Modern computing complexity theory of the Enlightenment of Economics
September 05, 2023 Source: "China Social Sciences" September 5, 2023 Issue 2728 Author: Cao Zhigang

Economics is often criticized as "Economics Imperialism"。With its advantage in methodology,Economics has penetrated into many disciplines of humanities and social sciences,Including politics、Psychology、Sociology and History, etc.,Research territory is constantly expanding。Computer science is a "imperialism",Extension to almost all disciplines we can think of,Including basic sciences such as mathematics and physics。No doubt,The encounter of these two "imperialism" will stimulate a series of new ideological sparks。

Many articles have made many popular discussions on the impact of artificial intelligence, especially machine learning, especially machine learning.。These discussions mainly focus on computer science as tools similar to statistics,The value of empirical research on economics,Especially for supplement and alternatives to alignment economics。The author mainly introduces a topic that rarely involved in the past,That is the theoretical computer, especially its enlightenment of the theory of computing complexity theory。Professor Deng Xiaotie of Peking University said,Computers and markets are artificially created,This makes computer science and economics not natural science。Andrew Mcronan also said,After the Internet appears,Computer science has become a social science。We can understand the market as a distributed computer,Its intelligent and resource allocation efficiency comes from its data、Algorithm and computing power。Data is the information related to buyers and sellers,The algorithm is a series of market rules such as transactions and distribution,Computing power depends on the degree of rationality Bet365 app download of the main body of decision -making。Economists focus on "invisible hands" and "visible hands" how to affect resource allocation efficiency and fairness,and computer scholars study how to improve the computing performance of the computer from both hardware and software。These natural connections make the collision and communication of the bottom -level thoughts of the two disciplines have a solid logical basis。

Theoretical computer knowledge system is mainly divided into two major pieces of algorithms and complexity,Study what the computer can do and what can not do。Economist traditionally pays little attention to algorithms。In recent years,With the booming of the digital economy,Many aspects of our production and life are taken over by algorithms,More and more economists are also interested in special technologies such as algorithms,alternative to people from algorithm、Algorithm conspiracy、Algorithm Fairness and other angles Study。Especially since the rise of the new round of artificial intelligence,Due to data、Algorithms and computing power have become well -known three major elements of artificial intelligence,Economist's interest in algorithms and its influence is increasing。The algorithm not only has a huge impact on the economic development itself,It also became a tool for economists to conduct theoretical research。Mathematical Theories such as calculus and optimization have long become the daily tools of economics research,But most economists are not familiar with the new research tools of algorithms。Many reasons behind this,For example, economists generally do not pay attention to discrete problems,Most of the theoretical computers involved in discrete problems、Limited Questions,Its mathematical skills are usually not related to calculus。

Slowly changes in the above situation。2012 Nobel Prize in Economics awarded Royd Shapli and Elvin Rose,Affirming their foundation bet365 best casino games in market design, especially stable matching。Market design and stable matching mainly involves discrete mathematics,Among them, the DA algorithm and TTC algorithm are the core content of related theories。Except for economists,The development process of this direction is also jointly promoted by theoretical computer scholars and operational studies,The cross -integration of economics and theoretical computers is becoming more closely。Another,Algorithms and mechanisms also have natural connections: the operation of any complex mechanism requires the support of the algorithm,and algorithm can also be regarded as a mechanism after people's incentives。For the above reasons,More and more micro theoretical economists and theoretical computer scholars have been more than 10 years of perspective research algorithms from mechanism design,This is an important content of the design and computing economics of the algorithm mechanism。

The creation process of computers and markets is obviously different,That is, the computer is a consciousness of mathematics researchers、Planning creation,The update iteration of each hardware、The invention of important algorithms has a clear source and history; and the market is the unilateral result of the unity of collective collaboration,is a product of social evolution,Various transaction rules usually do not have a clear inventor,The group wisdom is assembled behind。Although the origin method is different,The two objects of the market and the computer are extremely complex。The market allows economists to first appreciate its exquisitely running.,Just as a biologist who appreciates the beauty of biological evolution to life of life。Whether it is a natural evolution market or a central design computer,Its limitation and ability boundary is particularly worthy of attention。So,Computer scholars' research on calculation complexity bet365 best casino games What are the inspirations for the economist research market?

