 So good morning everyone. I welcome you to our last lecture of the course Collective Dynamics of Firms as you have Been informed by my email last night. So we have a special program today. I apologize for not Presenting you more new material, but I think If I look back on the whole course, you already learned a lot So maybe we should spend the time discussing the outline of the course today answering your questions and Comments that you may have Okay, I'd like to start with the With the evaluation Yes Okay, so you probably recall that everyone was kind enough to fill in This evaluation sheet and this is what we get back here. I would like to discuss this with you First to give you some feedback, but secondly because it's also required by the recto rate, right? So I mean I have to do it So the evaluation is anonymous first of all secondly the evaluation has a number of flaws or Drawbacks which will Lead to a complete new layout of this evaluation in the coming years This is the last time where we did this with the punch stamped sheets Alright, so there were six people of this course who Returned their evaluation sheets That's very nice, but you can already guess that there is a Bad statistics on that. That's the first thing the second thing is Every elective course is Evaluated better than a core course, right? Why is this because you have decided yourself to participate in this course, right? that's a difference to the core course at least for the for the M-tech students they have to participate in this core course Whereas in the elective course that was your free decision Consequently, and that's a psychological issue You usually Rate a course that you have chosen yourself better This is not to question your own decision. That's a psychological issue We know this from any other survey or Voluntarily work and so on that people give a better judgment about things if they voluntarily decide to do this As compared to they are paid for something, right? Okay, let us go through this. So this is So the number of m-tech students for the number of physics students three, I think except of From of warhan. There's no other physics student, right? What what are you what department are you in? m-tech, okay. No, there are alexander god. Okay, so I'm one person from Mars and then you see here most of them were Master students So I scrolled through this so there is the first block One two three are the rector's question and this is all yeah Yeah Yes, you're That's interesting. Yes, I would assume it's eight. Yes. It's eight I don't know maybe I was mislead by this but maybe not everyone has crossed His her agenda, right? Okay, you are right. Thanks a lot. Yeah, there are eight people Okay, this is how it looks like you see the first three questions of the answers are returned to the rector No, and if there are problems with the course then of course this will be discussed With the study delegate and the professor and in urgent case all there was a rector and the professor So this was all very positive. This is about the language. This is about the course material and this is about Commitment to good teaching if you have comments or questions and we can discuss it. So then we come to the second part The blue one which is arcs by m-tech. So well structured so people are not that optimistic about this I come to This in a moment when we look into The personal comments that's on another sheet, right? You could also write something Learning objectives. So this is also something which I would like to discuss afterwards Yeah, what were the learning objectives of this course because it seemed to be not so very clear But maybe I should do it right now. Let's go through this first So sufficient scientific details all the positive Real current issues That's positive Course material helped me to follow the lectures. So there, of course, I mean this means one person, right? So But here I would certainly like to know what this person may expect you maybe a Script or something like this. I Don't know exactly, but that would be of interest to us, right? Encourage active participation. That's also like in the normal range motivated Think independently instructor deployed media. Um, um, um fine Enthusiastic so here you see maybe A by model distribution, huh? There is a peak Of this why is There are a lack of enthusiasm on your side that could be another question number three, right? So and then let me go to the last slide here No This okay here practical work 5050 I think you usually appreciate it. So this refers to Pavlin All the positive and most of you will recommend it of course, so that's fine. I show you the second sheet first So this is there were there's place for comments, right someone two people in your particular case Wrote something here and we read this first and then we discuss The course is very interesting possible improvement will be to make the learning objective more clear This will all the refers to one of the questions here for example being more explicit about what We must focus on What is not important, okay all of the material is interesting But it's not possible to understand and remember everything at all the levels. That's certainly true So this was the second comment excellent slides were structured outlook further material very helpful. Okay, very good So let me go to this Question about the learning objective. I switch to this other one or do you need to? Read this again. No, certainly. No, but this is how we get it. Yeah in these pdf files. Let me Go to this So The learning objectives So what would what should you learn in this course according to my understanding? The most important thing is to get a Quantitative approach towards dynamics of firms We have Courses in the department and the mTech