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Game Equilibrium#

Game equilibrium refers to a relatively static state in which all participants in a game achieve their perceived maximum utility and are unwilling to make changes.

Of course, in the equilibrium state where all parties are satisfied with the game results, the actual utility and satisfaction of each party are different.

Game equilibrium not only reflects the competitive relationship between the parties in the game, but also reflects the cooperative relationship between the parties. For example, the restructuring of assets between companies through acquisitions and mergers to achieve a win-win strategy is a practical manifestation of game equilibrium.

Game is essentially a process from dynamic competition (bargaining) to relatively static cooperation (consensus), so game equilibrium is not only a requirement of market competition, but also an inherent requirement of enterprise development.

Nash Equilibrium#

Nash equilibrium (also known as non-cooperative game equilibrium) is an important term in game theory named after John Nash.

In a game process, regardless of how the other party chooses their strategies, one party will choose a certain strategy, which is called a dominant strategy.

If any participant's chosen strategy is optimal under the determined strategies of all other participants, then this combination is defined as Nash equilibrium.

A strategy combination is called Nash equilibrium when each player's equilibrium strategy is to maximize their expected payoff, while at the same time, all other players also follow such strategies.

Strictly dominant strategy equilibrium, iterated elimination of strictly dominant strategies equilibrium, pure strategy Nash equilibrium, and mixed strategy Nash equilibrium are generally referred to as Nash equilibrium.

Strictly dominant strategy equilibrium is a special case of iterated elimination of strictly dominant strategies equilibrium, iterated elimination of strictly dominant strategies equilibrium is a special case of pure strategy Nash equilibrium, and pure strategy Nash equilibrium is a special case of mixed strategy Nash equilibrium.

Classic Cases#

Prisoners' Dilemma#

In 1950, Merrill Flood and Melvin Dresher of the RAND Corporation formulated the theory of relevant dilemmas, which was later presented by consultant Albert Tucker in the form of prisoners and named "Prisoners' Dilemma".

The Prisoners' Dilemma is a game theory model and a representative example of non-zero-sum games in game theory. It includes dominant strategy equilibrium, reflecting that the best choice for individuals is not necessarily the best choice for the group, or that individual rational choices often lead to irrational outcomes for the group. Similar models frequently appear in price competition and environmental protection in reality. The classic Prisoners' Dilemma is as follows.

The police arrest two suspects, A and B, but do not have enough evidence to charge them. So the police separate the suspects and meet with them separately, providing them with the following three options.

1. Option 1: If both remain silent or deny (cooperate with each other), both will be sentenced to 1 year in prison.
2. Option 2: If both accuse each other or confess (betray each other), both will be sentenced to 8 years in prison.
3. Option 3: If one confesses and testifies against the other (unilateral betrayal), while the other remains silent or denies, the confessor will be released immediately, and the other will be sentenced to 10 years in prison.

The Prisoners' Dilemma payoff matrix is as follows:

If both choose Option 1, it is the optimal choice for both, which is the Pareto optimal solution that takes into account the interests of the group. However, from the perspective of individual rationality, because they do not know what choice the other will make, choosing "confess" is the most reasonable, safest, and optimal strategy. Therefore, in the end, both A and B will choose to "confess".

Thus, it is clear that choosing "confess" is a dominant strategy for either A or B, and both choosing "confess" is a set of dominant strategy equilibrium.

This example demonstrates that in non-zero-sum games, Pareto optimality and Nash equilibrium are conflicting, and Nash equilibrium is more common.

Although A and B both chose "confess" for their own self-interest, it is not the best outcome for the group as a whole.

The Prisoners' Dilemma reflects a profound meaning in real society: the conflict between individual rationality and collective rationality. The pursuit of self-interest by individuals often leads to a Nash equilibrium, which is an outcome that is not beneficial to the group as a whole. This clearly contradicts Adam Smith's view in "The Wealth of Nations": "By pursuing his own interest, he frequently promotes that of the society more effectually than when he really intends to promote it."

