Government intervention modeling in microeconomic company market evolution
GGovernment intervention modeling inmicroeconomic company market evolution
Micha(cid:32)l Chorowski ∗†‡§ and Ryszard Kutner § Abstract
Modern technology and innovations are becoming more crucial than everfor the survival of companies in the market. Therefore, it is significant bothfrom theoretical and practical points of view to understand how governmentscan influence technology growth and innovation diffusion (TGID) processes.We propose a simple but essential extension of Ausloos-Clippe-P¸ekalski andrelated Cichy numerical models of the TGID in the market. Both models areinspired by the nonlinear non-equilibrium statistical physics. Our extensioninvolves a parameter describing the probability of government interventionin the TGID process in the company market. We show, using Monte Carlosimulations, the effects interventionism can have on the companies’ market,depending on the segment of firms that are supported. The high interven-tion probability can result, paradoxically, in the destabilization of the marketdevelopment. It lowers the market’s technology level in the long-time limitcompared to markets with a lower intervention parameter. We found thatthe intervention in the technologically weak and strong segments of the com-pany market does not substantially influence the market dynamics, comparedto the intervention helping the middle-level companies. However, this is stilla simple model which can be extended further and made more realistic byincluding other factors. Namely, the cost and risk of innovation or limitedgovernment resources and capabilities to support companies.
PACS number: keywords: government interventionism, Monte Carlo simulation, technologygrowth, econophysics ∗ [email protected] † Presented at the 10th Polish Symposium on Physics in Economy and Social Sciences (FENS)2019, NCBJ Otwock-Swierk. ‡ College of Inter Faculty Individual Studies in Mathematics and Natural Sciences, Universityof Warsaw, Stefana Banacha 2C, PL-02093, Warsaw, Poland § Faculty of Physics, University of Warsaw, Pasteur Str. 5, PL-02093 Warsaw, Poland a r X i v : . [ q -f i n . GN ] J un Introduction
New technologies have a tremendous impact on our economy. Ongoing globalizationopened a new space for competition between firms all over the world, and it fuelsthe race for the most innovative technologies. Nowadays, the most technologicallyadvanced firm is often the winner. The new technologies change how particular firmsoperate and perform, so it is interesting to study how technology can influence themarket as a whole. This impact can not be underestimated, and it is no surprise thatphysicists are also interested in this many-body problem. A non-linear statisticalphysics simulated model for technological growth was recently proposed by Ausloos,Clippe, and P¸ekalski (ACP model) [2] and next extended by Cichy [3] (Ci-model).Our work is directly inspired by Ci-model. It describes the influence of technologydiffusion on market growth dynamics. The central assumption is that the companies’survival depends only on their technology level. It might be a simplistic assumption;nonetheless, the results agree with the empirical data [3]. Therefore, we also makethis assumption. However, we expand the model to make it more general, versatile,and realistic by taking into account the interventionism.The companies operate in certain countries, and these countries’ politics influencethe way those firms operate. The government and its policy can change the firms’behavior, and those changes should be visible on the aggregate level as well. Wepropose a model that expands the existing technological growth model [3] to allowfor modeling the influence of government intervention on company market growth.We do so by using a single parameter 0 ≤ q ≤
1, which is the probability of thegovernment intervention in case of a firm’s incoming bankruptcy. In practice, theintervention can be realized by government stimuli such as, for example, subsidies,grants, tax reliefs, taking over the company’s majority stake, and ultimately even bynationalizing the company. We also consider how the influence of this interventiondiffers when the government targets only specific segments of the company market.It should be emphasized that the problem of state interventionism in the freemarket of companies is still at an early stage, although this problem is as old as thefree market [1, 5, 6].
We define the model as follows. In the beginning, a two-dimensional rectangularlattice of size L x · L y is created ( L x = L y = 10 in our case for simplicity). It is thenoccupied with pairs of numbers that represent the states of firms in the market.Two numbers describe each firm (e.g., the i th): (i) its market share ω i ≥ A i ≥ < c ≤
1, which means that c percent of the lattice sites are occupied with firmsat the beginning of the simulation. Other lattice sites are empty. For example, wechose c = 0 . c > .
5) as it is more promising than thedilute case ( c ≤ .