students know this Quite well Where the focus is on strategies of individual firms on how you position yourself in the market and all these important issues But these courses lack the big picture the overall picture, right? what do we see in terms of regular patterns if we look into a whole economy and That was the focus of this course So the first learning objective was to get this picture To understand that on the macroscopic level, which is the systemic level we see patterns emerging that you would not guess from looking into case studies, right? So there are regularities in the development of films, right? That's something extremely interesting That's the first learning objective. The second learning objective was how to quantify this And we did this in two different cuts the first one looking into data and the second one looking into models and And in the ideal case we were also able to Recover some of the stylized facts from The data analysis with the models that means at the end you should have Gotten skills both on the practical side in particular if you are confronted with data sets You know how to handle this, you know what our studio is you have no Fear to to use these things. I mean, of course you need to educate yourself. There is no question about this, but So this entry Per year. Yeah, that's hopefully gone And the second thing is you learn how to model these kind of things The models if you are a bit more General the models can be applied in various areas but the basic understanding of how to pose an agent-based model how to Extend agent-based models that was taken in this course here That's a learning objective from my side. Basically, it refers to Basic science data analysis and modeling with an emphasis on a Parent that you would not see and not know about if you would not have taken this course So that's my comment. Maybe you want to comment on this Learning objectives and what was clear and what was not clear Any question about this is a clear learning objective or not? I don't know I think If I'm correct in the first lecture, I was all the mentioning some of these things What this course is about and what this course is not about I remember that I have taken some of this Does this answer your question about the learning objective? If not, then it's a perfect time to Now tell your own opinion about Okay, so then the second issue Oh So yeah here as I said, okay I would like to know from this person what is the expectation actually because we did a lot of work to first of all Revises slide secondly provide additional hints in the notes Then provide you with additional material So there was where was this other? Here so see Instructor of roused my enthusiasm for the subject and motivated me, okay So you took the course, but you were not really enthusiastic about it. That's a message basically This first of all relates to expectations Usually students have expectations when they attend the course and these expectations are not met Why should they be enthusiastic about it, right? Yes, of course, but this is I mean if you compare the distribution, then you see okay, this this one is different therefore Okay, I would like to Maybe learn a bit more about this Someone who wants to comment on this What what I thought, okay, let's assume at some point in time you find out That's the content is of no interest to you. Yeah, you are the physicist and then You probably are not interested in in firms per se and it took you like Six to eight weeks to get to this point Or what you can still learn is how to analyze this data how to build an agent to miss model Where to put in economic assumptions as compared to basic dynamics assumptions About stochasticity and these kind of things so my Enthusiasm at some point would then come from the fact that I learned a lot here, right Different things and please also recall that there are The self-study talks which are partly yeah, I would say They're not demanding but they require your time and effort to spend that's not something you can do in like 15 minutes or so right and this is not about reading something as in other courses or Discussing with your neighbor about something. This is about practical skills So my personal hope is that everyone here Independent of the subject and the end to the other subject got a solid Feeling about stochastic processes. What's their role in certain agent based models and that's the idea of this Yes, please No one will be blamed for this I mean we need to understand it, right? Yeah, yeah Yes, that's okay That's a good idea. Why didn't I follow this suggestion earlier first thing in Every single course and m-tech you have a project, right? That's a problem So I did not on purpose wanted to create the same situation for you as a student again As in whatever supply chain management and all these kinds of things so and even professor So net told me the other day that he has switched to projects now Which had to do with the exam and the grading and these kind of things, right? I would wanted to avoid the situation I did not want to be the whatever 31st course where you also have to do a project and For me it was important that for example if you're if you're from different departments as This is the case here that you could follow the course independently. I Mean I'm not sure how it was this year, but last year there were I think two or so students Who were abroad and they took still the course they followed these video lectures They did the exercise and then they showed up in the summer for the exam Okay, that's all the possible. Therefore. I thought okay something that educates you on a Solitary basis and not in a teamwork that would be appropriate I'm also a bit skeptical about projects and when we started with this course we