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# bitcoin inflation vs. time .

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Conference Paper
Full-text available
Under Bitcoin protocol and payment scheme, anyone can send any amount of bitcoins that he owns to anywhere in the world via internet, near instantly for near zero fees. While the popular crypto-currency enjoys low transaction fees, a feature that is highly promoted and is working fine for the current state of the Bitcoin ecosystem, we argue that in...

## Contexts in source publication

Context 1
... of all, the supply of new bitcoins is only through the block rewards for miners. There is a periodic halving in the block reward, resulting in a logarithmic supply of wealth, decreasing gradually over time as in monetary base, figure 1. The reason why a linear supply is not offered is to avoid inflation. ...
Context 2
... a logarithmic supply of the number of bitcoins in circulation as part of the design is the inflation to diminish shortly after the initial launch 9 . The relation of number of blocks issued at any time (in correlation with time) and the inflation of bitcoins is also illustrated in figure 1. As mentioned before, this inflation of supply is to be replaced by a deflation soon after a point when the accidentally lost bitcoins outnumber the newly minted ones. ...
Context 3
... in the block chain so that even if it is accomplished, the block chain does not really require a manual cleanup by the core developers. The attacker will be in control for a temporary period of time, and in that period, he can interfere with transactions in such a way that he can prevent them from gaining any confirmations and can perform a so-called double spend attack [11], but the attacker cannot reverse other users' transactions forever and cannot prevent transactions from being sent at all (they will show as 0/unconfirmed). Most importantly, the adversary cannot change specifications of the protocol, cannot create coins out of thin air, cannot send coins that never belonged to him and cannot steal somebody else’s coins. The aforementioned double spend attack is a type of counterfeit that is in analogy with that of physical currencies such as US dollar. It may be argued that a currency does not have to be perfect to be practical. US dollar actually has a serious counterfeit rate and many small merchants in the US do not accept 100$bills for that reason. But this does not stop the general public from using US dollar even outside of the mainland. Similarly, one may argue that an occasional double spend attack may not kill Bitcoin as it is in a loose analogy with counterfeit bills. However, such attacks should be prevented as much as possible and the way this works is the network having a large enough total hash rate and an incentive for miners to provide so. Actually, the reason why users of the system are encouraged to wait for enough many confirmations that are ideally proportional to the amount of BTC they are receiving is given as a precaution in [1] is the possibility of 51% attacks. The likelihood of a 51% attack is also highly related with centralization of mining pools, which is regar ded as ‘disturbing’, and ‘dangerous’ by the Bitcoin community. That is, in case of mining, pools are focus of attention as possible sources of attacks as briefly considered in [12]. We are ready to consider the problem 5 , Imposing a transaction fee is essentially tax revenue of the service provided by the miners. As more hash power that the miner pours in means a more secure network, it is reasonable that the reward of the miner is proportional to the hash power he contributes. However, how users should be charged is not as clear as how the wealth should be collected by the miners. Indeed, determining the right transaction fee as a policy and forcing it in the client software as a regulation is crucial for the future of Bitcoin and similar alternative crypto-currencies. The problem of determining the optimum transaction fees are interrelated with various surrounding aspects. Statistically speaking, the number of transactions per second (tps) of Bitcoin increases over time 6 , as well as the wealth carried by the transactions. That is, in the early days of Bitcoin, users usually experimented the protocol by smaller transactions, whereas today, the average value contained in a transaction is significantly higher. Although the idea that transaction fees should be proportional to the amount of bitcoins transferred would be quite disruptive among some bitcoin users, economically, this is plausible in the sense that the users transferring the largest amount of bitcoins are the individuals that have the most benefit of Bitcoin. This is obvious especially when one considers the daily transaction limits imposed by governments and banks. Such limits, varying by the monetary policy of the country that one lives in, are actually one of the reasons Bitcoin drives so much attention because Bitcoin allows one to simply exceed such limits. That is, there is no transfer limit on Bitcoin protocol imposed by any third party and this is one of the promoted features. It is not uncommon to see transactions in millions of US dollars 7 . On the other side, Bitcoin is currently promoted as the best transfer method for transactions carrying tiny amounts, often regarded as micro- transactions . This means that paying a certain fixed minimal fee (such as in magnitude of cents) for each transaction may hinder some possible future usage scenarios of Bitcoin, such as tipping online content providers (videos, forum answers etc.). Regarding this, there are discussions in