5) in respect to a possible dynamical phase transition.The market shares of all the companies have to sum up to 1 at any moment2ccording to the normalization condition, (cid:88) j ω j ( t ) = 1 , for any time t. (1)Initially all of the companies have equal shares ω i (0) = 1 /N (0), where N ( t ) is thenumber of firms at a given time (Monte Carlo step/site defined further in the text) t . In every time-step, the system is characterized by some average technology levelweighted by companies’ shares, (cid:104) A ( t ) (cid:105) = N ( t ) (cid:88) j =1 ω j A j ( t ) , (2)with the initial condition, e.g. (cid:104) A (0) (cid:105) ≈ .
5. This seems to be optimal in relationto the initial condition of world frontier dynamics given by Eq. (3) below.As in paper [3], the companies in the market can benefit from copying the worldfrontier whose technology is described by F ( t ) = e σt , (3)where σ is the parameter measuring the world technological progress rate. In thismodel, the growth of the world’s technological advancement is defined by Moore’slaw of exponential growth [7]. In our model we assume (as the most general case)that initially (cid:104) A ( t = 0) (cid:105) < F ( t = 0). We found a particularly interesting phaseappearing at the transition time t c , which we define as the first time-step for whichthe inequality (cid:104) A ( t ) (cid:105) > F ( t = 0) is fulfilled. We find t c numerically by calculating (cid:104) A ( t ) (cid:105) averaged additionally over time-dependent statistical ensemble of simulations(or replics of system). We show how the value of t c depends on the probability ofgovernment intervention q . The changes in the market evolution that come rightafter t c are an essential aspect of our model that has both theoretical and practicalmeaning.We note that the model parameters such as the current number of companiesoperating on the market ( N ( t )), the shares of individual companies in the market( ω j ) , j = 1 , , . . . , N ( t ), the world technological frontier progress rate (e.g., ofthe European Union) ( σ ), and even the likelihood of mergers of companies ( b ) canbe obtained from empirical data. The analogue of inverse market temperature ( s ),(auxilliary) concentration ( c ), and the minimal number of companies needed for themarket to work ( N min ) are free parameters of the model that can be obtained bymatching the relative level of technology ( (cid:104) A ( t ) (cid:105) /F ( t )) with empirical data. Letus add that the average level of market technology (cid:104) A ( t ) (cid:105) , as well as the currenttechnology level of the world leader ( F ( t )), can be measured separately (although itis complicated because it depends on the definition of technology level) [4]. As onecan see, our model is prepared both for the analysis of empirical data and extensionand generalization – it is a fully open model. In this paper, we extend the Ci-model [3] substantially. This extension is importantbecause it takes into account government interventionism supporting failing compa-nies. This interventionism is described in the model by the probability 0 ≤ q ≤ t MCS ) in which one cycle of the algorithm iscarried out for a selected, single company. The second scale is a Monte Carlo stepper lattice site (MCS/site or time step t ). We define it as such a number of MCSs,which is equal to the number of sites of the substrate lattice.Our algorithm is as follows:1. Randomly pick a single company from N ( t ) already existing firms by using auniform distribution. Let it have index i .2. Calculate the probability of the firm’s survival p i ( t MCS ) (defined by Eq. (4)).3. Compare value p i ( t MCS ) with a random number from a uniform distribution r ∈ (0 , r > p i ( t MCS ) the firm bankrupts and disappears from the sys-tem leaving its site empty. The shares of the picked firm are equally distributedamong all the other firms in the market in such a way that the normalizationcondition (1) holds. Compared to the original model we modified this step byincluding government intervention, modeled by the intervention parameter q .In this Monte Carlo step, when a firm should bankrupt because r > p i ( t MCS ),another random number q rnd ∈ (0 ,
