🤑 A game theoretic analysis of resource mining in blockchain | SpringerLink

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They considered two types of strategies. Although this work is motivated by BTC, it is more heavily influenced by the future of Blockchain. The blocks are connected with each other in the form of a chain. The original paper on BTC was improved in [ 23 ], mostly focussing on security analysis. We survey some of the closest related works next in Sect. Therefore, the social optimum strategy profile is given by Eq. The blockchain is a shared data structure responsible for storing all transactional history to date. Using this model, they studied the conditions under which the mining pools have no incentives to cheat against each other and the conditions under which one mining pool is marginalized by cheating. Nash equilibrium mining profile A Nash equilibrium mining profile is defined as a solution of our mining game where all miners behave selfishly and do not cooperate with each other. Salimitari discussed the mining profitability of a new miner or pool by calculating the expected value of profit [ 24 ]. Finally, we conclude this paper with some remarks in Sect. Kiayias considered the Blockchain Mining Game with incomplete information as a stochastic dynamic game in discrete time [ 15 ]. This efficiency plays a role similar to price in economic models of oligopolies defined by the so called inverse demand function. We propose three concepts of dynamic game theoretic solutions to the model: Social optimum , Nash equilibrium and myopic Nash equilibrium. Exploitation of a shared resource is a significant problem [ 5 ]. Our model is not a one shot game model or static game model. Such profiles often appear in dynamic games with many players, in which players treat their influence of the state variable as negligible. They can then sell the gained BTC to the prevailing market at the current market value. Laszka et al.

In this paper, we create a game theoretic model in continuous time. This yields two sets of values of the constants:. Formally it can be defined as follows. The electricity consumed by the mining systems is directly proportional to the computational power of the system being used.

Bitcoin [ 19 ] was introduced in Its security is based on a concept known as Proof of Work POAand a transaction is only considered valid once the system obtains proof that a sufficient amount of computational work https://anutka-17.ru/game/cowboy-poker-game-miniclip.html been exerted by an actively mining node.

Since electricity can be considered a semi-renewable resource, we have seen an unexpected growth of electricity or computational power consumption resulting from BTC mining [ 2122 ]. The linear quadratic differential game is the best-researched class of dynamic games see Engwerda [ 9 ].

They showed that for some network parameters, especially under high transaction loads, it is difficult or even impossible to distribute rewards stably: some participants are always given incentives to switch between pools.

However, there are state dependent constraints on decisions. The rest of the paper is organized as follows.

Hayes studied the model to check the marginal cost of production and proposed to set the market value of the digital BTC currency [ 13 ]. They use cooperative game theoretic tools to analyze how pool members may share these rewards.

Whenever we consider profiles in which decisions of the others are identical, by a slight abuse of notation, we write this single decision only, not the whole vector. It is a dynamic game meaning that players make a decision at each time instant that is based on amount of resource—electricity available at that time instant.

A social optimum mining profile can be the result of decision making by a single miner, known as a social planner, or just full cooperation of all miners.

First they considered when miners release every mined block immediately and secondly when a block is mined and announced immediately but not released. Social Optimum mining profile A social optimum mining profile is defined as a solution to our mining game bitcoin mining games all miners cooperate.

The fact is that at each new block creation only one miner will be rewarded the one who will win the mining game by first creating and updating the blockchain.

The work and game theoretic model presented here can be applicable to other mining systems that utilize a similar mining system to BTC, therefore well versed in many different potential Blockchain applications [ 31630 ].

We based our results with some discussion on how to enforce social optimality in Sect. We propose two ways to maximize the profit of miners: cooperative —all miners cooperate and bitcoin mining games to consume some fixed amount of electricity and in return, they get BTC market price as profit so, they jointly maximize their profit and the profit is equally shared among them—and non-cooperative —each miner behaves selfishly and individually wants to maximize the profit gained from BTC mining.

Miners are always strategic in choosing which blocks to mine. There just click for source also non-renewable types if it is produced from thermal power plants that use coal—a non-renewable resource.

The HJB equation is assumed to return the value function V as a function of state, with V x being the maximal payoff if the system starts from x as the initial condition.

They show a novel solution of the core issues can be found using linear programming. Efficiency measured in expected value of the reward in dollars in this process of a unit of energy consumption by a miner is a decreasing function of joint energy consumption by all miners.