the community that micro- transactions can be taken off the block chain into newly discussed structures called side- chains . However, more research on the topic seems to be required to determine how such a shift from the main block chain would function. Private exchange and online wallet companies may also help providing such a service 8 at the cost of centralization of the transactions. The transaction fees and bitcoin price are related as follows. First of all, the supply of new bitcoins is only through the block rewards for miners. There is a periodic halving in the block reward, resulting in a logarithmic supply of wealth, decreasing gradually over time as in monetary base, figure 1. The reason why a linear supply is not offered is to avoid inflation. As no central authority is present, there is no government to mint money. Although the network is still in a temporary low-inflation state, Bitcoin is eventually meant to be deflationary. Currently, there are about 12.5 million bitcoins in circulation as of 2014. In 2033, this number is expected to exceed 20 million and increase slightly each year thereafter until 2140. Such a logarithmic supply of the number of bitcoins in circulation as part of the design is the inflation to diminish shortly after the initial launch 9 . The relation of number of blocks issued at any time (in correlation with time) and the inflation of bitcoins is also illustrated in figure 1. As mentioned before, this inflation of supply is to be replaced by a deflation soon after a point when the accidentally lost bitcoins outnumber the newly minted ones. One may argue that the significant scarcity in the supply of bitcoins might not affect the incentive of miners as the lesser amounts of bitcoins rewarded carry higher and higher value in price as the price of bitcoin dramatically increases over time. In other words, to numerically exemplify, for the price to keep up with the incentive of miners, the tens of thousands of bitcoins produced each year after 2030 should have the same price with the millions of bitcoins produced each year now. However, this assumption cannot be correct. Although it is true that until now the price of a bitcoin has increased dramatically 10 , this cannot last forever as even the most optimistic prediction about continuation of price rice involves a slow down after half way as the number of potential users that may adopt Bitcoin in the globe is limited. Theoretically, the best case scenario about adoption of Bitcoin as a technology is the logistic growth as depicted in figure 2. The graph may arguably apply to both the price of a bitcoin and also the number of users of bitcoin. Actually, these two parameters are correlated as the price of bitcoin is determined by the demand and the limited supply. The increasing demand that emerges from an increasing number of users together with a limited supply naturally causes the price to rise. On the other hand, in financial terms, the limited supply over time and the eventual limit on the price of a bitcoin have a combined effect such that the marginal production cost of mining is going to increase dramatically, which must instead be set fairly constant over time. In the long run, the policy on transaction fees should be set so that enough many miners have incentive to run clients having a good enough combined hash power to protect the network. But on the other side of the coin, the fees that miners collect should not be any higher than sufficient in order not to discourage users from using Bitcoin as a means of transferring money. Miners with sufficient combined hash power are not the only requirement to secure the network. Another aspect is the number of full nodes, which have a similar level of importance. Full nodes are actually quite “smart” at running the network as they provide lookup of historic blocks, which is necessary for new nodes synchronizing, and they also validate blocks and transactions, and relay them. As the network right now is under trivial load, we do not exactly know how many full nodes are going to be needed in the future and this is one of the open question requiring further empirical studies. The number of full nodes in the globe dramatically decreases over time and end-users tend to switch to easy-to-run lightweight clients that are intended for personal usage instead of full nodes. However, the exchange and wallet services and other similar service providers will still have to run a full Bitcoin client, and the number of such services tends to increase over time and the indeed full nodes provided by these services only might suffice. We claim that the solution of setting the right transaction fee in the future is not trivial, and a fixed number (such as$0.41 per transaction) mentioned by a core developer of Bitcoin [13], as a study for cost per transaction, do not apply as a transaction fee right now as the block rewards are currently good enough to keep a sufficient number of miners provide a good amount of hash power to secure the network. The transaction fees collected as donations from each block is a mere fraction of the block reward 11 and this is good enough. Currently, Bitcoin nodes have the option to exclude transactions that do not donate. In general, there are interesting related technical trade-offs because of the structure of the Bitcoin protocol such as: the more transactions a miner include, the more his reward increases but also his probability to earn any reward decreases because the time needed for his block to reach consensus depends on its size due to network propagation. As mentioned before, fixing the transaction fee and requiring the same ...
