 First, I want to thank Kristoff Matthew and Katharina for accepting this paper into the program. It's really a fantastic conference. I mean, we have people talking about different aspects of tokenomics and blockchain, and also I'm looking forward to tomorrow's session where we are going to hear more from the practitioners. So this paper is really about platform, but we are not going to flesh out a lot of these details like two-sided market, for instance. What we are going to focus on, sorry, is more dynamic investment and financing model for the platform. So digital platform is playing an increasingly important role in our life. And increasingly, we see that payment innovation is very important. And what is recent is tokenomics. Basically, we see that digital platforms start to introduce tokens as the local currency on the platform. This is not something that we see in China, because the Chinese government is not allowing any private entity to issue money. But we do see a lot of other platforms start to issue their own fiat currency. It's not backed. So here we are not talking about tokens that are redeemable for goods and services from the platform. This is just the utility token, the set of transactions among the platform users. You can think about file calling as an example. You can think about basic attention token. Basically, the platforms we have in mind is an online market place where people can treat goods and services of a particular kind. Basically, the platform will serve a niche market. File calling is for transacting the digital space. And the basic attention calling is to buy people's attention. You download their browser, you see some advertisement, you get paid with tokens. And advertisers use the tokens to pay for the advertising space. So basically, what we have in mind is really an analogy between a token based platform and a country. A country can have a currency. A platform can have a currency. Like a country can issue currency to finance investment in infrastructure. For instance, a platform can also issue tokens to finance its development. In 2018, the total token-based financing is in a comparable magnitude with venture capital. But in 2019, we see quite a freeze of token-based financing. And this only begs the question, what really defines token-based financing? And what is special about bundling the usage of tokens as means of payment among users and as a finance instrument for the platforms? So basically, we can see that empirically, this is what we observe. Token are used to gather resources. They are paid to investors in exchange for their dollars. And then you can use dollars to buy all kinds of resources. Or you can just use tokens to buy resources directly. You can pay engineers, consultants with tokens. And the tokens enter into circulation gradually. So we do have a lot of papers focusing on ICO, where tokens enter into circulation once fall. But this is not what we're observing in reality. We see tokens are gradually paid to people who can contribute to the platform. And tokens are gradually paid to the funder entrepreneurs. So it's really a very dynamic process. And in this paper, we want to understand it. We want to understand from the platform owner's perspective, what is the optimal token supply policy? And what is the associated platform development, i.e. investment policy? And what are the potential inefficiencies? So we are going to basically build a model everything is a surrounding token. Users use tokens to settle transactions. And we are going to model in a very reduced form, following the money utility tradition. And of course, users will speculate on tokens, their expectation of future token price matters. This is about the token demand. And then you have the token supply determined by the platform owners, who basically have two considerations. If I issue more tokens, I can issue to myself. And then I can sell tokens in the secondary market for consumption groups. And then I can have a good time. That's my utility. Or I can issue new tokens to the potential resource contributors and improve the platform. And then basically, the dynamic program is going to maximize the present value of token platform owners' rewards that we can think about as a synergy. So here, you are also going to see something like a Laffer curve. You don't want to issue too many tokens to flood the market, reduce token price, i.e. reducing the token payout value for the owners. But on the other hand, you don't want to issue too little, because you want to compensate the owners. But at the same time, you want to issue tokens to gather resources for the platform's improvement. So this graph is basically the model. So if you do not remember any of the notations, I mean, the time is short, I'm going to go through this very fast anyway. Just remember this graph. So we try to capture all these elements indulgently in a coherent fashion. So we think about the model itself as sort of a conceptual contribution, because once we lay out a formal model, it makes really the discourse very clear. We can point our fingers and say, okay, this is what you are interested in, we are starting it, and this is what you are interested in, where we take as exogenous. So here we see the platforms can issue new tokens to the contributors and the contributors, they can just sell tokens in the secondary market for consumption boost. So that's how they get compensated. The platform