Why is the blockchain a brand new game arena?

What is the use of the blockchain?

In response to this question, Virgil Griffith, a member of the Ethereum Foundation, used Ethereum as an example to present an eye-opening view [t1]:

Ethereum is an unprecedented arena for playing cooperative games (Ethereum is an unprecedented cooperative game arena).

Blockchain and game theory are two different areas. At first glance, it seems that there is not much correlation, but this is not the case. Almost all game theory classic cases can build a new game relationship with the help of blockchain. In his article, based on Ethereum, Virgil Griffith explains how to use blockchain to establish new game relationships based on classic cases in game theory.

1

Both lose or hurt or cooperate and win? —— Transforming “non-cooperative game” into “cooperative game”

Game Theory is a branch of economics. It is the study of whether the parties to the struggle have the most reasonable behavioral schemes and how to find mathematical theories and methods of this reasonable behavioral scheme [t2]. An act with a competitive or confrontational nature is called a game behavior [t2].

There is a classic case in the game theory that everyone is familiar with – the prisoner's dilemma [t3].

Two prisoners, Zhang San and Li Si, who were convicted of crimes, were arrested and they could not communicate with each other. If neither party reveals the other party, each person will only be detained for one year; if one of them has a disclosure and the other chooses to be silent, the whistleblower will be released immediately, and the silent person will be detained for 8 years; Both parties will be detained for five years at the same time.

Obviously, if both sides remain silent, it is the most favorable choice for them. But in fact, eventually both parties will tend to expose each other.

What led to such counter-intuitive results?

We use the matrix below to explain it briefly.

01

For Zhang San, if you choose to silence, there are two results:

He was detained for 1 year, at which time Li Si chose to be silent and was also detained for 1 year;

He was detained for 8 years, at which time Li Si chose to expose and release it directly. If Zhang San chooses to expose, the two results are:

Direct release, at this time Li Si chose to be silent and was detained for 8 years;

He was detained for five years, at which time Li Si chose to be exposed and was also detained for five years. Therefore, no matter how Zhang San chooses, for Li Si, the disclosure of Zhang San is a more favorable choice for him. The same is true for Zhang San.

Therefore, under the premise that the two sides have not communicated and negotiated, Zhang San and Li Si will only make the most favorable choice for the individual. This kind of game relationship between the prisoners is called a non-cooperative game . The choice between the prisoners here is called decision-making based on individual reason, and the opposite is based on group rationality. Here, the two sides reached the Nash equilibrium point of the game after making a decision to expose the other party.

The classification of the game also has different classifications according to different benchmarks. It is generally believed that games can be mainly divided into cooperative games and non-cooperative games [t2]. Cooperative game theory refers to the game in which some participants form alliances and cooperate with each other. The opposite of the cooperative game is the non-cooperative game, which means that the participants cannot form an alliance or any cooperation mechanism must be a self-compliance contract (for example, by means of a confidence threat) [t4].

The “Nash Equilibrium Point” refers to the state in which the interacting economic entity chooses its own optimal strategy under the assumption that all other selected strategies are established. If no participant can increase the return by acting alone in a situation, this combination of strategies is called the Nash equilibrium point [t5].

In game theory, the formation of cooperative games needs to meet two basic conditions [t6]:

1. For the Alliance, the overall return is greater than the sum of the benefits of each of its members when operating separately.

2. For the inside of the league, each member can get more than the benefits of not joining the league. The problem with the prisoner's dilemma is that, without knowing the choice of the other party, choosing not to cooperate will be held for a shorter period of time (ie, they gain more personal gains), so they do not satisfy the basic conditions of the cooperative game.

Virgil Griffith presents a solution for a cooperative game – creating new rules with blockchain smart contracts to create new contract relationships.

We first explain the problem by converting the number of years in which the prisoners are detained into their earnings on the Ethereum (if the income is -1ETH means being held for 1 year).

Before Zhang San and Li Si were arrested, they deployed a contract on the Ethereum. The contract was as follows: The two mortgaged 1000 ETH at the same time and promised to choose silence. If either party chooses not to keep the promise, it will burn 1000 ETH locked in the contract, that is, he will lose 1000 ETH, which is far greater than the loss they originally chose to silence or expose, so the Nash equilibrium of the prisoner's dilemma is break in.

