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# Probabilistic decision making

## on Jul 14, 2010

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## Probabilistic decision makingDocument Transcript

• If there are finite number of competitors called players
• A list of finite or infinite number of possible courses of action is available to each player
• A play is played when each player chooses one of his courses of action. The courses are assumed to be made simultaneously, so that no player knows his opponent’s choice until he has decided his course of action.
• Every player i.e, combination of course of action is associated with an outcome, known as the pay off generally money, which determines a set of gains, one to each player. Here a loss is attributed to a negative gain.
• A game involving n players is called n-person game.
The value of the game theory is in understanding the likely outcomes of a business<br />issue when the outcome is dependent on actions taken by other parties with potentially<br />conflicting interests. In Game Theory we assume that every party acts rationally and<br />takes action based on their preferences.<br />
• Game theory solver explains explain the basic listing of players, options available to them and their preferences.
Game theory SolverStrategy <br /> Options <br />preferencesOutcomes PlayersTactics<br /> A typical game theory project would consider 20 – 25 different<br /> options. The output of the process is a set of outcomes<br /> one is called the “Natural Outcome”, resulting from all players <br /> following their natural self interest. Another is the “Best Attainable<br /> Outcome” (for the client), resulting from the client also taking subtle <br /> and possibly counter intuitive actions.<br />Probabilistic decision Analysis:<br />Probabilistic decision analysis processes have high value in cases where the value of different<br />outcomes is highly dependent on quantifiable external uncertainties that are not determined by<br />actions taken by identifiable players. Examples of such uncertainties could be the weather, the<br />foreign exchange rate, and the future price of oil. Uncertain future events are represented as<br />decision trees or probability distributions. <br />Decision Analysis can be well explained like the game theory block diagram.<br />Quantitative Decision AnalysisStructure<br />Expected Value<br />Options <br />Uncertainty <br />The input of a decision analysis process is the structure of an issue (influence diagram or<br />decision tree), with identified external uncertainties and decision variables.<br />Typically, a decision analysis would handle two to four actions (or decisions). The outcome of a<br />formal decision analysis is a recommended or preferred set of decisions for the client.<br />Similarities:<br />Although the analysis processes and tools are quite different, success of a project using either<br />methodology is quite dependent on participation by the right individuals from the client company<br />and skilful facilitation of the process. A strong knowledge elicitation methodology is essential to<br />either process and several facilitation tools can be applied equally well. Secondly, organizations that are receptive to objective and structured decision-making processes tend to like both processes, whereas purely intuitive decision cultures are not receptive.<br />Differences:<br />Game Theory has advantages in situations where the best course of action is dependent on<br />actions by other players. It is easier to apply where there are multiple value measures (where<br />a single decision criteria such as expected Net Present Value is not feasible). A typical<br />Game Theory project can be done in a little over a week, with 10hours of client team<br />involvement. Last, the Game Theory process is strong when there are too many outcomes to allow financial analysis (a typical case has 20 options, or 220 = 1 Million outcomes).<br />Decision Analysis is advantageous in cases where the decision uncertainty is caused<br />primarily by quantifiable uncertainties (e.g. the probability of success of a technology, the price of a commodity, an exchange rate), not dependent on the choices made by other<br />players. Decision Analysis requires the issue to be condensed into a small number of outcomes<br />and two or three decisions. Last, decision analysis provides a financial result (Expected<br />Value), which is often necessary to justify an investment.<br />Choosing the correct methodology:<br />Both the methodologies have their own application areas. In some instances, both could be used as a combined product. For issues pertaining to preferences where uncertainty and amount of calculated risks are involved game theory will be the preferred choice. This can be explained with a block diagram.<br />Decision Analysis block diagram<br />Game theory Solver<br /> <br /> Players <br />Strategy<br /> Options Tactics<br /> Preferences Outcomes <br />Quantitative Decision Analysis<br /> Uncertainties<br />A critical input for a game theory case is the preferences of the various players, including the<br />client company. The preferences are elicited from the client team. If the client has undertaken<br />quantitative analysis, taking into account uncertainties, than this quantitative analysis<br />influences the client’s preferences. However, it must be recognized that a client team will<br />always have a set of preferences, whether they’ve done formal analysis or not. Then the<br />game theory analysis will show what the possible outcomes will be.<br />Where feasible, we recommend that the Natural Outcome and the Best Attainable Outcome<br />be further analyzed using a Decision Analysis process. This may or may not result in a revised<br />set of preferences.<br />This can be explained with an example to make one understand probabilistic decision making. Let us consider a management which has a preference in order of priority. This issue has a major concern for labor relations.<br />
• Cutting wages
• Downsizing
• Limiting early retirement
