MEQU (Market Effects of Quality Uncertainty)

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WHAT IS IT?

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.

QUICK GUIDE

1. Set up the model by selecting values for the following parameters:
• 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 applicable).
2. Press the setup button.
   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.
3. 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

Social network

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, sec. VII-B).

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.

Supply

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 msp_i = i. A seller i is willing to sell her product if price p >= msp_i. 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 to, num-sellers).

Demand

• 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 (q^exp_i,n): The initial expected quality (q^exp_i,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.

R_1,n >= R_2,n >= … >= R_num-buyers,n

Market mechanism

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 R_i,n >= msp_i and the market price p_n is taken to be

p_n = ½ [Min (R_y,n, msp_y+1) + Max (R_y+1,n, msp_y)]

This price-setting formula takes into account the satisfied supply and demand ( msp_y <= p_n <= R_y,n ) and the pressure of the extramarginal supply and demand ( msp_y+1 >= p_n >= R_y+1,n ).

Quality expectations

• 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 a product:

  q^exp_i,n+1 = q^exp_i,n + individual-weight· (q_i,n - q^exp_i,n) + social-weight · (meanq_i,n - q^exp_i,n)

  where q_i,n is the quality of the product received by buyer i, and meanq_i,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 has:

  q^exp_i,n+1 = q^exp_i,n + individual-weight · (q_i,n - q^exp_i,n)

• If buyer i has not purchased a product but someone in her neighbourhood has:

  q^exp_i,n+1 = q^exp_i,n + social-weight · (meanq_i,n - q^exp_i,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 buyers.
    
  • 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 to 1.
• 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

1. Click on setup. This creates the buyers, the sellers, the social network (buyers and links), and displays the initial demand and supply.
2. 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.

Displays

• 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 runs
• 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 quality variability.

THINGS TO TRY

CREDITS

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.

REFERENCES

Akerlof GA (1970). The Market for Lemons: Quality Uncertainty and the Market Mechanism. The Quarterly Journal of Economics 84: 488-500

Hendel I and Lizzeri A (1999). Adverse selection in Durable Goods Markets. American Economic Review 89 (5): 1097-1115

Izquierdo SS, Izquierdo LR (2006). The Impact of Quality Uncertainty without Asymmetric Information. Agent Based Models of Market Dynamics and Consumer Behaviour, Pre-proceedings.

Izquierdo SS, Izquierdo LR, Galan JM and Hernandez C (2005). Market Failure caused by Quality Uncertainty. Artificial Economics - Lecture Notes in Economics and Mathematical Systems 564. Springer-Verlag, Berlin, 2005.

Macho-Stadler I and Pérez-Castrillo JD (2001). An Introduction to the Economics of Information. Incentives and Contracts. Oxford University Press (Second edition)

Newman M.E.J. (2003). The structure and function of complex networks. SIAM Review 45, 167-256 .

Rose C (1993). Equilibrium and Adverse Selection. The RAND Journal of Economics, 24 (4): 559-569

Stigler GJ (1961). The Economics of Information. Journal of Political Economy 69: 213-225

Stiglitz JE (2000) The Contributions of the Economics of Information to Twentieth Century Economics. The Quarterly Journal of Economics, Vol. 115, Issue 4 - pp. 1441 - 1478

Vriend N (2000). An Illustration of the Essential Difference Between Individual and Social Learning, and its Consequence for Computational Analyses. Journal of Economic Dynamics and Control 24: 1-19

Wilensky U (1999) NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Wilson CA (1979). Equilibrium and adverse selection. American Economic Review 69: 313-317

Wilson CA (1980). The Nature of Equilibrium in Markets with Adverse Selection. Bell Journal of Economics 11: 108-130