1) is generated and compared with the pa-rameter q . If q rnd ≤ q the firm is saved by the government and survives at thisstep despite the fact that r > p i ( t MCS ). The algorithm goes straight to item7. If q rnd > q the firm bankrupts anyway. Thus, the parameter q describesthe probability that the government will intervene and save the firm (withprobability (1 − p i ( t MCS )) q ) at risk from bankruptcy.4. If r ≤ p i ( t MCS ) the firm survives and gets an opportunity to be active. Itcan move to one of the four randomly chosen neighboring sites. If the chosensite is unoccupied then it does not move. However, it interacts with the firmin that chosen site, in a way described in item 6 below.5. If there was an empty site and the firm moved there, the algorithm checks if ithas any neighboring firms in the nearest and next-nearest lattice site of its newlocation. If there are no such firms, then the firm’s technology grows accordingto formula A i ( t MCS + 1) = A i ( t MCS ) + r ( F ( t MCS ) − A i ( t MCS )), where r ∈ (0 ,
1) is a random number. This growth corresponds to the external technologydiffusion since the company copies, although imperfectly, the technology ofthe world frontier. Of course, if the selected neighboring place was alreadyoccupied, the company remains in its site.6. There are two mechanisms of inner technology diffusion, merging and creatingnew firms – spin-offs. If the i -th company found, after moving to a new latticesite, some randomly chosen neighboring firm j , then with probability b , thefirm i merges with the firm j . The firm j disappears from the system andthe technology of the i -th firm changes according to relation A i ( t MCS + 1) =max( A i ( t MCS ) , A j ( t MCS )). The i -th firm also acquires the shares of the mergedfirm, so ω i = ω i + ω j . With probability 1 − b , firms i and j create a spin-off.In this case, none of the firms disappear from the system. A position k forthe spin-off is chosen randomly out of the eight neighboring sites of the i -thfirm. The spin-off appears, only if the picked site k is unoccupied. The spin-off’s technology level is A k ( t MCS + 1) = max ( A i ( t MCS ) , A j ( t MCS )) and the4hares are ω k = ω s ( ω i + ω j ), where ω s ∈ (0 , i decrease by product ω i ω s and thecompany j by ω j ω s . This step corresponds to the technology diffusion withinthe companies’ market.7. The algorithm returns to point 1. until all the N ( t ) firms have been cho-sen which ends this Monte Carlo step/site. Next, the algoritm goes to thesubsequent Monte Carlo step/site.In the case of a company’s bankruptcy, as described in item 3, the shares of thecompany are distributed equally between other firms in the system. We chose thesame way of shares distribution as used in previous model [3]. This way of distribu-tion allows for a straightforward comparison of our results with the correspondingin the previous work. It illustrates the role of the intervention parameter, whichwe introduce into the model. We also assume that after a company bankrupts, theother companies do not perform any additional actions. Their increase in shares isa result of the disappearance of one of the firms from the market and not a resultof competing for the shares. Other ways of shares redistribution are also possi-ble, for example, ones in which the freed shares are obtained by other companiesproportionally to their present shares (preferential selection rule).It is also worth realizing that random numbers r and r are parameterizing therandom risk component of investing in innovation by a company.Probability of a company’s survival is calculated according to the formula, p i ( t MCS ) = e − sG if G > , (cid:104) A ( t MCS ) (cid:105) <
11 if
G < , (cid:104) A ( t MCS ) (cid:105) < e − sH if H > , (cid:104) A ( t MCS ) (cid:105) ≥
11 if
H < , (cid:104) A ( t MCS ) (cid:105) ≥ , (4)where G = (cid:104) A ( t MCS ) (cid:105) F ( t ) − A i ( t MCS ) and H = F ( t ) − A i ( t MCS ).Eq. (4) divides the technological development of a country (or companies’ mar-ket) into two phases. The first phase for (cid:104) A ( t ) (cid:105) < F ( t = 0) = 1 and the secondphase for (cid:104) A ( t ) (cid:105) ≥ F ( t = 0) = 1. The first phase corresponds to the less technologi-cally advanced countries (or companies’ markets). The second phase corresponds tocountries (or companies’ markets) that are more developed and have a higher tech-nology level. The s parameter controls the market vulnerability to technologicalbackwardness and thus susceptibility to bankruptcy. If this parameter has a smallervalue, then this vulnerability is smaller and vice versa.We chose, for example, the same parameters for our simulations as used in paper[3]. Those are: σ = 0 . , s = 1 , b = 0 . , N min = 10 , ω s = 0 .