had projects and three times a Semester you had to submit this project and you did it in a group look Was never clear to me who did what? My assumption was that at the end the only one person who was able to treat some data did it and all the others Just signed in I wanted to avoid the situation No If you want to see some like practical applications of this then of course the chair has ample Talks to offer where you hand handle real data and applies us to real questions when you do a semester work Like one is doing or what Alex did before That's possible right, but I didn't want to make this the outline of the course That's my personal opinion right and by the way, I think that with with these weekly Exercises and with the self-study talks at the end personally you do a lot more, right? Just my personal impression then with a project that you have to hand in at the end Are there other comments? Yeah, yeah Yeah, it's not really enthusiastic No, yeah, I understand Yeah, I understand Okay for the comments question Okay, so these were I think the two point so then was there anything else? No, so then Let me come to this last question. What should I? Learn for the exam and what is not really necessary, right? So this was one of the comments So regarding the exam what we certainly will not do is to ask you for specific details of Deriving Solutions of equations or something like this Here I really make a difference between the physics department and the m-tech department This course is an offered in the m-tech department though that means for me It's very important that you understand the concept behind this That's the first thing that you are also able to argue about this. Let's take the Model of Simon and Ediri or something like this. What did they change compared to Deepra? Right, so that's something you should really understand Why did they do it? Second question third question is what changed in the outcome? Well These are the kind of things that you have to argue Well, of course, I would expect that you write down a dual Simon distribution as an equation. That's not a big deal from my perspective well, but But if you if someone one of you ever looked into this paper by Simon where he derived it Someone do it So that's a very mathematical paper right though once you touch it And you see okay, that's very heavy stuff This is not requested you should understand What has changed and what is the outcome the result in terms of the distribution and then of course you should argue over there? This is a better Result than the previous one compared to what you know, that's Then more about the argumentation of course I mean we agree that entry dynamics is very important No, what are we at the end when we look into this skewed distribution? Are we able to really distinguish the you will Simon distribution from a tail and a power law or some Part of the log normal distribution. Yeah, it's stretched part though. Is it really possible right? These are questions where you should think about That's the kind of What you should know and what you should not know right It is also appropriate that through that you recall some of the basic arguments in order to Tell what you have learned remember that for the Exam there are three different ingredients ingredient one is you had to pass the three online tests So one is yet to come The second thing is you had to participate in these self-study talks, which you did I assume and then of course you had to Follow this lecture right so that means we will Certainly ask question that are related to the self-study talks and this means that you should recall a bit of the practical things that you did right What's the command for the Karmogorov smirnoff test right for the one sided versus the two sided What's the difference between these two right so if you get an output like pump pump pump for D You know some numbers or is it now a confirmation of the Null hypothesis or a rejection of the null hypothesis you might should be able to understand some sort of code and to interpret these are Skills that you should have and That we certainly refer to in the exam So then I mean we can certainly discuss more about what what should we know for the for the Exam and what is Interesting, but not really needed. It's a bit difficult for me to give this an abstract world So of course the professor is always convinced that everything is important. What otherwise why should I spend my time on? But that's certainly not the case I Mean what is important on board not? There we had these questions at the end of each lecture which should guide you somehow to the important points If you want to find out what's important Then I would start with these questions and would double check am I able to answer these questions right As I said, I would also go and look into all the self-study tags I'm gonna understand. Okay. What what do did I learn from this? There are a few boxes like learning tasks and questions and These boxes you should basically check yeah with your own skills Okay, I think we should not follow further discussion on this general level it might be more appropriate if you ask your questions and then If needed I have all these slides here on the computer then we can Put it up and can discuss it together. You know, is it Yeah, or do you have further general comments on the course I? Maybe I finish with a general comment If you want to do your master's thesis without then you have to take the three courses that we offer and the third course is Economic Networks, right? Systems dynamics, which is a core course collective dynamics of first and economic networks That's maybe an important hint for you as well and I also explained I think some time before that we see this as These courses as Different