From General Equilibrium to Algorithmic Equilibrium

From General Equilibrium to Algorithmic Equilibrium Bin Li1 Equilibrium means a position in economics where human intelligence has reached its maximum. “Perfect rationality” implies that information transfers frictionlessly and human thinks or calculates costlessly, at infinite speed, or with zero time. In this sense equilibrium must be only “general” (Walras, 1969; Arrow, 1951 & 1954; Debreu, 1951), namely, no equilibrium can be tenable solely unless all people and all factors reach the equilibrium 2 simultaneously, and, all “partial equilibria” must integrate with the equilibrium, into an embracive wholeness, and thus are not independent. This logic forced economic theory into an aggressive and unstoppable trajectory that attempts to cover everything, hence Robert 3 Lucas had to deliberately revamp the concept of “rational expectation” to illustrate that general equilibrium would contain the future, despite that it is ridiculous in common sense. Then, cannot equilibrium be actual? Or, how should economists realistically describe and analyze equilibrium? The essay introduces a solution to them, which also bring a new scheme of a unified economics. Common sense tells that equilibrium, as a statics, can really exist, discretely, or in multiple units, and can also coexist with many dis-equilibria in the world, mixedly. We need to consider this whole scenario and explain why. The spatiotemporal properties of thinking or thoughts can be some of the reasons: information, data, or thoughts as entities are distributed in the brain or in the space, their gathering and interaction means “thinking” that consumes time and resources, like physical economic activities; then, the heterogeneity and marginal economic effects lead some thinking activities, with diminishing marginal returns, to converge into equilibria whereas others remain unchanged or diverge into dis-equilibria, maybe from some extant equilibria. Space and time can separate different entities, different thinking processes and different equilibria and/or dis-equilibria, making them coexistent at different locations, temporarily or permanently. In order to describe this scenario, Algorithm Framework Theory (AFT; Li, 2009-2022) as a minimal theory is needed, which says that human uses finite, innate, and universal “Instructions” in the brain to serially, selectively, and repetitively process informational pieces to think, at finite speed. The “ combinatorial explosions” happening between Instructions and data illustrate the expansive, infinite, and endless procedures of knowledge development, however, one must 1 Bin Li, a visiting scholar of Center for Urban & Regional Studies, University of North Carolina at Chapel Hill, used to be an independent economist and a columnist in Shanghai, China. Websites: https://unc.academia.edu/BinLi https://www.researchgate.net/profile/Bin-Li-121 Emails: binl@unc.edu libinw2014@hotmail.com 2 A realistic concept of “partial equilibrium” was proposed and properly used by Alfred Marshall (Marshall, 2013), however, its basis need to be interrogated and rebuilt, as in this essay. 3 See Lucas, 1971. Under the logic of “rational expectation”, any changes in the future can be divided into two parts: the predictable, and the “random walk”. stop or close his/her thinking somewhere, so as to make decisions in time, and to act. Providently, one must exert his/her best efforts to have a decision containing knowledge as much as possible, despite his/her limited thinking speed and capacity. How to do? From empirical observations we learn that one uses various methods other than deduction, such as induction, assumption, analogy, approximation, omission, and negotiation, to make the rash, rough, or vague conclusions on part or whole of the world. These conclusions as cognitions, beliefs, attitudes, or strategies cover wide domains, but only in limited depth or correctness, and in concise forms. In other words, they are in principle the “makeshifts” or “stopgaps”. Philosophical ideas, habits, traditions, common sense, and all taught knowledge can be their examples. They are broadly, repetitively, and maybe implicitly invoked as parameters for enormous computations to reach specific equilibria; thus, an equilibrium achieved in this way would be “general”, more or less; it can be a smaller and special “general equilibrium”: containing the contents relating to the globe; emphasizing something while neglecting others; resulted from finite and affordable workload of computations; with various methods subjective than neoclassically objective; possibly appearing flawed and arguable, etc. It may represent the psychological states as satisfaction, desperateness, or confusion while further continuous computing attempts are deemed unnecessary or uneconomical, hence, the actor chooses to stop here, despite other many problems staying unsolved. According to the terminology of AFT, this equilibrium can be called “Algorithmic Equilibrium”, different from, but relating to, neoclassical partial or general equilibrium. Since computing time and costs are certainly real, any statics in the real world can be seen as an Algorithmic equilibrium that exists relatively independently, and co-exists with other equilibria and/or disequilibria. This independence and coexistence can be explained further. The decisive reason is the feeble capacity of a thinking or computational operation, which confines any computational task within its limited scope and depth. One cannot carry out many or all tasks concurrently. It is far from all variables that are allowed, neoclassically, to change simultaneously and accordingly. Instead, one must invoke certain ready-made knowledge stocks that have been