1. The minimumnumber of companies N min necessary for the market survival (i.e., ensure the du-ration of the simulation) should be calibrated to empirical data. In principle, thischoice is optional and the obvious condition N min ≤ L x · L y = 100 must be met.When the number of firms in the system equals N min at time t MCS , then a randomlypicked firm i does not face the danger of bankruptcy. It means that items 2 – 3 ofthe algorithm are omitted and the firm goes directly from item 1 to 4.In our program, the shares of every company are written in a double-precisionfloating-point format (double). However, it is not an exact representation. Toensure the normalization of market shares with satisfactory accuracy, we additionallyintroduce a dynamic correction of these shares in each Monte Carlo step per site.It ensures that the normalization condition is met with controlled accuracy (in ourcase, not exceeding 1%). 5 Results and discussion
Figure 1 shows the results for the case of no government intervention ( q = 0) that is,for the free companies market. Three basic quantities are measured at the beginningof every Monte Carlo step per site t : (i) the current number of firms in the system N ( t ), (ii) the weighted average technology of existing firms (cid:104) A ( t ) (cid:105) , and (iii) theaverage to frontier technology ratio (cid:104) A ( t ) (cid:105) /F ( t ). The results shown in Fig. 1 arethe reference situation for other cases where interventionism is present (i.e., for q > q = 0).The three plots show the values of the current number of firms N ( t ) (panel (a)), theaverage technology (cid:104) A ( t ) (cid:105) (panel (b)) and the average to frontier technology ratio (cid:104) A ( t ) (cid:105) /F ( t ) (panel (c)) as functions of time t . The vertical straight line marks thetime t c at which (cid:104) A ( t ) (cid:105) ≥ F ( t = 0) = 1 for the first time. The average values over400 simulations (or replics of the system) are shown with the black curve and the ± SD over the simulations is marked as the grey band.In this model, the evolution of the companies’ market goes through three stages[3]. For the case of free companies’ market, the firms with the lowest technology levelare eliminated in about 50 time steps (the first stage), and the average technologyincreases as a result. In the second stage, which lasts for about another 150 steps,the technological advancement of the market comes mostly from internal technologydiffusion, namely from spin-offs and merges. In the last (third) stage (that lastsuntil the end of the simulation), the technology grows exponentially, benefiting fromexternal diffusion – getting the technology from the world frontier. Apparently, inthe third plot of Figure 1, (cid:104) A ( t ) (cid:105) /F ( t ) value is decaying slowly to a stable level afterreaching its maximum around MCS/site t = 220. The relative average (cid:104) A ( t ) (cid:105) /F ( t )reaches a plateau when the number of firms N ( t ) reaches its plateau. Both plateausare determined by parameter N min , which we set, for example, equal to 10. In thisthird stage, when the number of remaining firms is already small, item 5 of thealgorithm is the primary source of technology growth. Therefore, as N ( t ) decays,so does the (cid:104) A ( t ) (cid:105) /F ( t ), since the pool of firms that can copy the leader shrinks.Indeed, all of those stages are well seen in Fig. 1.In Secs. 3.2 – 3.5 we investigate four significant cases of interventionism. Theegalitarian in which all the companies have access to the government’s aid, and threeother cases in which only the companies with certain technology level can receivesupport. In the egalitarian case, any company at risk of failure can be chosen6o receive another chance thanks to the government intervention and possibly besaved as described in point 3 of the algorithm. In the other three non-egalitariancases, the government chooses to support only companies with low, medium, or hightechnology levels. A given company is qualified for one of these three cases whenits technology is below one standard deviation σ g from the mean technology in thesystem, in between ± σ g or above one σ g , respectively. We define σ g as: σ g ( t ) = (cid:115) (cid:80) N ( t ) i =1 ( A i ( t ) − (cid:104) A ( t ) (cid:105) ) N ( t ) . (5)Several values of q for all of the cases were examined. However, only results for a fewcharacteristic q values are selected in this work to portray changes in the dynamicsas q increases within the wide range 0 . ≤ q ≤ . Figure 2 presents some of the results for the egalitarian intervention case. First ofall, as the probability of government intervention q grows, the first stage lasts longer.In the egalitarian case, any company can be a beneficiary; in particular, a companywith a low technology level. Therefore it takes more time for those companies todisappear from the system. This makes the initial growth of the average technologylevel slower. This can be seen in Fig. 2 when comparing the shape of (cid:104) A ( t ) (cid:105) /F ( t )in the first 100 steps for different values of q . For sufficiently high q , the average tofrontier technology ratio is dipping instead of growing since the frontier technology F ( t ) grows much faster (exponentially) than (cid:104) A ( t ) (cid:105) .The most surprising results are for the very high intervention probability q =0 .