Context 4
... aforementioned double spend attack is a type of counterfeit that is in analogy with that of physical currencies such as US dollar. It may be argued that a currency does not have to be perfect to be practical. US dollar actually has a serious counterfeit rate and many small merchants in the US do not accept 100$bills for that reason. But this does not stop the general public from using US dollar even outside of the mainland. Similarly, one may argue that an occasional double spend attack may not kill Bitcoin as it is in a loose analogy with counterfeit bills. However, such attacks should be prevented as much as possible and the way this works is the network having a large enough total hash rate and an incentive for miners to provide so. Actually, the reason why users of the system are encouraged to wait for enough many confirmations that are ideally proportional to the amount of BTC they are receiving is given as a precaution in [1] is the possibility of 51% attacks. The likelihood of a 51% attack is also highly related with centralization of mining pools, which is regar ded as ‘disturbing’, and ‘dangerous’ by the Bitcoin community. That is, in case of mining, pools are focus of attention as possible sources of attacks as briefly considered in [12]. We are ready to consider the problem 5 , Imposing a transaction fee is essentially tax revenue of the service provided by the miners. As more hash power that the miner pours in means a more secure network, it is reasonable that the reward of the miner is proportional to the hash power he contributes. However, how users should be charged is not as clear as how the wealth should be collected by the miners. Indeed, determining the right transaction fee as a policy and forcing it in the client software as a regulation is crucial for the future of Bitcoin and similar alternative crypto-currencies. The problem of determining the optimum transaction fees are interrelated with various surrounding aspects. Statistically speaking, the number of transactions per second (tps) of Bitcoin increases over time 6 , as well as the wealth carried by the transactions. That is, in the early days of Bitcoin, users usually experimented the protocol by smaller transactions, whereas today, the average value contained in a transaction is significantly higher. Although the idea that transaction fees should be proportional to the amount of bitcoins transferred would be quite disruptive among some bitcoin users, economically, this is plausible in the sense that the users transferring the largest amount of bitcoins are the individuals that have the most benefit of Bitcoin. This is obvious especially when one considers the daily transaction limits imposed by governments and banks. Such limits, varying by the monetary policy of the country that one lives in, are actually one of the reasons Bitcoin drives so much attention because Bitcoin allows one to simply exceed such limits. That is, there is no transfer limit on Bitcoin protocol imposed by any third party and this is one of the promoted features. It is not uncommon to see transactions in millions of US dollars 7 . On the other side, Bitcoin is currently promoted as the best transfer method for transactions carrying tiny amounts, often regarded as micro- transactions . This means that paying a certain fixed minimal fee (such as in magnitude of cents) for each transaction may hinder some possible future usage scenarios of Bitcoin, such as tipping online content providers (videos, forum answers etc.). Regarding this, there are discussions in the community that micro- transactions can be taken off the block chain into newly discussed structures called side- chains . However, more research on the topic seems to be required to determine how such a shift from the main block chain would function. Private exchange and online wallet companies may also help providing such a service 8 at the cost of centralization of the transactions. The transaction fees and bitcoin price are related as follows. First of all, the supply of new bitcoins is only through the block rewards for miners. There is a periodic halving in the block reward, resulting in a logarithmic supply of wealth, decreasing gradually over time as in monetary base, figure 1. The reason why a linear supply is not offered is to avoid inflation. As no central authority is present, there is no government to mint money. Although the network is still in a temporary low-inflation state, Bitcoin is eventually meant to be deflationary. Currently, there are about 12.5 million bitcoins in circulation as of 2014. In 2033, this number is expected to exceed 20 million and increase slightly each year thereafter until 2140. Such a logarithmic supply of the number of bitcoins in circulation as part of the design is the inflation to diminish shortly after the initial launch 9 . The relation of number of blocks issued at any time (in correlation with time) and the inflation of bitcoins is also illustrated in figure 1. As mentioned before, this inflation of supply is to be replaced by a deflation soon after a point when the accidentally lost bitcoins outnumber the newly minted ones. One may argue that the significant scarcity in the supply of bitcoins might not affect the incentive of miners as the lesser amounts of bitcoins rewarded carry higher and higher value in price as the price of bitcoin dramatically increases over time. In other words, to numerically exemplify, for the price to keep up with the incentive of miners, the tens of thousands of bitcoins produced each year after 2030 should have the same price with the millions of bitcoins produced each year now. However, this assumption cannot be correct. Although it is true that until now the price of a bitcoin has increased dramatically 10 , this cannot last forever as even the most optimistic prediction about continuation of