فرمول بندی تئوری بازیها و رقابتهای تصمیم گیری تحت شرایط عدم اطمینان و خطرپذیری

A game setting is developed for decision making under conditions of uncertainty and risk for a general class of problems. The methodology is illustrated using assumptions governing future oil prices and environmental degradation to evaluate long term investment alternatives.

The essence of a decision is the decision maker’s personal balance of expected payoff and risk. A game theory formulation of decision making under conditions of uncertainty and risk, made possible by an appeal to the Central Limit Theorem, allows us to extend our basic understanding of decision making to a large class of complex decision problems with time as an independent variable. In general, the decision maker plays against NATURE in a single move game. At the time the decision maker moves, NATURE’s time dependent strategy is hidden forcing the decision maker to consider NATURE’s strategy as uncertain. The formulation presented here maintains a distinction between uncertainty modeled without assuming a distribution and risk arising from quantifiable random variability, i.e., with a distribution. A standard definition of game theory: “Game theory is the study of the ways in which strategic interactions among rational players produce outcomes with respect to the preferences (or utilities) of those players, none of which might have been intended by any of them.” (Stanford Encyclopedia of Philosophy) provides motivation for our development and indicates the hopes we have for its application. As an illustrative example, we will demonstrate how assumptions governing future oil prices and environmental degradation can be used to evaluate long term investment alternatives in a game setting, supporting strategic thinking in a real world problem scenario. We are presenting a complete decision methodology. Using the example, we will show how easily and transparently the modeling and decision methodology can be implemented. Outline of the paper: Section 2. An introduction to the problem of evaluating long term investments in a decision environment of increasing oil prices and environmental degradation. This decision problem both motivates and illustrates our modeling/decision methodology. Section 3. We are faced with two tasks: making sense of this unexplored complex investment environment, i.e., constructing meaningful models of the decision environment accounting for what we know, what we are willing to assume, and what is unknown, and developing a rational decision methodology based on the models. In Section 3 we develop a family of investment models. Section 4. In this section we develop a family of general decision models. Basically, we introduce a two person game with players NATURE and PLAYER. NATURE’s strategies are future oil prices and environmental degradation. PLAYER’s strategies are rational investment decisions. We provide a complete computational example illustrating the construction of the decision models. Section 5. We introduce a decision methodology which is an extension of multi-criteria decision analysis, replacing random criteria values with deterministic surrogates specifying risk. The criteria and surrogates are functions of the uncertainties. The decision goal is a balance of expected payoffs and risk. Section 6. In the concluding remarks we address questions of more than two uncertainties and more than one criteria for evaluating an investment.

Decision problems with more than two uncertainties might present themselves. We are presenting exploratory models which suggest that more than three uncertainties might make the analysis unwieldy. Rather than employing a large number of uncertainties, the modeler might attempt problem decomposition. We have found that considering a larger problem as a collection of smaller problems that result from a multilevel decomposition is a fruitful approach [5]. Producing the second order statistics for an investment alternative using triangular distributions seems to fit the usual thought pattern for many investors. Binomial distributions are also common. The game formulation for investment decisions can handle a range of possibilities. Our interest is decision problems for a new era. Rapidly rising oil prices and degradation of the environment on the scale discussed reduces the relevance of past history. Still estimations of the second order statistics for an investment alternative based on history might have a place. We certainly experienced massive social changes which impacted investment valuations in the 20th century. An important point in our presentation is the possibility for a wide ranging decision analysis. We can visualize alternate visions of the future. Indeed, environmental degradation could have a major impact on the price of oil resulting in precipitous price declines. We have modeled the two uncertainties as independent variables. The decision models could be more complex in a different sense. We might have more than one criteria for evaluating an investment alternative and the criteria could “interact”. The performance of an alternative measured by one criterion might influence the performance measured by another [5]. This additional complexity could be modeled within our framework and support still more decision analysis for the decision maker.