owners can also issue new tokens to themselves as payouts. And also, of course, you have the automated token owner, the users, right? They hold tokens to settle a transaction and also they speculate. One thing that I want to emphasize is that we do allow the platform owners to reduce token supply. So they can use consumption boost to buy back tokens, reduce token supply, support token price, why they want to do that, because they are concerned about their continuation value, their franchise value. A lot of their value is derived from future token based payout. So they do not want the token supply to be too high, the token price to be too low, and they basically want to dynamically manage the token price a little bit through both issuance and token buyback. All right. So some basic questions we are after. The first one is that, well, if you issue a digital token, the marginal cost is zero, it is digital. If you want to issue, you issue. And then why the token price can be positive? Why don't you just issue an infinite amount of tokens and drive the token price to zero? If you think about tokens, they are very similar to durable goose. If you issue more, you increase the supply. Well, you can reverse it in the model, but we are going to assume there is a cost. Basically, it's a financing cost. You use consumption boost to buy back tokens. It's costly because you need to reduce external financing. So it's costly, reversible. Therefore, once you increase token supply, it's somewhat permanent. So that's why you think tokens and the durable goose, they have an analogy. But then from the caution hypothesis, we know that if the marginal production of these tokens is zero, then the equilibrium price, the only equilibrium price we can expect is zero. So why don't we see zero? So what we are going to show you is that, well, the franchise value really imposes a discipline against excessive issues. But where the franchise value comes from, it really comes from the dynamic development of the platform. It's getting better and better. So basically, the platform owners are very patient. They want to milk the users gradually and they want to wait when the future platform is more productive in the future. And then we are going to look into the value chain here. You have the users who derive value ultimately by holding tokens. And then you have the platform who can issue a token for development and payout. So where things go wrong in this value chain? So we are going to identify the potential inefficiency. We are going to introduce a concept called token over. And this is where we build that analogy between corporate finance and the tokenomics. And finally, there's the rule of blockchain technology. We have a conflict of interest between users and platforms as you will see. Naturally, there's a dynamic inconsistency. Like when you talk about fiscal policy and monetary policy, right? Basically, you have one big player facing a continuum of small players. There's dynamic inconsistency. We also see it here, right? You have a platform and then you have a lot of users. And then that's how blockchain can add value because you can use decentralized consensus to enable some commitment. All right, so I'm going to skip the literature review and dive directly into the model. So here we have a platform. Well, the platform is captured by this AT variable. Right now, you can just take it as a snapshot, okay? We just think about AT's current value and then think about how users can derive value from token holdings. As I said before, right? It's just a money utility. So the real balance of tokens, that is the KIT units of token, multiply the token price PT in terms of the numeric consumption goods. So XIT is the real balance of tokens. It goes into the flow utility of token holdings. And what else? There's also the user network effect, NT, that's the total number of users that go into the convenience yield, the flow utility of token holdings. And then you have the user heterogeneity captured by UI. Of course, users care about token appreciation. Individual users, they are atomic. So they take as given the equilibrium token price dynamics. Here the mu PT and sigma PT, they are all endogenous. We are going to solve it. But users take as given, right? So the users know that given KIT units of tokens, they hold, they are exposed to price fluctuation. If it's appreciation, they like it. If it's depreciation, it's a negative term. They don't like it. So we introduced the participation cost. That's five DT. And when we do that, that's how we pin down the user base. Because only the users with sufficiently high UI, they participate. And the participation threshold can be potentially time varying. And that is U low of RT. And then NT is the user base. GT is the distribution of UI, the cumulative distribution. Users basically want to maximize the net return from tokens, including convenience yield and also the expected price appreciation minus participation cost. And then eventually you are going to get the token demand, which is a linear UI that helps to do the aggregation. Some basic properties. If the users expect the token to appreciate over time, and then they want to hold them all tokens, that's a secondary inequality. If the platform is very good, AT is high. Of course, the users derive a high flow utility from holding tokens. You can think about this while the platform is really serving very important economic