The Prisoners' Dilemma also provides an insight: to achieve overall benefits and cooperation as a "self-interest strategy" that is beneficial, it is necessary to follow the golden rule, which is to treat others the way you want to be treated, and at the same time, be followed by all participants, similar to "do unto others as you would have them do unto you".

Pigs' Payoffs#

Pigs' Payoffs is a famous example of "Nash equilibrium" proposed by John Nash in 1950.

Assume that there is a big pig and a small pig in a pigsty. One end of the pigsty has a feeding trough, and the other end has a button that controls the supply of pig feed. Pressing the button will provide 10 portions of pig feed, but pressing the button requires consuming the energy equivalent to 2 portions of pig feed. The button and the feeding trough are located at opposite ends, so the pig that presses the button not only consumes energy but also loses the opportunity to eat first at the trough. There are several choices between the big pig and the small pig.

1. If the small pig runs to control the button while the big pig waits at the feeding trough, then the big pig can eat 9 portions of pig feed first, leaving only 1 portion for the small pig.
2. If the big pig runs to control the button while the small pig waits at the feeding trough, then the small pig can eat 4 portions of pig feed first, leaving 6 portions for the big pig.
3. If both the big pig and the small pig run to control the button together, then the big pig can eat 7 portions of pig feed, and the small pig can eat 3 portions.

The payoff matrix of Pigs' Payoffs is as follows:

If the big pig chooses to wait, what will the small pig do? In this case, if the small pig chooses to wait, the payoff is 0; if it acts, the payoff is -1. No matter how it chooses, the small pig can only starve to death, so the best strategy for the small pig when the big pig waits is to wait, and they will starve together.

The big pig also knows the small pig's choice, so the big pig can only choose to act in order not to starve to death.

Since the big pig can only act in any case, is there any need for the small pig to act? If the small pig waits, the payoff is 4; if it acts, the payoff is 1. Obviously, the best strategy for the small pig is still to wait. Therefore, it can be seen that the situation where the big pig acts and the small pig waits is the inevitable outcome of Pigs' Payoffs, which is Nash equilibrium.

Pigs' Payoffs can still be explained in the context of market competition in real enterprise. For example, large companies are often willing to explore the market or invest in technological innovation, while small companies tend to enjoy the benefits and follow the large companies to make quick profits. This is not because small companies lack innovation spirit, but if we analyze it from the perspective of this game, small companies do not need to innovate. The relationship between small companies and large companies is similar to the relationship between small pigs and big pigs.

If a small company invests a lot of costs in innovation, it is like a small pig controlling the button itself. At this time, the large company can imitate and earn most of the profits with its own size advantage, while the small company will not gain much and eventually become a "starving" small pig. Therefore, out of rational decision-making, large companies can choose to innovate, while small companies generally can only choose to follow and ride the wave.

The phenomenon of "the small pig lying down while the big pig runs" is caused by the game rules, and changing the core indicators of the rules will inevitably lead to changes in the results. For social rules, the behavior of "free-riding" by the small pig affects the optimal allocation of resources. Therefore, to achieve effective allocation of social resources, the rationalization of the core indicators of the rules should be the first step.

Game Theory and Blockchain#

Blockchain integrates multiple disciplines and is a clever combination of existing mature technologies. Game theory is one of the eight pillars of blockchain technology and drives blockchain thinking, while the birth of blockchain provides a deeper technical guarantee and lower opportunity cost for game theory.

From a macro perspective, the ideal state achieved by various games is Nash equilibrium, and the ultimate goal is to achieve Pareto optimality. The decentralized, autonomous, and collective maintenance characteristics of blockchain strongly support the development of multi-level and multi-dimensional games. Through the cycle of game-compromise-game, a consensus mechanism is developed, which leads to smart contracts.