levels of formalization and abstract thinking and economic network certainly is there The most abstract and demanding one, right? But it's also the one that is very close to research No, this is a bit more to basic knowledge and to skills and systems dynamics and complexity is about Dynamic thinking in general Okay, so then with this we start with specific questions Yeah, this is fine Yeah, so Alex you want to start Shall I do it like this I open it and then Yeah, let's see so ten yeah, so which slide This one Yes, it's selected and then the core breaks down correctly on the end on the x-axis first is a time right so That's a good question. We have two different times here in this model You know, maybe I should recall this there's a dynamics on two time scales So on one time scale which was plotted here. That's related to the end you modify the network And on the other time scale you let the notes relax right remember for every note There is a dynamic X I dot equal something right so and you first let The notes relax to the equilibrium state Which is on a short time scale and then on a larger time scale you modify the network After the note have relaxed then you modify the network the note relax again You modify the network the note relax again, so there are two times scales and one at which the notes written equilibrium state and the other one at which I Modified the network so what's plotted here though first of all This is the the number of modifications of the network if you want so and this is the average density of the link Yeah Mm-hmm. That's correct. So the M is related to the that's all the M is related to the Probability to Assign a link randomly, right? I think this was on the previous slide or somewhere now. These are the pictures Where do you see this? Yes, exactly exactly. So, okay, and it's constant and the P basically the P basically Various so and this is of course here what you see here is the average Density L of the links is of course related to the M if you choose a low P Then the network is quite sparse and you have a low density here So if you choose a higher P, then the network gets quite dense Right, so that's a so now the question is why are these crashes and recoveries more visible if you have a Smaller M that's a Yeah, yeah, but this is this is this is really the average Links that's the average number of links per node so, okay, and If I have a larger P Then of course I have a denser network Right, so therefore if I increase the M or the P then this L gets up So, okay. Why is the Crash larger for a sparser network. That's very clear I mean if you have a dense network and you can assume that we are part of one cycle But you may be all the part of another cycle. Remember there are many cycles co-existing in fact Once you are part of one of the cycles and your production or your innovation is boost But the others by input of the others Someone is removed from the system in new node and the system and is randomly linked to other nodes And that means it's also with a certain probability linked to you again Even that you are already part of the cycle, right? So that means you are then part of different cycle and therefore if you are part of different cycles Which occurs only for denser networks then of course a Crash in one of these cycles will not affect the system as much as if we have a sparse network No, that's understandable. If we have only a few links, then the system is very vulnerable. That's correct That's what you see here. What you also see is I mean, that's one message The other message is how long does it take before a cycle emerges? You see here like for for for this red curve. It's about 4,000 iterations So here it's only 1000 iteration and here it's only like 200 iterations Yes Okay So that's something I cannot answer because then we have to look into the set study again Mm-hmm Yeah, that's that's something then I have to recheck the self study tasks again Yeah, because I'm not so sure that you have defined the average L the same the same way as As this was done in the paper There could be a difference, right so but you understand why denser networks are A bit more robust against these crashes, you know, because you can be part of different cycles, hopefully Yeah, but so that's something we then have to find out I can also look into the paper and we find then how the L is defined, right? I think that's the issue Other questions. Yeah, I know this is the hard part now because to ask the question basically Means that you have gone through all of the lectures, which you certainly didn't do For today because the exam is only in August, right? I can understand But there might be things that you want to rediscuss also about the different topics What do we need to learn? From whatever the marks model or something like this Yeah, I can also Open the syllabus and when we go through this Please yeah 15 yes We choose the empty graph because in this model we were basically interested in what I call the past dependent process Okay The past dependent process is best shown if I have a sequence of decisions Where the next decision is based on the previous decision and so on and so on, right? That's the meaning of past depends if I start with a random network Then the past dependence is basically mixed with the randomness of the network I can create random log ins. Yeah, which I'm not past dependent in order to avoid this We started like this and this by the way the assumption for the economist is usually to start with an empty network because here we talk about strategic network formation and Strategic network formation means at any time the agents decide about a link, right? So whereas Alex if you'd start with a random network, then you have the idea Okay, there was a time