99. From Fig. 2 we see that when the system enters the regime with (cid:104) A ( t ) (cid:105) ≥ t = 600, with higher q , the market has,paradoxically, a lower average technology compared to the situations with lowerintervention probabilities q . For the case in which the government supports only the firms with technology overone standard deviation ( SD ) above the average, there are no visible differencesfrom the q = 0 case shown in Fig. 1. This type of intervention does not influencethe market significantly because the firms with high technology are already notlikely to go bankrupt as follows from Eq. (4). Hence, there is a negligible numberof government interventions involved in this case. For this reason, we have notvisualized the results in the form of plots. When the government supports only the firms with low technology level, then thefirst stage, when typically low technology firms are usually eliminated, is prolonged.It is similar to the egalitarian intervention case. However, in contrast to the egalitar-ian intervention case, once those protected firms are eliminated, the growth continuesundisturbed. That is, the ratio (cid:104) A ( t ) (cid:105) /F ( t ) is almost unaffected for the third stage.7igure 2: Selected results for the egalitarian intervention case. Three columns showthe values of the number of firms N ( t ) (panels (a),(d),(g) in the first column), theaverage technology (cid:104) A ( t ) (cid:105) (panels (b),(e),(h) in the second column) and, the averageto frontier technology ratio (cid:104) A ( t ) (cid:105) /F ( t ) (panels (c),(f),(i) in the third column) asfunctions of time. The results shown are for different values of the interventionprobability q , with q = 0 . q = 0 . q = 0 .
99 inthe third row. The vertical straight line marks the time t c at which (cid:104) A ( t ) (cid:105) ≥ F ( t =0) = 1 for the first time. The average values over 400 simulations are shown withthe black line and the ± N ( t ) (panels (a),(d),(g) in the firstcolumn), (ii) the average technology (cid:104) A ( t ) (cid:105) (panels (b),(e),(h) in the second col-umn), and (iii) the average relative to frontier technology ratio (cid:104) A ( t ) (cid:105) /F ( t ) (panels(c),(f),(i) in the third column) as a function of time. The results shown are for dif-ferent values of the intervention probability q , with q = 0 . q = 0 . q = 0 .
99 in the third row. The vertical straight line marksthe time t c at which (cid:104) A ( t ) (cid:105) ≥ F ( t = 0) = 1 for the first time. We show the aver-age values over 400 simulations with the black line together with the band ± SD marked by the grey color. 9oreover, Fig. 3 shows that for about 100 steps, the number of firms in thesystem and the average technology to frontier ratio oscillate. After the weaker firmsdisappear, the dynamic is very similar to that shown in Fig. 1. The government’s aid towards the firms with the medium technology level, namelybetween ± SD , can have a visible impact on the growth dynamics of the market.Figure 4 shows that high intervention probability, in this case, destabilizes the mar-ket growth in the later stage. This is due to huge fluctuations expressed by the veryhigh SD value. The first stage lasting about 50 steps is undisturbed and is the sameas the no intervention case in Figure 1. In this stage, mostly the weaker firms aregoing bankrupt as the government rarely intervenes. In the second and third phases,the dynamic is similar to the one with random intervention shown in Figure 2. Thisshould be expected since the low technology firms have already disappeared, and theintervention in the high segment does not influence the dynamic. Therefore, it is theintervention in the medium segment that can potentially have the most significantimpact on the growth dynamic in the long term. Presumably, one of the most interesting results is a rapid increase of the quantity (cid:104) A ( t ) (cid:105) /F ( t ) vs. time t (in MCS/site) for q = 0 .
99, as shown in Figs. 2 and 4. Afterthe system reaches the range (cid:104) A ( t ) (cid:105) ≥
1, the formula for the survival probabilitychanges according to Eq. (4) and the system enters a new (last) stage. That is, thesurvival probability goes from the definition given by the first and third lines in Eq.(4) to the second and fourth lines. Hence, the average technology grows rapidly inan unstable manner in the q = 0 .
99 case, as its large fluctuations are observed herein(i.e., the large standard deviation SD ). This sudden change to a highly fluctuatingdynamic of (cid:104) A ( t ) (cid:105) /F ( t ) requires an explanation, which we provide below. However,the question why the dynamic switches to a rapid growth only after the technology (cid:104) A ( t ) (cid:105) ≥ q , since the intervention is very likely at any time.If the concentration of companies is greater than the minimum concentration(equals N min L x · L y ), then instead of item 5 of the algorithm, the less effective item6 of the algorithm works. It results in companies’ technology growing signifi-cantly slower than F ( t ) or almost in technological stagnation. As a result thequantity (cid:104) A ( t ) (cid:105) /F ( t ) decreases, since F ( t ) grows (exponentially) according toEq. (3).(ii) Near the t = t c threshold (when (cid:104) A i ( t ) (cid:105) > q = 0 . (cid:104) A i ( t ) (cid:105) > N (panels (a),(d),(g) in the firstcolumn), the average technology (cid:104) A ( t ) (cid:105) (panels (b),(e),(h) in the second column)and the average to Frontier technology ratio (cid:104) A ( t ) (cid:105) /F ( t ) (panels (c),(f),(i) in thethird column) as functions of time. The results shown are for different values of theintervention probability q , with q = 0 . q = 0 . q = 0 .