From a micro perspective, game theory ensures that the database encryption system is not vulnerable to internal attacks, while blockchain uses distributed open consensus and cryptography to achieve Nash equilibrium in game theory. It is the combination of these two interesting concepts that makes game theory such a special existence in blockchain. The consensus mechanism formed by the game leads to institutionalized standardization and smart contracts, which will always exist in digital currencies.

Smart Contract Technology#

Smart contracts were first proposed in the late 20th century, but it was not until recent years with the development of blockchain technology that they gradually became familiar to the public. The concept of smart contracts includes three elements: commitment, protocol, and digital form. Therefore, it can expand the application scope of blockchain to various aspects of financial industry transactions, payments, settlements, and clearing.

A smart contract is a contract that is immediately executed when a pre-programmed condition is triggered. Its working principle is similar to the if-then statement in computer programs.

Classification of Smart Contracts#

Smart contracts are mainly classified into two categories based on whether they are Turing complete or not, namely Turing complete and non-Turing complete.

Common reasons for not achieving Turing completeness include limited loops or recursion and the inability to implement arrays or more complex data structures.

Turing complete smart contracts have strong adaptability and can program complex logical operations, but there is a possibility of falling into an infinite loop.

In contrast, non-Turing complete smart contracts cannot perform complex logical operations, but they are simpler, more efficient, and more secure.

Applications of Smart Contracts#

Smart contracts reduce the cost of contract signing, execution, and supervision. Therefore, they have obvious economic value for contracts related to low-value transactions. Smart contract technology also brings opportunities. For example, the influence of public supervision can be mixed with legal and technical codes, rather than relying solely on legal rules. In essence, technical codes can be used to ensure compliance with legal rules, thereby reducing compliance costs. This can be regarded as an application case of technology to enhance supervision (RegTech, mentioned in a FinTech report by the UK Government Technology Office).

In the field of blockchain, smart contracts are used to encapsulate various types of script code in the blockchain system. These script codes specify how transactions in the contract are executed and the specific content of the transactions. Smart contracts make blockchain a programmable currency that is more flexible and efficient than traditional currency transactions. Usually, the execution time and triggering rules of the contract can be set in the contract. Smart contracts are the functions that blockchain systems such as ETH are committed to achieving.

The construction and execution of smart contracts based on blockchain usually involve the following three steps.

1. Contract generation: Design script code to implement the content of the contract according to the needs of the contract participants.
2. Contract storage: The script code that implements the contract needs to be stored in the blocks of the blockchain.
3. Contract execution: The script code of the contract can be automatically executed without human intervention or operation. The smart contract layer is responsible for implementing, compiling, and deploying the business logic of the blockchain system, achieving condition triggering and automatic execution of established rules, and minimizing human intervention.

Risks of Smart Contract Applications#

Smart contracts mostly operate on digital assets, and their characteristics of being difficult to modify once they are on the chain and having strong triggering conditions determine that the use of smart contracts has both high value and high risk. Avoiding risks and realizing value is the difficulty of the current widespread application of smart contracts. The application of smart contracts is still in its early stages, and it is the "disaster-prone area" of blockchain security. From the security incidents caused by smart contract vulnerabilities in history, there are many security vulnerabilities in contract writing, which poses great challenges to its security.

Currently, there are several approaches to improving the security of smart contracts.

1. Formal verification: Ensure that the logic expressed by the contract code conforms to the intention through rigorous mathematical proofs. This method is logically rigorous but difficult, and generally requires third-party professional organizations to conduct audits.
2. Smart contract encryption: Smart contracts cannot be read in plaintext by third parties, reducing the risk of smart contracts being attacked due to logical security vulnerabilities. This method has low cost but cannot be used for open-source applications.
3. Strictly standardize the syntax format of contract language: Summarize excellent patterns of smart contracts, develop standard smart contract templates, and standardize the writing of smart contracts according to certain standards to improve the quality and security of smart contracts.