assumed relatively reliable and not to change any longer, to support current computations. One must choose among stocked knowledge, even purblindly. Since the stocked knowledge is one’s historic accumulative results, endogenously, one can neither precisely examine their reliability for the time being nor revamp them all to adapt to the current computations. Even if one determines to do so, s/he can only do it marginally, and perhaps very slowly. Moreover, due to the scale or scope economy, the current computations should be intensive on certain domains to some extent, lasting a certain long period of time, until an equilibrium is obtained, then it can be economically rational to turn to another task. And, while undertaking other tasks, the same limitations are also true. The above logic suggests that in most cases, one must tolerate both the independence and coexistence of many equilibria, even unknowing of their exact relations. From this perspective we can comprehend the relationships between Nashian equilibria (Nash, 1950 & 1951) and other Non-Nashian ones. There must be explicit or implicit conflicts among various equilibria since they arose from their specific contexts respectively. Moreover, there must be abundant disequilibrated phenomena occurring beside the equilibria – no matter how a disequilibrium is defined. While confining equilibrium locally, theorists should also admit the possibility and reality of local existence of disequilibrium, to make the concept of equilibrium falsifiable and hence methodologically meaningful. Then, we will find out that equilibria like invoked knowledge, means patterns, modules, or “anchors” that use fixed mode or output fixed responses upon certain stimuli from their diverse and changing contexts, in this way equilibria are used to deal with disequilibria, or certainty is used to deal with uncertainty -- since tight relations are juxtaposed or mixed with loose or unknown relations or irrelevance. Therefore, current computations are stratified as: some variables applicative to invoked knowledge + the rested variables assigned at one’s discretion. Both actors and researchers must face the mixedness and plurality herewith. Since it is an arbitrary, subjective, vague, and coarse conclusion of the objected world, an Algorithmic equilibrium embeds innovations as its negation or improvement. Then, some extant equilibria collapse, computations return active, and other new equilibria may establish again. History is neither a procedure of linear knowledge accumulation nor a “random walk” without diachronic continuum. Every decision or everyday means both a destination and a start. On the one hand, human must “make mistakes” to conclude computations to decide and to act, thereby forming an edition of knowledge; on the other hand, s/he will have the opportunity to correct the mistakes and to make new knowledge, thereby forming a new edition of knowledge, in this way the loop recycles. This is like the structure of an onion: a small layer of leaf is covered by a big one, then by a bigger one … thus the bulb grows. From this angle we can obtain an appropriate outlook of history: accumulative, expansive, developmental, innovative, even progressive, but also kind of chaotic, conflictive, destructive, devious, and even retrogressive. Thanks to human’s intentional selection, the former positive aspects overwhelm the latter negative ones, leading to the overall, continuous, and quite stable economic growth as a prominent social phenomenon. Apparently, all economic branches or schools has been essentially and critically included in the above panorama. Communicational costs and time make actors preferring their own businesses to social issues. However, interpersonal conflicts give rise to institutions and organizations that are used to simplify social interactions and hence bring additional benefits. People act in the institutional infrastructure as if a person computes with knowledge stocks. Price as a kind of quantitative information sensitively but limitedly coordinates behaviors, whereas other kinds of data guide various behaviors besides transactions. Thoughtful entities endogenize money and financial phenomena. All goods are unnecessary to sell out instantly, because assets, inventory, innovation and many other measures can be taken to mitigate the necessity and difficulty of market clearance. This all-factor-inclusive approach can make economic analysis easier and more effective than that of neoclassicism. Nonetheless, the market running with subjectivities, flaws, mistakes, failures, innovations, and wastes will never appear perfect, or “generally” equilibrated, as supposed by neoclassical microeconomists, thereby macroeconomic issues and policies arise. In the long run, all factors, including institutions and cultures, may be changing at their respective different speeds, and the Algorithmic discovery of infinite knowledge development will enlighten actors and researchers. The longer an equilibrium lasts, the more economical the computations with it will be. Hence, both actors and researchers often strategically pursue high-quality and longstanding equilibria. However, equilibria need not to be the only contents or ends of all analyses. An analysis can start or end anywhere as long as it is competitive in explaining or predicting realities, or in advising actions. In this boundedly rational and endogenously heterogenous framework, social researchers compete, cooperate, or trade with actors, and theoretical explanations can be occasionally superseded by predictive or advisory work, or by empirical studies. References Arrow, K.J. (1951). An Extension of the Basic Theorems of Classical Welfare Economics. 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