where no one thought about creating links and then there was another time but they were very Curious about why they have the link, right? So that's an assumption that you can basically That you can hardly defend right because then you assume okay, there was no in previous times firms never cared about Well with whom they had a link therefore we can assume it's random That's a it's an issue of argumentation. What's the most important thing is here the the past dependent process Maybe I should open the syllabus and then we go through this and if you have specific questions for the content Then would be good if you ask them Where's the syllabus or the syllabus is on mender layer, right? Okay, I don't know where the outline here Syllables I don't see the latest version here, but let's basically that was something else So this was not the most recent one it was from last year, but basically it's kind of similar So questions or comments regarding the first part data and empirics. I Already answered the question should I know some are commands the answer is yes, okay Regarding the distributions you should basically know What kind of distributions we have discussed I Would assume that at least the structure the mathematical structure of these distributions can be written down So you know what the power law is you know what a normal distribution is and then once you know that then you also know What a log normal distribution is right? These are equations that we assume you should be able to write down So but more important are the stylized facts that we have tried to recover here It's about the Size dependence of the variants for example. This was one of the important things There were although there was one slide where we mentioned what we have not found in the data Namely that the mean value doesn't depend on the size classes That's something you should also look into right because it helps you a bit better understanding what what we what we did So then second part is Okay Regarding the maximum likelihood estimation I I do not assume that you can calculate this in the exam Even that we spend a lot of time doing this on the slides This was to give you a hint that it's doable right so what you should understand from the whole part is How is this related the maximum likely has the estimation to the testing of the Distribution right because these are two sides of the same problem, right? If you test a distribution then you assume that you know the sigma and the mu Right, but the maximum likelihood Estimation only tells you what's the sigma and what's the mu conditional on the distribution, right? That's a very important thing So then regarding the stochastic growth model. So there I think you should understand The difference between additive and Multiplicative noise and why was an assumption Like multiplicative noise chosen for the G-bride model, right? Why? What what was the reason behind this? Well, these are things that we should certainly That we have certainly discussed then regarding the entry and exit dynamics So there We discussed also some some stylized facts from the data This is a minor. Is this a major effect? That's something we have already shown and then What how does the distribution changes if we include for example entry dynamics as in the case of the Simon model, right? Regarding this competition and cooperation part Marks the marks model. I would for example expect that you are able to write down the Competition equation that's the result. It appears three times in the lecture, right? Always the same equation. That's something you should be able to write down Then you probably in the in the most simple form, but the alpha was the same, right? Then you should be able to understand How we got there there were these two processes the limited resource and the positive feedback, right? So I explained this three times in the same lecture No, you should understand the basics and then we gave an Economic meaning to the selection value, which was the cost price And here I would assume that you are able to explain the economic meaning of the cost price There were two slides just on the cost price how is the cost price written it depends on the exploitation rate and these on the organic Composition of capital and so on right that you understand this slide Shouldn't there's no derivation, but you should understand. What is the economic meaning of this? What's the story and how I as the entrepreneur? Or the capitalist can increase my profit. What should I do given that this is a selection? Okay, my suggestions. We just continue and then we close if there are no further questions, right? so Inequality distribution though, that's I think was a lecture that you were only Recovering yourself, I mean of the handout and last year's Video recording Are there particular questions or what's the genie coefficient? What's the Lawrence curve? Yeah What's the meaning of inequality basically? There was also the self-study tasks where you had looked into a growing loquat normal distribution, right and then you had to plot the Inequality And then I mean once you did this exercise yourself and you better understand what people discuss in the newspapers Yeah, that inequality has again increased this year, right? It's not a real surprise for you Once you understood the basic dynamics of this and I mean Then you can start thinking of what kind of processes do I need to decrease in equality? That's No, that's not the topic of the exam But that's a topic maybe for those people who complain about increasing inequality I would like to hear from them what they have in mind, right? Okay, so then adoption of behavior this was then About this polio processes There we discussed The simple polio process and there was a more advanced