transactions. So the users want to hold these tokens to settle some transaction. And it's more convenient to hold tokens that hold US dollars. So that's where the convenience yield flow utility comes from. Why this is so, maybe if the platform settles transactions using token, and then you hold the dollars, you have to do the exchange, right? You have to sell dollars by the tokens, there might be some transaction costs. Or maybe token is just a programmable money, and they just have small functions. So you want to hold tokens. And maybe tokens can serve as collateral in a smart contracting setting. And that's why you want to hold tokens. So we're modeling it in a very reduced fall. But the general idea is that when the users expect token price to appreciate, they hold more. And when the platform is better, they hold more. So we can do the token market clearing, MTS, the total outstanding amount of tokens. And then basically once we have the market clearing condition, we immediately say that, okay, here we can characterize a Markov system, okay? Taking AT, the platform's productivity and MT, the total outstanding supply of tokens as the two state variables. And then this token market clearing condition basically gives us a differential equation for token price. And that's how we can solve the drift and diffusion, okay? Basically, all these slides summarize the user side. So now let me talk about how the state variables evolve over time. So first, the platform can become better. Okay, here's the growth rate of the productivity. It depends on the resources that you gather, that LT you will pay for with tokens. And then there's a productivity shock, okay? DHT is basically a normal random variable. Well, we can think about this as coming from entrepreneurs, the initial contribution to the platform, how the platform is designed, et cetera. We take that as exogenous. Why? Because we have a lot of papers that describe entrepreneurs' contribution, entrepreneurs' effort, moral hazard problem before the launching of the platform. This paper is about after the launching. It's about resources from decentralized contributors, not the entrepreneur, okay? So here we differentiate ourselves from the literature. So if you want to get LT, you better pay the contributors. We are not going to model the optimization of the contributors. We just assume that the contributors, they want F, LT, NT, this amount of goods. But you pay the contributors in tokens, right? So F divided by PT, that's how you gather units of tokens. And when you pay more tokens to the contributors, you know, you gather resources, but you also increase token supply. This tends to depress the token price. So now you can see the trade-off. DT is the cumulative tokens paid to the owner. So if we take the differential, right, as the instantaneous payoff, if the owners receive a payout, token supply increase, right? But the platform owners, they can burn tokens. They can buy tokens out of the circulation using consumption goods. And that is when small DT is negative. And that's how you reduce token supply. So LT and DT basically, these are two control variables of the platform. And that's how the platform's decisions can impact the evolution of state variables. The objective function here captures the payout. That's the first term here. And also it captures the external financing cost. If you want to buy back tokens, you need to raise external financing. Okay, there's a proportional cost kind. And the basic property of this value function is that the platform's value or the owner's value, to be more precise, is going to be lower if there are more tokens circulating. Why? Because this depress the token price. Remember, the payout that the platform owners get is in tokens, right? If the token price in numerous groups is lower, then the value for the platform owners is lower. So this is also the disciplinary factor that we talk about. When we see more token supply, you see lower value of the platform owners. So that's how they really resist against excessive token supply. And then when the platform is better, you see the platform owner's value is higher. Okay, so this slide is basically summarizing all the ingredients here. All the users side of the bells and whistles just give us a token market clearing condition that connect the state variables with the indulgence token price. And then all the platform side, you can think about that's how the token price involves driven by state variables and how the state variables MT and AT involved driven by the platform's decisions. Eventually, we have a homogeneity property. The ratio of token supply to platform productivity drives a lot of actions, especially token price. And then we have some results I want to talk about. So first, there is a strong analogy between durable goods and tokens. And we know that durable goods producers, they are always tempted to meet the residual demand, right? They face heterogeneous consumers, some value their goods more, some value their goods less, like UI in the model, right? Another problem is that because the customers expect the platform or the producer, the seller to decrease price over time to meet the residual demand, they will wait for the price to get lower and then they will buy. But here the residual demand has a marginal value of token equal to zero, right? That's when UI equal to zero. And the marginal cost of production for token is zero. So you