We consider a continuous time dynamic game model of exploitation of a semi-renewable resource—electricity. As a result of successfully mining a block into the blockchain, he produces BTC.

If miners mine a valid block, indian spirit game publishes the block in the blockchain and extends the blockchain by one new block. However, a feedback Nash equilibrium, besides solving n dynamic optimization problems, requires finding a fixed point of the resulting best response correspondence in the space of feedback profiles.

For each successful attempt, miners get rewards in terms of bitcoin and transaction fees. For example, solar energy, hydro-power, and windmill power are bitcoin mining games versions of electricity.

The quadratic structure of the social optimum problem suggests that the value function is of bitcoin mining games form. Houy considered the BTC mining game where they studied the mining incentives as a decision regarding how many transactions they should include in the block they are mining in order to win the game and update the block first [ 14 ].

The latter causes other miners to continue mining transactions that will soon be committed. The creator of the block is rewarded with BTC. However, there are still transaction fees that can keep the BTC market profitable for many years to come.

Since the problem is symmetric and the current payoff strictly concave, we look for symmetric solutions i.

The total payoff or profit of miner i at this myopic Nash equilibrium strategy profile is given by. This is typical for economic problems. Therefore, we assume that the value function has the form. The work of Niyato et al. We consider a dynamic game model of the bitcoin market, where miners or players use mining systems to mine bitcoin by investing electricity into the mining system. Therefore, optimizing the consumption of electricity is one of the essential and most challenging problems effecting bitcoin mining. Electricity plays an essential role in the bitcoin mining process since created blocks and solving computationally hard problems uses large amounts of electricity. So, depending on if renewable non-renewable resources, it is considered semi-renewable. If a regular solution V of the HJB equation exists, an optimal control can be found as the maximizer of the right hand side of the HJB equation with the actual value function V. Miners participate in mining voluntarily in exchange for rewards as income. Two types of agents participate in the Bitcoin network: miners , who validate transactions and clients , who trade in BTC [ 4 ]. Mining, however, may end up with a failure. We can consider electricity as a semi-renewable resource—depending on the source of resources used for its production. Note that the right hand side of Eq. SHA takes any size plaintext and calculates a fixed size bit cryptographic hash. Dynamic games with linear quadratic structure and with linear state dependent constraints were studied by Singh and Wiszniewska-Matyszkiel in [ 26 , 27 ] but in the discrete time horizon. Each header contains the address of the previous block in the chain. Since the early days of BTC, blockchain technology and cryptocurrencies have caught the attention of both researchers and investors alike. In this work, we assume that miners are honest and follow the protocol as described thus far. In their model, they assume the cost of mining was linear to the price of electricity consumed in the mining process. Furthermore, the work presented here can be easily adapted to other mining schemes in the future making this a pivotal model and work on game theory and its relation to the mining process for Blockchain. First, we calculate the social optimum strategy profile—solution of the cooperative game and the value function—the total profit of a cooperative miner. The average time to create a new block in the blockchain is 10 minutes. Zohar et al. In other words, it is a profile where all miners jointly maximize their current payoffs or profits. We follow this with the formulation of our mode in Sect. We then give our main results in Sect. The process of adding a new block to the blockchain is called mining and these blocks contain a set of transactions that have been authenticated confirmed. Players can be either individual miners or mining pools. They also show that how the profit model changes as mining scales from the individual to the industrial level. Each block in the chain is identified by a hash in the header. The cost of mining for miner i in dollars, is linearly proportional to the price of electricity consumed i. In this paper, we use the tools of dynamic game theory to solve a novel dynamic game model. Showing an attack in which large pools can gain more than their fair share, Eyal et al. Harvey et al. The first block of the chain is known as Genesis. So, in this economic model, the net profit of each miner is given by the expected net revenue minus the mining cost. The miners responsible for creating blocks constantly try to solve cryptographic puzzles in the form of hash computations. The state of resource x is the stock of resource used for electric energy production which may be used for mining—proportional to the amount of available computational power and to the maximal available electricity consumption for mining. Since in our problem, the state is one dimensional, the HJB equation becomes an ordinary differential equation. Presence of constraints on energy consumption dependent on x makes the problem so compound that it is not solvable in a way analogous to that used in the proof Theorem 1 , i.