model by Brian Arthur Where you had this R and S agents and each of them had a preference to either iPhone A or iPhone B or something, right? So and then There is no need to Redo these equations That's not the important point But there was a graph as you recall which gave us an upper and a lower bound and once the trajectory has hit this Then the process was locked in that means it was not reversible After that point in time you will not see a community Switching back to some other gadget once they are locked in there, right? So that was the result of this model And I think you should understand this that's basically It's in Modification of the simple polio process, but even more important is the question that we then discuss afterwards what how realistic is this? Yeah for the m-tech students I mean that's the most important question Do we have to live with this or what can we do in order to to mitigate this situation, right? There were a few slides why the simple lock-in processes Wrong in some sense, right? That's something I recommend for you to look up for the exam as well that you can critically discuss about the Importance of lock-in effects Right because you as a company let's assume you are a company that then basically Yeah, you could close the books of that was it then yeah if this was a real economy Then you can basically go home, right because there was nothing you can do Well in fact you can do a lot you as a company and you should understand, okay? What are the additional dimensions that I can do or use or exploit, right? But some innovations are not considered there There's also the lifetime of the gadget or these kind of things is not considered there You can influence the lock-in effect before it actually locks in by modifications of Incentive schemes if you buy the iPhone then you get whatever a whole Apple computer plus the full software For free of those kind of things, right? Okay, yeah, that was basically it and number 12 as I said We stopped or we dropped this year, right? No, because we didn't include it in The course right now as I mentioned in my email. It's a bit more technical I'm a bit hesitant to just give you this slide without further explanation because I do not want to confuse you Then I would rather like to present this here and say well This is the difference to the previous adoption model So the difference by the way is not so much in the dynamics the difference is in the formalism That's more of interest for the physicists then we write what we would basically do for stochastic dynamics We will write down a master equation. We have transition rate and so on that's a better or the more Appropriate formalism to address this in a stochastic context. That's what you can learn from there Okay further questions Content wise The only thing we can say that's correct, that's correct. Yes. Yes Not really. Yeah, so the log norm of distribution would usually results in a Symmetric just Lowance curve. Yes, that's correct. So but It's really then depends on It really depends on Features of the distribution you cannot give a general Explanation for this By the way just for your information if you look into the Lorentz curve and you should notice that there is there are two axes one is the percentage of the firm that own a percentage of the Occupied have or are responsible for a particular Share of the sizes, right? So that's a normal scale We now talk about Lorentz curves that can be only seen on the logarithmic scale You may want to think about It means the Lorentz curve is so steep So steep that you do not see anything if you plug this on a normal That's something you can really what kind of economy is behind this That I that's the inequality is so huge that I cannot really see this in a normal scale Yeah, that's something that we did in our own research when we talked about ownership concentration This is now this can be only discussed on logarithmic scales Because everything is in this 0.1 percent range One percent of all firms own 99% of all revenue something like this, right? So that means your Lorentz curve looks like this You don't see anything in a normal scale This is for those who are afraid of inequality The real inequality if you go out and look in this is much much much Larger than you can plot in any Lorentz curve, right? That's a message of it. Okay Other questions Comments So if this is not the case, then thank you very much for your attention and for participating in the course and I hope that you can convince a few Students of mTech or maybe the physics department to attend the course next year one of the lessons I learned is that I will not Do this video recording again Which is by the way The mTech students know already the conclusion that my colleagues have drawn some years ago, right? Currently, I think I'm the only one This was for the for me the last time I appreciate more to have students in the lecture Rather than following these courses discourse at some other time Okay, so I wish you good luck with the exam Exam is in august as far as I was told and then you just come here There was no need to Have any whatever material with you. You know a pencil is enough No, and then you just answer these questions. So they are with ABCD There was no multiple choice question. You really have to go through the material and And you should write other in a way that we afterwards are able to read this some students lost Considerable number of points because we could not read what they were But they have written right. This is my personal advice to you Otherwise, I think if you really follow the course the exam is doable. This is not something That's beyond your expectations Okay, thank you very much and then I hope I see some of you maybe and some of the other courses