of the num-buyers buyers is indexed in i (i = 1, 2 ... num-buyers), and buyer i has initial reservation price equal to i. The initial reservation price for each buyer is constant throughout the simulation.
- Expected quality (qexpi,n): The initial expected quality (qexpi,0) for every buyer is equal to 1. The quality expected by each buyer may (and most often does) vary throughout the simulation, depending on the learning rule and the particular buyer's experiences.
R1,n >= R2,n >= … >= Rnum-buyers,n
This order will be useful to determine the price (see below). Finally, note that, given the description above, the initial demand is such that at price p (p <= num-buyers), the number of products demanded is the integer part of [num-buyers + 1 - p] (with the additional restriction that it always must be less than, or equal to, num-buyers).
Buyers and sellers trade in sessions. In each session, each buyer can buy
at most one product, and each seller can sell at most one product.
In each session n, the market is centrally cleared at the crossing
point of supply and demand. Specifically, the number of traded units y
in session n is the maximum value i such that Ri,n
>= mspi and the market price pn is taken to
pn = ½ [Min (Ry,n, mspy+1)
+ Max (Ry+1,n, mspy)]
This price-setting formula takes into account the satisfied supply and demand
( mspy <= pn <= Ry,n ) and the pressure
of the extramarginal supply and demand ( mspy+1 >= pn
>= Ry+1,n ).
In general, buyers form their quality expectations considering both their own experience and their social neighbours' experience. More precisely, after every trading session, every buyer i updates her quality expectation if and only if
In either of those cases, buyer i updates her expectations according
to the following rules:
- she has bought a product and she somewhat considers her own experience (individual-weight > 0), or
- someone in her social neighbourhood has bought a product and she somewhat considers her neighbours' experience (social-weight > 0).
- If both buyer i and someone in her neighbourhood has purchased
qexpi,n+1 = qexpi,n
+ individual-weight· (qi,n - qexpi,n) + social-weight
· (meanqi,n - qexpi,n)
where qi,n is the quality of the product received by buyer i, and
meanqi,n is the average quality of the products received
by buyers in i's social neighbourhood.
- If buyer i has purchased a product but no one in her neighbourhood
qexpi,n+1 = qexpi,n
+ individual-weight · (qi,n - qexpi,n)
- If buyer i has not purchased a product but someone in her neighbourhood
qexpi,n+1 = qexpi,n
+ social-weight · (meanqi,n - qexpi,n)
HOW TO USE IT
Setting the parameters
- Choose the number of sellers in the market: num-sellers.
This parameter is used to create the supply function, which remains constant
all throughout the simulation.
- Choose the number of buyers in the market: num-buyers.
This parameter determines buyers' initial reservation prices and, consequently,
the initial demand function.
- Select a value for the parameters individual-weight and social-weight.
These two parameters determine how buyers update their quality expectations.
The parameter individual-weight measures the sensitivity of buyers to their own individual experiences,
and the parameter social-weight measures the sensitivity of buyers to their neighbours' experiences.
The social neighbourhood of buyer A is the set of other buyers to whom A links
(see next bullet point). Thus, social-weight = 0 implies
individual learning only (provided that individual-weight > 0).
- Customise buyers' social network by selecting the network-structure.
- For a random network, select also the number of random links to be formed:
num-links. The network is formed by creating num-links random directed links between
- For a preferential attachment network, select also the number of
links pref-attachment-links. This is the number of outgoing directed
links for each new buyer which is added to the network as it is formed.
- More links can be created or deleted at runtime using num-links,
given any initial network structure.
In that case, every possible directed link between two buyers has the same probability of
being created or deleted.
- Select a statistical distribution for the quality of the items. The
quality distribution of every item produced is determined by two parameters:
quality-distribution and quality-variance.
- Parameter quality-distribution can take one of three possible values:
uniform, exponential, or trimmed normal. The mean of all three distributions
is 1. The trimmed normal is a normal distribution where every value greater
than 2 is set back to 2, and every value less than 0 is set back to 0.
- Parameter quality-variance determines the variance of the quality
distribution, if applicable. The maximum variance for the uniform distribution
is 1/3, which correspond to the maximum range allowed: [0,2]. The variance
of the exponential distribution is necessarily 1, since its mean is fixed
- The show-network-formation switch determines whether the dynamics of the
network formation are shown (value = on) or not (value = off).
Starting up the model
- Click on setup. This creates the buyers, the sellers, the social network (buyers and links), and displays the initial demand and supply.
- To make the model run once (i.e. one trading session) press go-once. To run the model indefinitely, press go. Press go again to halt the model.
Interacting with the model at runtime
There are a number of ways in which the user can interact with the model. Except for the number of sellers and buyers, the value of every parameter described above can be changed at runtime. Thus, except for potentially those two parameters, the model is always using the values that are shown in the interface. Note that, in particular, the user can create and delete random links in the network as the model runs. This can be conducted by modifying the number of links directly. All links are created or deleted at random. There are also other ways, all of them related to the social network, in which the user can interact with the model at runtime:
- Clicking on resize buyers will switch between (a) showing every buyer with the same size and (b) making buyers' sizes proportional to the square root of the number of social neighbours they have.
- Clicking on drag and drop allows the user to change the position of buyers using the mouse. Please click on the button again when finished.
- relax network changes the position of buyers in the network, trying to find a better-looking spatial configuration. Please click on the button again when satisfied.
- Main display. The black square in the centre shows, after setting up
the model, the sellers aligned at the bottom, and the network of buyers, above
the sellers. The slider at the top lets the user control how fast the model
- The market display shows the supply function (blue) and the demand function
(red), together with the initial demand (green).
- The "Accessibility Distribution" graph shows a histogram of the accesibility
in a selected number of steps (accesibility-steps). The accesibility
of a buyer in n steps is the number of social neighbours within her reach
going through up to n links. For instance, if buyer A links only to buyer B, who
links only to buyer C, who has no social neighbours, then A's accessibility
in one step is 1, and in two steps is 2; B's accessibility in any number of
steps is 1, and C's accessibility in any number of steps is 0. Please remember to click on
Update accessibility to update the graph after changing the
value of accesibility-steps.
- The "buyers' surplus" is calculated by summing up, for every buyer who
has bought a unit in the session, the difference between her reservation price
and the price she paid for the unit she bought. The green dotted line shows
the reference value, i.e. the buyers' surplus if there were no quality variability.
- The "sellers' surplus" is calculated by summing up, for every seller
who has sold a unit in the session, the difference between the price at which
the unit was traded and the seller's minimum selling price. The green dotted
line shows the reference value, i.e. the sellers' surplus if there were no
THINGS TO TRY
Create a market without social network (num-links = 0). Use
some quality variability and individual-weight which are not very low
and observe the market failure.
Select a social-weight greater than 0, increase the
number of links in the network and observe the recovered dynamics. The market
failure is also visible if there is a social network but the social-weight
is set to 0.
MEQU was developed by Segismundo
S. Izquierdo and Luis R. Izquierdo. The authors would like to gratefully acknowledge
financial support from the Scottish Executive Environment and Rural Affairs
Department and from the SocSimNet project 2004-LV/04/B/F/PP.
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