price rice involves a slow down after half way as the number of potential users that may adopt Bitcoin in the globe is limited. Theoretically, the best case scenario about adoption of Bitcoin as a technology is the logistic growth as depicted in figure 2. The graph may arguably apply to both the price of a bitcoin and also the number of users of bitcoin. Actually, these two parameters are correlated as the price of bitcoin is determined by the demand and the limited supply. The increasing demand that emerges from an increasing number of users together with a limited supply naturally causes the price to rise. On the other hand, in financial terms, the limited supply over time and the eventual limit on the price of a bitcoin have a combined effect such that the marginal production cost of mining is going to increase dramatically, which must instead be set fairly constant over time. In the long run, the policy on transaction fees should be set so that enough many miners have incentive to run clients having a good enough combined hash power to protect the network. But on the other side of the coin, the fees that miners collect should not be any higher than sufficient in order not to discourage users from using Bitcoin as a means of transferring money. Miners with sufficient combined hash power are not the only requirement to secure the network. Another aspect is the number of full nodes, which have a similar level of importance. Full nodes are actually quite “smart” at running the network as they provide lookup of historic blocks, which is necessary for new nodes synchronizing, and they also validate blocks and transactions, and relay them. As the network right now is under trivial load, we do not exactly know how many full nodes are going to be needed in the future and this is one of the open question requiring further empirical studies. The number of full nodes in the globe dramatically decreases over time and end-users tend to switch to easy-to-run lightweight clients that are intended for personal usage instead of full nodes. However, the exchange and wallet services and other similar service providers will still have to run a full Bitcoin client, and the number of such services tends to increase over time and the indeed full nodes provided by these services only might suffice. We claim that the solution of setting the right transaction fee in the future is not trivial, and a fixed number (such as$0.41 per transaction) mentioned by a core developer of Bitcoin [13], as a study for cost per transaction, do not apply as a transaction fee right now as the block rewards are currently good enough to keep a sufficient number of miners provide a good amount of hash power to secure the network. The transaction fees collected as donations from each block is a mere fraction of the block reward 11 and this is good enough. Currently, Bitcoin nodes have the option to exclude transactions that do not donate. In general, there are interesting related technical trade-offs because of the structure of the Bitcoin protocol such as: the more transactions a miner include, the more his reward increases but also his probability to earn any reward decreases because the time needed for his block to reach consensus depends on its size due to network propagation. As mentioned before, fixing the transaction fee and requiring the same small amount such as in [13] would make micro-transactions under that amount too expensive to process. Limiting the maximum block size so that the maximum number of transactions per block is capped has its own inconveniences. The underlying idea in such an approach is that it makes the number of transactions that can be included so scarce that the ones providing fees under a certain threshold might not reach destination or might face serious delays. Indeed this threshold will be a dynamic one depending on the instantaneous traffic of transactions so that the sender will not be able to figure out whether her transaction will be delayed or not in advance. It is also interesting to note that, [14], in a simplified setting, forcing ...

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Bitcoin is the first and most successful Blockchain system so far. In the Bitcoin system, miners use transaction attached fees as a driving force to mine a new block and package transactions, while users compete by bidding transaction fees for faster confirmation. Considering the particularity of Bitcoin trading system, we take time series into consideration to analyze the transaction rules of Bitcoin system from the perspective of multiple cycles and establish a dynamic game model related to time under Generalised Second Price(GSP) mechanism, and also confirm the model’s superiority on saving users’ fees, compared with the static game model. Also,we propose the quantification of the user experience quantified by calculating the price difference between the transactions uploaded by the same user within adjacent times, making the transaction process of the Bitcoin system no longer the final say of the transaction price. The dynamic game model shows that there is a perfect Bayesian game equilibrium solution in the payment decision, so there is no incentive for users to change the attached fee, and the whole system is maintained stably. In addition, we verify the dynamic game model from computational experiment. Firstly, it is proved that with the help of revenue discount, the cost saving of the dynamic model is generally higher than that of the static model. Then the user’s revenue under the dynamic model is showing an upward trend, and the transactions order under the dynamic model is more stable than that under static model, which can be illustrated mathematically and computationally that the proposed dynamic game model in this paper will help all transactions be processed more efficiently in a uniform pipeline.