The general theory of utility is an attempt to substantially generalize the majority of classical and modern theories that link the concept of utility with decision-making under uncertainty.
Content
Introduction to the problem
The basis of scientific and applied research in the field of utility theory is the fundamental assumption that a rational individual, in the process of free choice, tries to maximize a value that reflects the usefulness of making a particular decision in comparison with other possible alternatives. Such a choice is actually the main subject of the theory of utility throughout the entire history of economics from the fundamental works of Bernoulli to the present day. If a - vector of all outcomes and - probabilities associated with each of them, then utility in the most general form is expressed by the model of the form
which predicts or even prescribes the rational behavior of the individual as the desire to maximize this function.
Research Directions
The existing modifications of the utility theory with different degrees of success are applied in problems of analysis and forecasting in economics, market research, as well as in other areas of decision making.
Meanwhile, numerous paradoxes, observed in real situations, have led to numerous attempts to improve the basic model and its complications, which, however, lie in a purely technical plane.
Paul J.Shoemaker contains a detailed analysis of this movement of thought and an evolution of the main forms of the utility function.
one. Expected cash prize.
2 Bernoullian expected utility.
3 The expected utility of von Neumann-Morgenstern.
four. The theory of reliable equivalents (Schneeweiss, 1974; Handa, 1977, Finetti, 1937).
five. Subjective expected utility (Edwards, 1955).
6 Subjective expected utility (Rasey, 1931: Savage, 1954; Quiggin, 1980).
7 Weighted Cash Gain
eight. Perspective Theory (Kahneman and Tversky)
9. ∑w (pi) u (xi) Subjective weighted utility (Karmarkar, 1978)
Where , , , - Functions used to refine the base model.
Despite these clarifications, it can be stated after A.Tversky, D.Kahneman that the theory of utility, considered as a rationale for rational decision making, is fundamentally unstable due to all the inherent errors of human thinking (heuristic, references, forms, and the like).
This instability is very significantly manifested in the tasks of practice.
For example, with reference to the tasks of analyzing and predicting the behavior of markets, suppose that - the price of some asset considered as a function of time, but - its somehow measured utility. Let's combine the graphs of these functions on the same plane as follows:
From the graph it follows that (with some delay) the growth of the utility function should be observed and the growth of the asset price; following peak 2, utility begins to decline, and the price of the asset also decreases. And so on until the next peak, after which the utility and price grow and the picture repeats.
This logic often turns out to be wrong, and the practice will come up with counterexamples refuting the connection of these arguments with real events in the markets.
In addition, within this approach, there is no place for forecasts and even explanations of crises that shake markets, since the fall and collapse of asset prices can occur in an environment of growing or at least non-decreasing utility.
Generalization
The general (generalized) theory notes that if there is an asset on the market that maximizes subjective utility for the buyer, this does not mean that the asset will actually be bought (at least at the moment of the decision).
At the same time, the following obvious, but nontrivial fact takes place:
if among the assets that a freely acting buyer assesses in the market, there is at least one whose purchase he (the buyer) considers to be obviously unacceptable for himself, then the transaction is guaranteed not to take place (at least at the moment of making the decision).
The basic principle of the general theory of utility is:
the most attractive asset will not necessarily be bought, but the most unattractive asset will not necessarily be bought.
Let be - vector of possible outcomes. Unattractiveness is viewed as functional. on a set that matches each possible outcome x some numeric value characterizing the dislike of this outcome. The value of unattractiveness can be the magnitude (subjective, expected, imaginary, etc.) of damage, loss, overpayment, risk, rejection, etc .; wherein is a function of time.
Based on the above reasoning, it can be argued that an asset, the unattractiveness of which for most market participants is high, will not be bought by them and the price of such an asset (at least in the short term) will not grow.
Analysis and forecast based on the general theory
On this basis, a number of new approaches and trading strategies in global markets can be formed.
Without touching upon the features of building the function of unattractiveness, it can be assumed that at key points of market reversals its chart will be symmetrical to the price chart of the asset relative to the t axis, i.e. maximum at the top of the graph matches minimum Price at the bottom.
The upper part illustrates the function changes. the unattractiveness of the estimated asset for the market participant, the lower - changes in the market value of the asset.
The logic of visual analysis is as follows.
1. In the interval t0-t1, the asset’s unattractiveness increases, and the market price rises too. If this opinion is shared by the majority of participants in this market, then we can predict a price reversal with its further decline.
2. In the interval t1-t2, the asset’s unattractiveness increases, and the price falls. This situation is logical and reflects a diminishing self-sustaining trend.
3. On the interval t2-t3, the asset’s unattractiveness falls, and its price increases. The graph shows the increasing trend as the general opinion of the participants.
4. In the interval t3-t4, the asset’s unattractiveness falls and the price falls. If this opinion is shared by a significant part of market participants, then we can predict a price reversal.
Similar examples of symmetry can often be observed when comparing current price charts for underlying assets with futures and options quotes, as well as analyzing some intermarket interactions.
It is necessary to note the fundamental possibility of a quick and even spasmodic growth of the function d (x), which can be used as an explanation (and sometimes a forecast) of avalanche-like sales in the markets.
A somewhat different formulation of the problem is also possible.
Let be - probability of making a decision on the purchase of some asset . It can be assumed that there is a value such that from inequality
equality follows
That is, the value is essentially a threshold value, starting from which the outcome with a value of unattractiveness greater than or equal to q becomes completely unacceptable (“revolts”) for the buyer.
For example, the price of land plots near Kiev (Ukraine) decreases non-monotonously with distance from the center of the capital, but turns to zero when reaching a distance of 30 km from Chernobyl (the site of the accident of a nuclear reactor in 1986).
Thus, a specific asset, accompanied by a “roll over” of the unattractive functionality, can be excluded from further selection even with an increase in expected utility, which is a manifestation of investor rationality.
There is a stronger problem statement. It is assumed the existence of two thresholds: utility - close to max and unattractiveness - close to min .
In this formulation, the decision to purchase assets x in the free market is made if and only if the conditions are simultaneously fulfilled:
- no less than the predetermined value ; - no more than a predetermined value .
Such “filters” with step-by-step change of thresholds and can be used to develop short-term forecasts of global markets.
Conclusions
The general theory of utility postulates: a market participant is not always guided by its behavior by maximizing subjective utility, but acting without coercion in the decision-making process always seeks to minimize the subjective unattractiveness d (x).
In addition, it should be noted that it is possible in principle to use the methodology of the general utility theory in tasks of a different kind: for example, in diagnostics with the subsequent choice of treatment methods, in pre-election forecasts and the design of political technologies, pre-design engineering and economic research.
Literature
- Paul J.Shoemaker. The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations. - Journal of Economic Literature, June 1982. - 529-563 p.
- Tversky A., Kahneman D. Advances in Prospect Theory: Cumulative Representation of Uncertainty. - 1992.
- J. von Neumann, O. Morgenstern. Game theory and economic behavior .. - M, 1970.
- Rosenfeld A.I. Abstracts to the general theory of the utility of economic behavior .. - Kiev: Economy of Ukraine, 2007. - №10 p.
See also
- Theory of Unexpected Utility
- Perspective theory
- Theory of subjective expected utility