Payoffs

Fig. 11. Wke-coatiag line A, unwinding of wine (payoff) B, stiaightenei C, pieheatei D, extrudei E, watei trough F, tester G, capstan (puUer) and H,...

These rolls are driven by motors and /W, whose speed is controlled through the tension of the travelling sheet. The tension of the sheet is adjusted by monitoring the diminishing diameter of the payoff roll and the thickness of the sheet. 

Scheiman, A. D., Analysis Shows FCC Power Recovery Payoff, Oil and Gas Journal, October 2, 1978. 

Payoffs to Using Agent-Based Models of Combat... 

The payoff of an agent-based approach is a radically new way of looking at fundamental issues of land combat. Models such as these are emphatically not to be used for prediction rather they are best used to enhance understanding. Specifically, agent-based models of combat are designed to help military theorists... 

As you study organic chemistry, take the time to work the problems. Do the ones you can, and ask for help on the ones you can t. If you re stumped by a particular problem, check the accompanying Study Guide and Solutions Manual for an explanation that will help clarify the difficulty. Working problems takes effort, but the payoff in knowledge and understanding is immense. 

The pursuit of operations research consists of (a) the judgment phase (what are the problems ), (b) the research phase (how to solve these problems), and (c) the decision phase (how to act on the finding and eliminate the problems). These phases require the evaluation of objectives, analysis of an operation and the collection of evidence and resources to be committed to the study, the (mathematical) formulation of problems, the construction of theoretical models and selection of measures of effectiveness to test the models in practice, the making and testing of hypotheses as to how well a model represents the problem, prediction, refinement of the model, and the interpretation of results (usually as possible alternatives) with their respective values (payoff). The decision-maker generally combines the findings of the... 

We give the payoff matrix of a game whose two players are X and Y... 

Here ai is the payoff that Y, using strategy Yjt makes to X for using strategy X. Obviously the payoff from X to Y is — ow. 

In a continuous game both the choice of strategy and the payoff as a function of that choice are continuous. The latter is particularly important because a discontinuous payoff function may not yield a solution. Thus, instead of a matrix [ow], a function M(x,y) gives the payoff each time a strategy is chosen (i.e., the value of x and y are fixed). The strategy of each player in this case is defined as a member of the class D of probability distribution functions that are defined as continuous, real-valued, monotonic functions such that... 

Special cases of continuous games have received considerable treatment. These are games whose payoff function is convex (which we have already defined) or separable, i.e., can be written in the form... 

Note that essentially each person has an investment of 1.5 when he starts. Thus the reader may forget the object and play the money game according to the rules given. For example, the element in the first row and second column shows that X who bid zero loses the object and therefore Y gets the object which is worth 3, thereby making a profit of 1.5. Since the matrix represents the payoff from Y to X we use —1.5 indicating that thereby X pays Y, i.e., he loses his investment. 

Example 4.—The following fighter-bomber dual illustrates a continuous game.15 The payoff (given by the probability of hitting) when... 

Decision Theory Formalism in the Behavioral Sciences.46—A formal method for examining decisions is developed through the use of a utility matrix [ tj] similar to the payoff matrix of game theory. In this matrix the rows correspond to the various possible acts of a decision-maker (e.g., to invest money in enterprises AltA2, -, Am) and the columns to various states, i.e., circumstances (e.g., possible levels of development of each enterprise) under which the acts are performed. The element y gives the utility (return or value) for using act At when state sf prevails. 

Particles spin Vz, 517 Dirac equation, 517 spin 1, mass 0,547 spin zero, 498 Partition function, 471 grand, 476 Parzen, E., 119,168 Pauli spin matrices, 730 PavM, W., 520,539,562,664 Payoff, 308 function, 309 discontinuous, 310 matrix, 309... 

There is exciting new engineering and science in the old field of fuel cells. Even more important, the payoff of this research may be a truly stunning advance in our use of energy. 

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