99 in the third row. The vertical straight line marks the time t c at which (cid:104) A ( t ) (cid:105) ≥ F ( t = 0) = 1 for the first time. The average values over 400 simulationsare shown with the black line and the ± SD over the simulations is represented asthe grey area. 11ompany survival p i ( t ) is given, in general, by the third and fourth lines inEq. (4). In principle, the inequality A i ( t ) > F ( t ) never fulfills, so only thethird line works effectively. Since the concentration of companies is low, theexternal technology diffusion (defined in item 5 of the algorithm) becomes apossibility for the firms to increase their technology level. The meeting oftwo companies (located in neighboring lattice sites) is improbable, causing defacto disabling of item 6. The relative mean value (cid:104) A ( t ) (cid:105) /F ( t ) achieves theplateau. It happens when the increase of mean value (cid:104) A ( t ) (cid:105) is (to a goodapproximation) in a hundred percent caused by a global (external) frontier.We can conclude that the dominant process for the case (cid:104) A ( t MCS ) (cid:105) > (cid:104) A ( t MCS ) (cid:105) and next to the plateau of its relative value.Moreover, we investigated the specific time t c for the unmodified algorithm atwhich the transition ( (cid:104) A ( t ) (cid:105) ≥
1) occurred and depicted it in Fig. 5. The resultobtained is very characteristic because it shows that the level of market technologywill never exceed the particular threshold (cid:104) A ( t MCS ) (cid:105) = 1 as the level of interventiontends to 100%.Figure 5: Specific time t c at which (cid:104) A ( t ) (cid:105) ≥ F ( t = 0) = 1 for the first time, asa function of the probability of the government intervention q . The results wereaveraged over 400 simulations (or replicas) in this case. Despite the increasing helpof the government parametrized by q , the time needed for the market to catch upto the initial world frontier technology level rapidly gets longer.Figure 5 shows that as q grows, it takes the market more time to reach the hightechnology phase in which (cid:104) A ( t ) (cid:105) ≥
1. When q approaches 1, t c goes to infinity, i.e.,the market will never reach the high technology phase.When q = 1, the firms never bankrupt (cf. item 3). They can only disappearvia merging with neighboring firms. Besides, new firms are created in the form ofspin-offs (cf. item 6). To further investigate the source of the unstable growth of the (cid:104) A ( t ) (cid:105) /F ( t ) value,we modified the item 3 of the algorithm. The modification is as follows: after theintervention, the firm can still act, which means the algorithm goes to item 5 instead12igure 6: Average technology to globalfrontier ratio for q = 0 .
99. The solidcurve is the result when the firms cannot move after they were supported bythe government. The dashed line con-cerns the case when firms can moveand act after the intervention. Av-eraged over 400 simulations (or repli-cas) is sufficient herein. The verticalstraight line marks the time t c at which (cid:104) A ( t ) (cid:105) ≥ F ( t = 0) = 1 for the firsttime. Figure 7: Number of firms N ( t ) for q = 0 .