So far,The theory of computing complexity that focuses on studying computers cannot be done by economists。Computing complexity and algorithm are two sides of a "coin" of modern computer science。The inspiration of the theory of modern computing complexity should not be ignored。Calculating complexity theory sets the border of the market and the government's capabilities at the same time,It can provide a new understanding of the relationship between the market and the government from a different perspective of economics。Just as "prisoner's dilemma" reveals the basic contradiction between individual rationality and collective rationality,"Aro's impossible theorem" reveals the basic contradictions in social choices,Monadier's "San Yuan Paradox" reveals a basic contradiction that open countries must face when formulating economic policies,Calculating complexity of balanced calculation conclusions can provide beneficial inspiration to understanding market operation from the following novel perspective。

First,Calculated friction。We know that the market is not running in vacuum,The ideal complete competitive market does not exist in reality。Market failure except for market forces and externality,Factors such as transaction costs and information frictions are also actual constraints often considering economists。There is also a limited rationality that economists rarely strictly model research,That is the limitations of decision -making subject computing power,Can be called "computing friction"。Effective operation of the market depends on the detailed calculations of both buyers and sellers,Relying on the ideal infinite computing power in the assumption。People often indicate when criticizing this complete rational hypothesis,Can't imagine the decision -making subject in the market as a mathematician。bet365 live casino games There is a natural response for this criticism,That is accompanied by the improvement and extensive popularity of artificial intelligence,The market is getting closer to every decision maker is a mathematician。But mathematicians are not omnipotent。Facing enough complex、Speakers with large scale,Many balanced calculation complexity results indicate,Even if everyone is equipped with a super computer,It is also likely that the equilibrium strategy cannot be calculated in acceptable time。Can't,Not in the future。With the help of calculation complexity theory,Make a corresponding distinction on p question and NP -difficult problems (or ppad -difficult problems),It can help economists to understand the impact of computing friction on market operation efficiency in different scenarios。

2,Relators of rationality。From the perspective of the algorithm,The market economy is a distributed algorithm,The planned economy is a centralized algorithm,Need to assemble all the private information,By calculating output production and allocation of all details。Efficiency of the market economy is constrained by the theory of calculation complexity,For the planned economy,This constraint is more obvious。Traditionally,Economists' criticism of the planned economy is more concentrated in incentives and information,In fact, calculation is also an important constraint。They generally default,As long as you have a strong enough super computer,Calculating problems can always be solved。It can be known from the theory of Modern Calculation Complex,Calculating efficiency is the border,Some problems not only the current supercomputers cannot solve it accurately,It is likely that in the future, it is likely that you cannot create a new type of computer that can be accurately solved。So,Even if the government has all relevant information,Even if all subjects do Bet365 app download not have any incentives,The planned economy still does not necessarily be effectively implemented。It is self -negative,It may cause painful tragedy,This history repeatedly repeatedly commented。This perspective is still effective for market design and a wider mechanism design theory: the optimal mechanism of certain problems may not be accurately calculated in acceptable time,It can only be pragmatic to consider enough simple approximation of the optimal mechanism,Only in reality can be implemented smoothly and achieved the expected purpose。

third,The power of faith。Economics is a kind of social science,It is also a philosophy in a certain sense。No theory can accurately apply reality,The application of theory depends on firmly believes that it has a certain generalization ability,You don't need to care about many unimportant details。Computing complexity is also a philosophy in a certain sense,P NP because the millennium conjecture is actually a belief,No one can prove P≠ NP so far,No one can prove p = np。But most scholars believe that P np,This is also the logical starting point of the previous discussion。The reason why most scholars hold this view rather than the opposite view,Because I believe that this world is complicated,If P = NP, the world will be too simple and boring (blocking the ding pillar)。Human cognition is border,Beyond the current cognition、Fields where rationality should not bear,Philosophy and beliefs are bound to play a powerful role。Market is the product of social interaction,Its operation depends on the interaction of faith and belief。Attitude to the market,Neither over -superstitious,There must be enough awe。This world is not so simple,The market is not so simple,Before we have enough theory and practice to support us to transform the market,It is better to fully trust it。There are too many painful lessons in history to tell us,Bet365 app download The ineffective rate and harm generated by the market itself,It is far from the harm of the lack of awe that is great。

Market、Economy and society are complex giant systems,In -depth understanding and governance of it requires systemic thinking and complex thinking。Calculating complexity theory is a theory that is mature and rare in complex science,and have played a basic role in the development of computer science。Basic ideas of calculating the theory of computational complexity should attract more attention from economists,Therefore, it plays a more important role in the fierce confrontation of computer science and economics.。

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