Tag: Nash Equilibrium

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Blockchain and Cryptocurrency Game Theory

A block is a sequence of blocks in which individual transactions are stored. That block also includes the previous block’s hash, which in effect binds that subsequent block to the previous block creating a chain. Hence the word “blockchain” is a rough visual representation of a blockchain.

Rough visual representation of a blockchain

There are two players in a Bitcoin blockchain-based system: Users, Miners. 

Users: Users have only two roles at their fingertips in Bitcoin: send coins or get the coins. They need two keys to do that, the public key, and the private key.

Miners: What miners are doing is authenticating the transactions and doing the mining process. Mining is how to discover new blocks and add them to the blockchain. Miners have a lot of power in the blockchain system and they can cause havoc in the process if they choose to cheat for their own personal gain. They can cheat in several ways. For example, they can include an incorrect fee and provide extra coins for themselves. Additionally, they can add blocks randomly without thinking about proof of work. To get more BTC, mine on top of invalid frames. Mine on top of a block that performs sub-optimally.

Example of “double investment”

The key chain is blue frames. Now imagine there is a miner who invests 20 bitcoins (hypothetically) in blue block 51 to get 500 litecoins (a different cryptocurrency because of a different parent block). And now, with a new block 51 (red), he wants to create a parallel chain where he never made this transaction. So, let’s make a quick recap to simplify what he’s just done: 1. In blue block 51 spends 20 bitcoins to get 500 litecoins. 2. Creates a new chain (fork) from block 50 and in the alternate block 51, he doesn’t do the litecoin transaction. 3. In the end, he comes out with his original 20 BTC and 500 new litecoins. What has just happened here is called “double investment“. Theoretically, miners can now mine on top of the new red chain and continue double-spending and extra bitcoins mining. As you can imagine, the bitcoin network can be broken in this case!

To counter this, the blockchain uses concepts from game theory to maintain the bulletproof system. It was designed in a way that it is a self-enforcing Nash Equilibrium.

The Nash Equilibrium in mining and the punishment system (Miner)

If a miner produces an invalid block, then due to a rule that has been established in blockchain mechanics, others will not mine on top of it. Any block mined on top of an invalid block becomes a block that is invalid. Using this rule, miners simply ignore the invalid block and keep the blue chain in the diagram on the top of the main chain. A similar logic stands for block scoring sub-optimally. Check again at the diagram. No miner on Red Block 52 will want to mine as the Blue Block 53 is going to have a higher score than the red block.

Both of these situations are mitigated as miners choose the most stable state or with a Nash Equilibrium as a group. Clearly, all the miners can mine on the red block and make it the new blockchain, but the number of miners is so large that it’s simply impossible to organize an activity like that. According to the Diffusion of Decisions, if a majority of the group’s citizens do not switch their state, the minority will have no incentive to stay in the new state. (For most of the cryptocurrency, q is near 1) Seeing this, a miner is less likely to spend all their computing power and risk ostracising in a futile cause.

Why users prefer the main chain than the other chain?

The first thing that we need to keep in mind is that cryptocurrency has value is because the people give it value. So why is a normal user going to assign value to coins that come out of the blue chain and not to coins that come out of the red chain? The explanation is clear. From the users’ point of view, the main chain is a schelling point (It is a solution that, in the absence of interaction, people will continue to use because it feels unique, meaningful or natural).

Diffusion of Decisions: Another reason consumers are more interested in the main chain is that they are actually used to it. Unlike bounded claims of rationality, each time people choose the simplest solution. Going through a new chain complicates things unnecessarily.

From this example, we can see that game theory makes blockchains so different. There is nothing new about the mechanics, but the combination of Nash Equilibrium and Diffusion of Decisions has made cryptocurrency free from internal corruption. Even if Bitcoin collapse recently for whatever reason, because of this path-breaking relationship, cryptocurrency will always live on.

Reference:

1. Cryptocurrency. (2019, November 11). Retrieved from https://en.wikipedia.org/wiki/Cryptocurrency.

2. Rosic, A., Rosic, A., Pontoriero, L. E., Dosunmu, O., Derosa, F., Warraich, J. A., & Marinkovic, M. (2019, October 3). What is Cryptocurrency Game Theory: A Basic introduction. Retrieved from https://blockgeeks.com/guides/cryptocurrency-game-theory/.

3. Digital Currency, Bitcoin and Cryptocurrency. (2018). Inclusive FinTech, 33–82. doi: 10.1142/9789813238640_0002

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Predict the Voting System with Game Theory

When people have different voices or opinions, voting seems to be the best method to make a decision. There are various types of electoral systems, and today, we will typically be interested in the First-past-the-post (FPTP) voting method and how game theory has an impact on it. Intuitively, we may think voting is the most trustworthy and civil way to pick a candidate. However, an article by Wesley Sheker has revealed that the recent elections have been disastrous due to the abuse of the game theory.

The major cause of these disastrous elections is gerrymandering, meaning the governing parties intent to take advantage of a party by manipulating the political map in their favour. However, gerrymandering alone is not accountable for this failure to reflect the democratic standard of honesty and integrity. Another assistance lies in the voting system itself, which is the FPTP method.

The power of prediction comes from game theory’s Nash Equilibrium, either it’s pure or mixed. People always tend to make their strategy according to other people in order to optimize their outcomes.

Suppose we have 5 voters and 5 candidates, each voter has a preferred candidate and the outcome of the election (i.e. winner) is measured as a utility (high: 16, low: 0, scales down with the preferred candidate). Now we have to consider whether Nash Equilibrium will bring an optimal outcome for the voting system. Consider the first case: all voters vote their preferred candidates and the winner is candidate 1

all voters vote their preferred candidates and candidate 1 as winner

The net utility for this election will be 48 (16 + 16 + 16). Now we change the winner from candidate 1 to 3, the table will look like this

all voters vote their preferred candidates and candidate 3 as winner

None of the voters are very happy as their preferred candidate is the winner. However, the net utility of this election is 60 (>48), meaning in an election with many candidates, voters and their preference, the outcome of the election will not be optimal as the voters just blindly vote for their preferred candidate. This simple mock election has demonstrated the philosophical result of an FPTP system which conveys the fact it fails to deliver an optimal outcome.

If game theory would bring us a negative impact, how should we avoid it? In fact, it is impossible to escape from game theory’s power since we are constantly in the game. Our life is affected by other people’s choices, changing our own behaviour will not be enough, as the philosophical rhetoric originating from game theory says: “We can create a better world by becoming better human beings ourselves”.

Reference

Das, Sangeet Moy. “Game Theory 101 for Dummies like Me.” Medium, Towards Data Science, 2 Oct. 2019, https://towardsdatascience.com/game-theory-101-for-dummies-like-me-2e9ab92749d4.

Sheker, Wesley. “Disastrous Elections: Predicted by Game Theory.” Penn Political Review, 13 Jan. 2018, https://pennpoliticalreview.org/2018/01/disastrous-elections-predicted-by-game-theory/.

Wines, Michael. “What Is Gerrymandering? And Why Did the Supreme Court Rule on It?” The New York Times, The New York Times, 27 June 2019, https://www.nytimes.com/2019/06/27/us/what-is-gerrymandering.html.