Knightian Uncertainty in Capitalism and Socialism.

• Author: Julian, Juan Ramon Rallo
• Position: Economist Frank H. Knight

Last year marked the centenary of the publication of Frank Knight's magnum opus, Risk, Uncertainty and Profit, which entails important and still neglected insights from a comparative economic point of view. Knight ([1921] 1957) famously discusses the importance of risk and uncertainty in the economy: he analyzes how economic agents deal with risk and reduce uncertainty--and he emphasizes the role of the uncertainty-bearing entrepreneur, explaining the function and importance of profits that arise under uncertainty.

Uncertainty exacerbates the problem of coordination in any economic system. Within the institutional framework of capitalism, people are rewarded with profits of a potentially unlimited nature when they deal successfully with uncertainty. In contrast, within the institutional framework of socialism, not only is it difficult to know when individuals have successfully handled the problem of uncertainty, but also the system of rewards is determined by an arbitrary decision of central planners.

In this article we compare the means by which capitalism and socialism deal with the problem of uncertainty emphasized by Knight and later developed by economists in the Austrian tradition. Whereas socialism and capitalism have been compared in many other respects in the past, the main contribution of this article consists in offering a comparative economic analysis of these systems' different types of uncertainty and of their capacity to reduce that uncertainty. In a world in which the idea of socialism still exerts attraction (Niemitz 2019), we shed new light on the problems of socialism. Ultimately, we show that within the institutional framework of socialism, economic agents must face an amount of unmitigated pure uncertainty that under capitalism is either completely absent or significantly reduced by profitseeking entrepreneurs.

After the publication of Risk, Uncertainty and. Profit Knight himself dedicated much of his research and writing to the comparative analysis of political and social institutions and a general defense of a free society. Indeed, his wider interest in social institutions permeates his work as an economist and social philosopher (Emmett 2009). And Knight addresses the way in which the problems that uncertainty poses for planning in a firm are relevant to planning for society (Emmett 2021). Nevertheless, Knight never systematically applied his concept of uncertainty to a comparative analysis of capitalism and socialism, even though he touched upon the issue and discussed problems of socialism (Knight 1939; 1940). This paper helps fill that gap.

How Institutions Reduce Uncertainty

Games and Uncertainty

A game-theoretical framework is useful for examining how institutions reduce uncertainty through the three strategies that Knight thought were essential for that purpose: consolidation of probabilities, dissemination of information, and incentives to specialize in bearing immeasurable risks.

Interactions among people can be described in the form of games. Every game is composed of the players (or agents) who participate in it, the potential strategies (or action plans) of each player, the payoffs that each player receives under each strategy, the rules--physical and social--that define the nature of the game, and the information that each player has about the other(s). For example, chess is a game with two players in which the players sequentially make strategic decisions that have certain payoffs. The number of players, the types of strategic decisions that are admissible, and the payoff linked to each type are defined by the rules of the game. If the rules were different, the game--that is, the terms of strategic interaction--would be different (von Neumann and Morgenstern [1944] 1953, 49-50).

When all players know all the information about the elements of the game, including the past decisions of other players, and all know that they all have that information, all those elements are common knowledge and, consequently, it is a game with complete and perfect information (von Neumann and Morgenstern [1944] 1953, 49-50) in which the payoff of each strategy is certain. For example, chess is a game of complete and perfect information because all the players know the structure of the game (and all know that all know it) and, moreover, actions are taken sequentially: each player can fully observe the strategic decision of the other player before making his own decision and therefore can know perfectly what all the possible decisions he can make during his turn imply.

When, in contrast, players have common knowledge about the structure of the game but not about the past or simultaneous decisions made by the other players, it is a game of complete but imperfect information (von Neumann and Morgenstern [1944] 1953, 183): the payoff of each player's strategy is not certain, but each player knows the structure of the game and therefore also knows the totality of the potential strategies that the other players could follow and the payoff linked to each of them. That is, each player is able to estimate the expected payoff of each of the strategies based on the information available about the structure of the game. Expressed differently, since the structure of the game restricts the potential states of the world and predetermines the probability of each of them, each player can estimate the expected value of her strategy from the information she has about the structure of the game.

For example, poker is a game of complete but imperfect information. Each player knows the rules of the game and the potential card combinations of her opponents, but she does not know the specific combination of cards that each player has in each hand, so she can only estimate probabilistically the payoff of her own combination of cards. Thus, a player can estimate the probability that another player will use the five-of-a-kind strategic move in a poker game:

P(five of a kind) = P(five of a kind \ poker)

Finally, when there is no common knowledge about the structure of the game, it is a game with incomplete information (von Neumann and Morgenstern [1944] 1953, 30). Information is incomplete when, for instance, some of the players do not know the number of players participating in the game, the different strategies available for each of them, the payoffs linked to each of the strategies, the rules of the game, or the information that the rest of the players have about each of these elements. In games with incomplete information, not only are the payoffs of each player not certain--as in games with imperfect information--but, as the structure of the game is also unknown, the number of states of the world is potentially infinite. Therefore, the players cannot estimate the probability distributions of the individual strategies based on the structure of the game. For example, if a player does not know whether he is playing chess, poker, blackjack, Go, or any other game, then he cannot estimate the expected value of his strategies based on the structure of the game; on the contrary, the structure of the game itself is the object of probabilistic estimation by each player:

P(five of a kind) = P (five of a kind\poker)* P (poker) + P(five of a kind\blackjack) * P (blackjack) + P (five of a kind\Go)* P(Go) ...

If the probabilistic estimation of the game's structure could be determined from the structure of some metagame (for example, if the game the agents are playing was determined by throwing a pair of dice), the game would still be one of complete and imperfect information. But if, on the contrary, there is no metagame from whose structure the probability of the different states of the world can be determined, then probabilistic estimates are based only on the beliefs of each player (their assumptions about the different states of the world). In this case, the distribution of probabilities is personal and depends on the varying degrees of confidence players have in beliefs B (Tarko 2013):

P (five of a kind | B) = [summation over i] P (five of kind|[game.sub.i], B) * P([game.sub.i] | B)

When players can determine the probability of the different states of the world from the structure of the game (or a metagame), those probabilities are objective. In other words, if the structure of the game (or the metagame) is common knowledge, the probabilities are necessarily objective, and all the agents will be able to discover them. Additionally, it is possible to speak of objective probabilities when all the agents share the same beliefs and all are conscious of that fact, so that their probability estimates based on those beliefs become identical when they possess the same information set. Conversely, probabilities are subjective when they cannot be derived from the structure of the game itself or when the beliefs of the agents are not convergent. In such a case, the probability estimates of the agents will diverge even when the agents possess the same information set (Cox 2006, 71-73).

The concepts of objective probability and subjective probability, or games with imperfect information and games with incomplete information, are equivalent to the concepts of risk and pure uncertainty as developed by Knight (Harsanyi 1967). Knight distinguishes between measurable risk and immeasurable uncertainty, which he regards as a unique kind of risk ([1921] 1957, 19-20, 48). For Knight, uncertainty is of utmost importance, and it forms the basis of his entire economic oeuvre. Not by chance, the term figures prominently in the title of his magisterial Risk, Uncertainty and Profit. Uncertainty is intimately tied to human nature. It is a consequence of free will ([1921] 1957, lxiii) and our incomplete knowledge (198). And "uncertainty is one of the fundamental facts of life" (347).

Measurable risk is foreseeable and can be converted into fixed costs because "the distribution of the outcome in a group of instances is known (either through...