99. The case when the firmscan move and act after the intervention.The results of this modified algorithmare averaged over 400 simulations (orreplicas).of 7. Hence, the phase with unstable technology growth disappears , which we showin Fig. 6 by the dashed curve. We emphasize that both algorithms can describe thereal situation. It is because there may be companies that, after the intervention,”rest on their laurels” (unmodified algorithm) as well as others that invest in newtechnologies (the modified version of the algorithm).The result obtained by the modified algorithm we present in Fig. 7. We showthat the number of firms in the system is on a very high, stable level throughout theentire simulation. It is because new spin-offs are created more often than companiesdisappearing through merging or bankruptcy. Therefore, the firms in the marketcan rarely ever subject an external technology diffusion, which happens if theyhave no neighbors. The external diffusion is the way that allows for the fastestincrease in technology in the long times. However, with large firm concentration, itis improbable. In the modified case, we observe that the system never enters a stageof fast (cid:104) A ( t ) (cid:105) /F ( t ) growth, which is shown by the dashed curve in Fig. 6. In our work, we considered two characteristic variants of the model of governmentinterventionism in the companies’ market. We describe interventionism by one pa-rameter 0 ≤ q ≤ More precisely, t c is much larger (longer than 2000 MCS/site) in this case. q .The value of q = 0 indicates the absence of such interventionism, and the value of q = 1 indicates the certainty of interventionism. Notably, the government inter-venes with probability q if the company is threatened with bankruptcy, i.e., whenthe probability of bankruptcy is greater than zero.Both model variants differ significantly in the behavior of companies followinggovernment intervention, although algorithms differ a little. In the first variant,after the intervention, the company is passive. In a given Monte Carlo step, itstechnological level remains unchanged. However, in the second (modified) variant,the firm is active, i.e., it can increase its technology level in the current Monte Carlostep.In both model variants, only three different growth channels of the mean tech-nology level of the companies’ market exist. They are determined by items 5 and6 of the algorithm (see Sec. 2.2 for details). These channels have a well-definedprobability of appearing.We show that government intervention leaves its mark on the growth dynamicsof the company market. We found that for most of the values of q , governmentintervention does not influence the market significantly. A significant impact ofgovernment interventionism takes place when q is close to at least 0.9.When the aid is given randomly, and the government does not distinguish firmsbased on their technology, it can have a disruptive effect on market growth. Highintervention probability means the companies do not have to compete anymorebecause the government will almost always save companies from going bankrupt.The most drastic effects of the strong intervention are visible when one comparesthe value of the average to the frontier technology ratio (cid:104) A ( t ) (cid:105) /F ( t ) at t = 600 fordifferent q . With high q , (cid:104) A ( t ) (cid:105) /F ( t ) is volatile, and with asymptotic times its valueis around 0.5, compared to the case with q = 0 when it is close to 1. It meansthat the country with strong government intervention might never catch up withcountries with lower intervention probability.We also found that the volatile (cid:104) A ( t ) (cid:105) /F ( t ) growth at long times disappearswhen the firms are allowed to act right after being saved by the government.We are aware that our model should also include the possibility of raising thetechnological level of companies through government interventionism. The posi-tive effect of interventionism on technological expansion was observed in a studycomparing Hong Kong and Singapore [8]. However, at the moment, none of thestudied variants of the model supply such a possibility. We plan to investigate thispotentially beneficial effect soon, as well as further extensions of the model. Forexample, we could add a budget variable to describe the firms more realistically andallow them to purchase assets from other companies to improve their technologyand increase their market shares gradually. We thank Professor Marcel Ausloos for an interesting discussion during the 10thSymposium FENS 2019 in NCBJ Otwock – Swierk, Poland.14 eferences [1] Stephen K Aikins. Political economy of government intervention in thefree market system.
Administrative Theory & Praxis , 31(3):403–408, 2009.https://doi.org/10.2753/ATP1084-1806310309.[2] Marcel Ausloos, Paulette Clippe, and Andrzej Pekalski. Model of macroe-conomic evolution in stable regionally dependent economic fields.
Phys-ica A: Statistical Mechanics and its Applications , 337(1-2):269–287, 2004.https://doi.org/10.1016/j.physa.2004.01.029.[3] K Cichy. Microeconomic evolution model with technology diffusion.
Acta PhysicaPolonica A , 121(2B), 2012. doi: 10.12693/APhysPolA.121.B-16.[4] Krzysztof Cichy. Human capital and technological progress as the de-terminants of economic growth.
National Bank of Poland Working Pa-per , (60), 2009. Available at SSRN: https://ssrn.com/abstract=1752094 orhttp://dx.doi.org/10.2139/ssrn.1752094.[5] Mrinal Datta-Chaudhuri. Market failure and government failure.
Journal ofEconomic Perspectives , 4(3):25–39, 1990. DOI: 10.1257/jep.4.3.25.[6] Pablo Ruiz N´apoles et al. Macro policies for climate change: Free market orstate intervention?
World Social and Economic Review , 2014(3, 2014):90, 2014.[7] Robert R Schaller. Moore’s law: past, present and future.
IEEE spectrum ,34(6):52–59, 1997. doi: 10.1109/6.591665.[8] Jue Wang. Innovation and government intervention: A comparisonof singapore and hong kong.