can just issue tokens. So why do we see the token price is still positive while the quotient conjecture predicts zero? The key idea is that here the token demand is now stationary. If we see different formalizations of the quotient hypothesis, the demand for durable goods is always stationary. But here we see that AT grows geometrically through token financing investment, the LT, and that's where we see the token demand is going to be higher in the future, right? As a result, the platform owners, they are willing to wait to issue more tokens in the future, right, rather than right now, and therefore to keep the token supply in a controlled path and without depressing the token price too much. Okay, I'm going to skip the intuition on real option. But the basic idea is that the state variable, the productivity and adjusted token supply is basically bounded by two indulgence boundaries. On the right boundary, this one supply is too high, that's when you burn the tokens. You are willing to pay the financing cost in order to boost the franchise value. We see a lot of durable goods producers, they also burn their products, right? There's an analogy here. And if the token supply is low relative to AT, the productivity, that's when you pay the token dividend to the platform owners. All right, so here I want to see where the inefficiency comes from when we have this token based on financing. Well, here you have the investment paid by new tokens. If the investment successfully increased AT, well, this will increase users flow utility. So I see a question in the chat room. Okay, five minutes left. No problem. All right, so the question is, well, can the platform seize all the surplus from investment? And the answer is no, because users are heterogeneous. And we have one token price that appears on the market. So basically, only the marginal user, remember the you lower bar T, okay, the threshold guy, only this guy breaks human. Anybody with the UI higher than the threshold will keep a positive surplus. So, so far, we are considering making investment, AT go up, that's good for users, right? But we have shocks in the model. So what if there's a negative shock? Remember, you get LT, but then you need to multiply a normal random variable that's a productivity shock. And then you see whether the platform is going to be better or worse, right? So if there's a negative shock, then you see the state of variable empty increase instead of decrease because you see a smaller denominator. And then that's when you get closer to the token buyback boundary, the upper bound, right? But at the upper bound to brand tokens, all of circulation to reduce token supply, maintain kind of in the target range, right? That's what the platform owners want. There is external financing cost. So the downside is basically born totally by the platform owners. That is the external financing cost. But the upside is shared with the users. So of course, there's complete of interest, right? So in other words, this will translate into the platform's underinvestment. Because every time the platform decides whether I want to issue new tokens to make investment, this loop comes into their mind, okay? And then the platform owners will think, okay, I should just issue a little bit less and invest a little bit less. But here we have the dynamic inconsistency because exactly the platform owners would rather commit themselves to a little bit high investment rates because high investment rate means faster trajectory of AT growth. This means a higher value that users can derive from token holdings. This means stronger token demand. And this in turn means higher token price and higher value of payout to the platform owners through the token-based payout, right? However, this exact optimization is not going to be destroyed, exposed to the platform owners taking into consideration this issue, this loop here, and then they are going to negate on the commitment. This is a typical dynamic inconsistency. So here is how the blockchain can add value. So basically, you can write an investment rule like this. There's a constant growth rate of token supply, and this part of growth is all going to the investment. And then you can increase the exact value of the owners by quite a lot. I mean, I'm not going to take this number seriously. The whole model is about qualitative predictions, but we do characterize one channel where the blockchain can add value by enabling commitment. So the model basically tried to try to conceptualize a token-based ecosystem where a lot of actions are endogenous. And here we want to emphasize token. It's not just durable, good. You need to really think about the non-stationarity of demand and how this can induce a discipline against excessive token supply on the part of the platform owners. And then if we put on the head of corporate finance guy, and then we see that there is this particular type of token overhand. Whenever you invest, the supply is going to be shared with the token users, and that's why you see on the investment. And even if the token market is perfect in liquid, here we have a perfect in liquid token market. There's no moral hazard. There's no friction other than the external financing cost for token buyback. But that is enough to get this token overhand. And the conflict of interest as a result can be mitigated by the blockchain if the platform can commit to an investment policy. Exactly. Thanks.