If we evaluate the given situation using game theory, we find that there a possible outcome of a strike. Subsequent decision analysis shows that the cost of strike is very high which exceeds the benefits of the wage cut. The early retirement policy scheme is very expensive. After considering these evaluations the management makes a decision as follows.<br />
• Limiting the early retirement
• Downsizing
• Not cutting wages.
From this situation, game theory was used to narrow down the cases that needed to be analyzed. Game theory provided a clear perspective on the likelihood of a strike and then a Decision analysis was used to get an optimal solution on the expected value alternative course of action as described in the block diagram.<br />Taking another example of making probabilistic decision making under uncertainty we can more understand this concept.<br />Subject images and feeling towards winning a lottery are likely to be the same whether the chance of winning is 1 on 1 million. Emotions in uncertain or risky situations seem to be sensitive to the possibility rather than the probability of strong positive or negative consequences, causing an overweight of very small probabilities-Loewenstein et al., 2001. Rottenstreich and Hsee (2001) found that the strong sensitivity to departure from impossibility and certainty and the insensitivity to changes in probability within a broad midrange of values is<br />even more dramatic for affect favorable for affect no favorable outcomes. <br />Introduction to Contextual variables lead to proximity of outcomes and see how choices affect them. Proximity variable can be defined over different dimensions like temporal, spatial and social factors. Proximity measures should not have any impact on a cognitive-driven decision process; however, they could play a role in affective driven one. The laboratory experimental method seems to be the most appropriate way to assess the impact of proximity on choices under uncertainty. In fact, relying on field data makes it disentangle, the impact that proximity has on the cognitive perception of risk and impact of proximity on choices under uncertainty. In fact relying on field data makes it disentangle, the impact it has on proximity of its cognitive perception of risk and impact that it has on the emotional system. When contextual aspect is considered many researchers question on do risk preferences change according to how outcomes are usually described? Do risk preferences change whether the resolution of uncertainty is immediate or delayed? Are the risk choices affected by the presence of other people at the moment of decision or at the moment of uncertainty resolution?<br />This paper is mainly concerned with empirical nature of the probabilistic decision making. The above mentioned examples provided the theoretical contributions to the economics and social psychology with the objective to develop a systematic approach and method to develop an empirical and theory validation model. This paper made me learn and go through various articles, journals and books from British council library pertaining to the decision making analysis and statistics journals and books helped on probabilistic decision making. However, this topic not only made me learn the existing theory but also the way these theories are involved in probabilistic decision making under risk and uncertainty of various dimensions.<br />A potentially useful and relatively unexplored source of data comes from websites where decisions under risk and uncertainty made me understand the most common and prevalent on line gambling which falls under probabilistic decision making.<br />Results:<br />Emotions are the fundamental element for decision making under risk and uncertainty. The way this paper was analyzed with emotions while making decision under risk and uncertainty made me feel a lot about how decision were made and how should decision be made in future concerning various parameters and emotional constraints.<br />References:<br />Operations Research –Prof .V.Sundaresan, Prof.K.S Ganapathy Subramanian, Prof.K.Ganesan<br />Miller and Freund’s Probability and Statistics for Engineers Edition 7<br />Operations Research – Taha edition 6<br />CSS online tutorial<br />Mellers, B.A., Schwartz, A., Ho, K., and Ritov, I. (1997). Decision affect theory: emotional reactions to the outcomes of risky options.<br />Mano, H. (1994). Risk-Taking, Framing Effects, and Affect. Organizational Behavior<br />and Human Decision Processes.<br />O'Donoghue, T. and Rabin, M. (2000). The Economics of Immediate Gratification.<br />Journal of Behavioral Decision Making.<br />Rubinstein, A. (2003). Instinctive and Cognitive Reasoning: A study of Response<br />Times. Tel-Aviv and NYU Working Paper.<br />Slovic, P., Finucane, M.L., Peters, E., and MacGregor, D.G. (2002). The affect heuristic.<br />In T. Gilovich, D. Griffin, and D. Kahneman (Eds.), Heuristics and Biases: The<br />psychology of intuitive judgment, (pp. 397-420), New York: Cambridge University<br />Press.<br />Loewenstein, G. and ODonoghue, T. (2004). Animal Spirits: A_ective and Deliberative<br />Processes in Economic Behavior. Social Science Research Network.<br />Loewenstein, G. (2000). Emotions in Economic Theory and Economic Behavior. The<br />American Economic Review, 90 (2), 426-432.<br />Ketelaar, T. and Todd, P.M. (2000). Framing our thoughts: ecological rationality<br />as evolutionary psychologys answer to the frame problem. In S.P. Davies and H. R.<br />Holcomb (Eds.), The evolution of minds: psychological and philosophical perspective,<br />Kluvier, Dordrecht.<br />Isen, A.M. and Geva, N. (1987). The influence of positive affect on acceptable level<br />of risk: the person with a large canoe has a large worry. Organizational Behavior and<br />Human Decision Processes, 39, 145-154.<br />Elster, J. (1998). Emotions and Economic Theory. Journal of Economic Literature,<br />36, 47-74.<br />Frank, R.H. (1988). Passions within reason: the strategic role of the emotions. New York:<br />W.W. Norton.<br />Bell, D.E. (1985). Disappointment in decision making under uncertainty. Operations<br />Research, 33, 1-27.<br />Bell, D.E. (1982). Regret in decision making under uncertainty. Operations Research,<br />30, 961-981.<br />