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Utility Load Model 2015

by Ulisses Lacerda de Morais (Submitted: 07/28/2015)

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The Utility Load Model was designed to study the relationship amongst entrepreneurship and market structure of an economic sector. The model allows direct interaction between firms and people via New-Issues Market (NIM) and indirect interaction through an environmental parameter. The goal is to explain under what circumstances are the decisions of entrepreneurs conditioned by the existence of the NIM as an opportunity cost for starting a new firm and the consequences for the sector’s concentration.


People, firms and investors are organized around three concentric circumferences with radius 15, 12 and 8, respectively. The firms’ circumference is visible and coincides with their product space, where each firm's position corresponds to a variety of the product, a variation of Salop’s circular model (1979). The innermost circumference is the NIM, populated by the investors. On each period, entrepreneurs (people) in the outermost circumference must choose between entering the market by creating a new firm (a.k.a. start-up prospect), investing on firms by acquiring stocks and/or bonds (a.k.a. portfolio prospect), or doing neither and delaying their decision to the forthcoming period.

The decision-making process of people in the Utility Load Model is based on a rather harmonious hybrid model of Prospect Theory (Kahneman & Tversky, 1979; 1992) and Random Walk model of perceptual decision-making (Smith & Ratcliff, 2004; Bogacz, 2007), where every person has an attribute named load, which the current value reflects how close from deciding one is. It’s assumed that people’s decision threshold is the amount of surplus evidence (or information) in favour of one alternative that one must gather (i.e. load variable must surpass) before deciding. People also own an attribute called bias which represents their personal inclination towards one of the prospects and it is simply defined as the initial value of load.

At each time step (tick), every person in the model compares the subjective utility of the start-up prospect against the portfolio prospect and aggregates the result on the load attribute. If, at any point, load is greater than threshold or lower than its additive inverse, a decision is made to become an investor (red circle) or a firm (green factory), respectively.


Press SETUP to create agents and a visualization of their starting positions.
Press RUN to make the model run continuously.
Press STEP to have the model make one iteration.

* SETUP button will create a number of firms (brown factories) equal the value in the «incumbents» slider, the analogous is true for people (businessmen) and the «newcomers» slider.
* The «life-expectancy» slider defines people's longevity and by subtracting their respective age we get people's investment horizon.
* The «total-cost» is the proportion of firm's resources and revenues that will be spent as cost on each period.
* The «interest» slider defines the interest periodically paid for bonds.
* The «without-market?» switch turns off the option of portfolio investment.
* The «no-bias?» switch turns off the bias attribute setting it equal to zero for all people.
* The «exogenous-death» slider will add a death rate for the population of people
* The «exogenous-exit» slider assigns a probability per period of firms exiting the market.

The interface contains ten plots whose initial values are determined at setup procedure and updated on every tick. Plots A, G and B display the progress over time of the quantity of agents from each breed, the environmental parameter and its mean, and the Herfindahl-Hirschman Index (HHI) and its mean, respectively. Additionally, C is a monitor that shows the current value of the HHI mean.

Plot J displays the number of positive (and negative) observations of the environmental parameter, over time, as a percentage of the total number of observations. Plot K indicates the firms’ mortality rate for each period.

Plots F and H display the subjective value of gains and the subjective probability of gain for each prospect, these values are requested from a random person at each time step and, as such, the value of the series in a particular period has little meaning, only the long-term trend of these charts are informative.

Finally, Plots D, E and I present the histograms for the current distributions of people’s biases and thresholds attributes, and the environmental parameter values, respectively.


The following combinations of parameters’ values:

no-bias? {on, off} vs. life-expectancy {36, 180}

Another interesting test is to combine the above with variations of the without-market? switch.


When a firm gets to be the only one in the market and continuously supplies bonds for the entire industry’s NIM, it can be brought to bankruptcy due to financial debt.

When three or more firms occupy the same address in the product space, if two of them start to grow concurrently, the other(s) is(are) pushed out of the market due to the shortage of local demand.

Even in recessionary periods there is a rather constant rate of start-ups entering the market, and this rate grows with the length of the recession.

A lengthier investment horizon attracts the vast majority of entrepreneurs to the NIM. The prior has a nefarious effect on the sector’s structure which is pushed towards a concentrated structure, reflected by higher HHI values. The relative impact on the HHI is even greater in scenarios with more incumbents and newcomers.


An alternative reading to the present model is a multi-brand duopoly, where the incumbent (brown firm) faces the threat of a potential rival (green firm) in the same product space. In this interpretation, the two firms not only compete for market-share through multiple varieties of a product, but also for equity and security investors (people).


I anticipate several ways in which the Utility Load Model could be improved, to mention a few: turning life-expectancy into a dimension of heterogeneity; refining the heuristic used to compute the prospective gain with a start-up; allowing for fluctuations in the price of stocks and bonds; refining firms’ behaviour regarding the issuing of securities; including non-linear cost function; adding government to the mix; and so on.


* Bogacz, R. (2007). Optimal decision-making theories: linking neurobiology with behaviour. Trends in Cognitive Sciences, 11 (3), pp. 118-125.

* Kahneman, D., & Tversky, A. (1979, March). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47 (2), pp. 263-291.

* Kahneman, D., & Tversky, A. (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty, 5, pp. 297-323.

* Salop, S. C. (1979). Monopolistic Competition with Outside Goods. The Bell Journal of Economics, 10 (1), pp. 141-156.

* Smith, P. L., & Ratcliff, R. (2004). Psychology and neurobiology of simple decisions. Trends in neurosciences, 27 (3), pp. 161-168.


Morais, U. L. (2015) New-Issues Markets as Behavioural Barriers to Entry: An Agent-Based Model of Choices and Market Structure. Master’s Thesis in Economics. University of Coimbra.


Copyright 2015 Ulisses Lacerda de Morais

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Developed as part of Master's thesis in Economics, in the specialty of Industrial Economics, presented to the Faculty of Economics of the University of Coimbra for the obtainment of the degree of Master. For further information on this work, please contact the Faculty:

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