03

By deploying an unmodifiable and auto-executable contract, a binding and enforceable agreement can be reached between prisoners. Decisions based on personal reasoning are replaced by mutually cooperative decisions. We succeed in non-cooperation. The game relationship is transformed into a cooperative game.

Not only the prisoner's dilemma, almost all non-cooperative games can use the smart contract to construct a new game relationship.

Let us look at an example of a non-cooperative game transformed into a cooperative game – the Deer Hunting Game [t7].

Two hunters, A and B, go hunting together, they can hunt deer or hunt hares. The deer needs two people to cooperate to get it, the hare can be hunted by one person, but the benefit of hunting deer is greater than the income from hunting hare. As shown in the following figure, we assume that the gain from hunting hares is 1 ETH, and the gain from hunting deer is 3 ETH.

03

Although the two hunters also chose to hunt deer at the same time, they had to bear the consequences of not choosing to hunt deer. Therefore, hunters may be more inclined to make hunting hares, which are small but less risky.

Similar to the prisoner's dilemma, here we can also use the blockchain to establish a cooperative relationship between hunters. The hunters first created a contract on the Ethereum, and each party mortgaged 1000 ETH to the contract. If either party finally hunted the hare, it burned its mortgaged 1000 ETH, so any hunter would not choose at this time. Hunt the hare.

04

In the above example, we convert the gains and losses of the players into the value symbols on Ethereum, but in the actual application scenario, whether this can be used instead of the actual benefits remains to be discussed; It is also relatively difficult to make decision results in actual scenarios and automatically trigger contract execution. So how to find the right mechanism to make the key operations of the real game and the contract on the chain are crucial.

2

Game Revolution – New Rules for Competition in the Arena

In fact, blockchain and smart contracts are not necessary to change the game, but blockchain smart contracts have great potential in applying and deploying game models.

Due to the fact that it is difficult for us to find a suitable trusted third party as a fair arbitrator, we can assist in the execution of the outcome of the game. The emergence of blockchains and smart contracts makes it easy, as emphasizedability is a bug[t8] As stated in this article, the greatest value of a smart contract is precisely its Trustless.

More than just non-cooperative games, almost arbitrary game relationships can be combined with blockchains to create new rules.

2.1

Cowardly game

Create a competitive advantage in a non-cooperative game.

The widower game is also called "the coward game". It means that the two drivers A and B are driving relative to each other. The first turn is ridiculed as a "chicken" and the other wins, but if the two refuse to turn, let the two The two cars collided and no one could benefit from it in the end [t9].

We assume that when two people turn at the same time, the return is recorded as 0; when one side turns and the other goes straight, the turning party is recorded as income -1 ETH, and the other side is 10 ETH; when both people go straight at the same time, the income is recorded as -100 ETH.

05

Obviously, this game only has one side to choose straight, the other side chooses to turn the most, but who chooses to go straight and who chooses to turn is difficult to judge.

In order to break the deadlock and get the most benefit, the driver can create a contract before the game starts, mortgage 1000 ETH, and notify driver B. If it chooses to turn, the contract will automatically burn its mortgaged 1000 ETH, which makes the driver must choose to go straight, and B has to choose to turn to minimize losses.

06

2.2

2. Jazz band performance

The use of smart contracts guarantees the fair distribution of benefits in the cooperative game.

The jazz band performance is a case of a cooperative game [t10]. Suppose a scene where a party needs to recruit a performer. The performers to choose from include a guitarist, a drummer and a singer.

If the result of the recruitment is to recruit only one person (singer, guitarist, drummer, any one), then only 1 ETH will be paid;

If a singer and a guitarist are recruited, they will be paid a total of 7 ETH;

If a singer and a drummer are recruited, they will be paid a total of 5 ETH;

If a guitarist and a drummer are recruited, they will be paid 4 ETH;

If you recruit singers, guitarists and drummers at the same time, they will pay 10 ETHs. 07

In the above performance fees, it is obvious that the singer, guitarist and drummer form a band to participate in the performance of the biggest gain, they have a lot of motivation to form an alliance to participate in the performance. After three people form a band to get 10 Ethereums, how many Ethereum should each person allocate to be reasonable?

We can briefly analyze the contribution of each member of the band:

The total income of the two-person cooperation with singers is: 7+5=12

The total benefit of a two-person cooperation with a guitarist is: 7+4=11

The total benefit of the two-person cooperation with the drummer is: 5+4=9

In the two-person cooperation, we can see that the value of the singer is the highest, the value of the guitarist is in the middle, and the value of the drummer is the lowest.

The 2012 Nobel Prize in Economics, Sharpley, proposed a concept of Shapley value that solved the problem of rationally distributing revenue to participants in a cooperative game [t11]. If assigned according to his theory, the singer should get 4, guitarist 3.5, and drummer 2.5.

The organizer can write the assigned Shapley value calculation formula into the smart contract, and automatically transfer the contract to the performance participants after the performance ends, thus ensuring the fairness of the distribution.

2.3

3. Arbitrage from the game of others

Empty gloves white wolf: Interfere with other people's game to arbitrage.

Suppose there are two participants in a game relationship: A and B. A can perform two actions, up or down; B can also perform two actions to the left or right.

If A chooses upward and B chooses to the left, both parties receive 10 ETH gains;

If A chooses upward and B chooses to the right, the two parties have no income;

If A chooses downward, B chooses to the left, A has no income, and B obtains 1 ETH's income;

If A chooses to go down, B chooses to the right, A gets 1 ETH's return, and B has no gain. 08

Obviously, at this time, A chooses to go up, and B chooses to the left is the most favorable choice for both sides.

Before the game starts, the third party C creates a contract, and A needs to transfer 5 ETH to C before the game starts.

If A moves to C ETH as required, C will no longer interfere with the game, eventually A will receive 5 ETH gains, and B will receive 10 ETH gains.

09

If A does not transfer C ETH to C as required, C will intervene in the game. If B chooses to the right after the game is over, the contract will automatically transfer 100 ETH to B, then A will get a maximum of 1 ETH, and B will get 100 ETH.

10 For B, he needs to decide his choice based on whether A transfers money to C in advance. For A, if he turns 5 ETH to C, he can still get 5 ETH's income. If he does not turn, he can only get 1 ETH's income. In the face of rational A and B, C only needs to create a contract, and without paying any fees, A can transfer some of the proceeds to him.

In the face of this naked "blackmail" behavior, can A use the blockchain to reverse the situation?

(If a smart partner thinks of a solution, welcome to add Xiao's WeChat secbit_xiaoanbi to participate in the discussion)

2.4

Obstruction and length – looking for binding mechanisms under the chain

As Virgil Griffith said,

Ethereum enables powerful economic vehicles we don't yet understand. (Ethereum supports powerful economic tools that we don't know.)[t1]

As a kind of decentralization, the blockchain has a clear implementation and cannot be tampered with "trusted third parties". It breaks the traditional thinking and provides a very effective way to break the game relationship and establish new rules. As a brand new game arena, blockchain and smart contracts will inevitably inject more inspiration into the application and change of the game.

But as mentioned above, how to find the right mechanism to bind the key operations of the real game to the contract on the chain requires further exploration. Perhaps we still have a long way to go before this "Arena" really works.

(Finish)

Author: Ann laboratories

Reference link:

[t1] https://medium.com/@virgilgr/ethereum-is-game-changing-technology-literally-d67e01a01cf8

[t2] https://en.wikipedia.org/wiki/Game_theory

[t3] https://en.wikipedia.org/wiki/Prisoner%27s_dilemma

[t4] https://en.wikipedia.org/wiki/Cooperative_game_theory

[t5] https://en.wikipedia.org/wiki/Nash_equilibrium

[t6] https://wiki.mbalib.com/wiki/%E5%90%88%E4%BD%9C%E5%8D%9A%E5%BC%88

[t7]https://en.wikipedia.org/wiki/Stag_hunt

[t8] Upgradeability Is a Bug https://medium.com/consensys-diligence/upgradeability-is-a-bug-dba0203152ce

[t9] https://en.wikipedia.org/wiki/Chicken_(game)

[t10] https://www.coursera.org/lecture/mathematical-game-theory/shapley-value-and-core-gWuz9

[t11] https://en.wikipedia.org/wiki/Shapley_value