Game Theory Strategy Philip Straffing

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X, 244 p.: 23 cmGame theory is the study of how people play games. What is the proper strategy to employ when the game situation is in constant flux and other players are forming different strategies? Since 1944, game theory has been applied to a variety of situations including economics, politics, philosophy, social psychology, and biology. This book serves as an introduction to game theory and requires no more math skills tha basic algebraIncludes bibliographical references (p. 217-224) and indexNotesObscured text on front cover.

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Book Description:This important addition to the New Mathematical Library series pays careful attention to applications of game theory in a wide variety of disciplines. The applications are treated in considerable depth. The book assumes only high school algebra, yet gently builds to mathematical thinking of some sophistication. Game Theory and Strategy might serve as an introduction to both axiomatic mathematical thinking and the fundamental process of mathematical modelling. It gives insight into both the nature of pure mathematics, and the way in which mathematics can be applied to real problems. Game theory is the logical analysis of situations of conflict and cooperation. More specifically, a gameis defined to be any situation in whichi) There are at least two players.A player may be an individual, but it may also be a more general entity like a company, a nation, or even a biological species.ii) Each player has a number of possible strategies,courses of action which he or she may choose to follow.iii) The strategies chosen by each player determine the outcomeof the game.iv) Associated to each possible outcome of the game is a.

We saw in Chapter 1 that a two-person zero-sum game where Rose has mstrategies and Colin has nstrategies can be represented by an m × narray of numbers, giving the payoffs from Colin to Rose for each of the m npossible outcomes. Such an array is called an m × nmatrix, so these games are also known as matrix games.Rose wishes to choose a row of the matrix which will result in a large number; Colin wishes to choose a column which will result in a small number.Before reading further, I would. We saw in Chapter 2 that in some matrix games the row maximin and the column minimax are different numbers, and in those games there is no saddle point. For example, considerSince there is no saddle point in this game, neither player would want to play a single strategy with certainty, for the other player could take advantage of such a choice. The only sensible plan is to use some random device to decide which strategy to play. For example, Colin might flip a coin to decide between A and Colin B. Such a plan, which involves playing a.

One important school of anthropological thought, known as functionalism,holds that customs, institutions or behavior patterns in a society can be interpreted as functional responses to problems which the society faces. One method, then, of understanding the organization of societies would be to identify problems and stresses, see what kinds of behavior would provide good solutions, and compare a society's behavior patterns to those solutions. For example, incest taboos can be interpreted as societal solutions to genetic problems caused by inbreeding.In the 1950’s some pioneering anthropologists began to use game-theoretic ideas in the service of functionalism. For example, Moore.

Zero-sum games represent conflict situations, and our solution theory for them prescribes rational strategies for conflict. Since the most extreme form of conflict is war, it is not surprising that some of the first proposed applications of game theory were to tactics in war. Haywood 1954 and Beresford and Peston 1955 describe some applications of game theory to situations from World War II. In this chapter we will consider two applications in more modern settings. Both will be far too simplified to be realistic, but they may give the flavor of what kinds of contributions zero-sum game theory might make.

One of the most persistent problems of philosophy is the problem of free will.Is human will free, or are our actions determined? One way to approach this problem is to consider the possibility of predicting any person’s decision in some unconstrained choice situation.

Suppose I ask you to decide consciously to hold up your left hand or your right hand, and tell you that I have written on a slip of paper my prediction of what you will do. Is it possible, in principle, for me to know enough about you to make my prediction with better than chance. In matrix games we have assumed that the players make their choice of strategy simultaneously, without knowledge of what the other player is choosing. This would seem to be a major limitation of the theory, since in real conflict situations decisions are often made sequentially, with information about previous choices becoming available to the players as the situation develops.

In this chapter we will consider a method of modeling such sequential choice situations by a game tree.We will find that, perhaps surprisingly, this new model can always be reduced to our old model of a matrix game.As a. In the business world, companies often have to make decisions which involve strategic uncertainty about what other companies will do.

Such decisions usually also involve uncertainty about future economic conditions, market size, costs, and other variables. In other words, companies often play games which involve both other players and chance. In games like this the role of information, both about what other companies might do and what chance might do, can be very important.In this chapter we will consider a simple example of a competitive situation which can be formulated as a two-person zero-sum game. We will focus specifically. In the discussion so far, we have mostly assumed that the numerical payoffs in our game matrices or game trees are given. We have not paid much attention to where the numbers come from or exactly what they mean. It is time to consider more thoroughly the process of assigning numbers to outcomes, for the applicability of game theory to real situations rests on the assumption that this can be done in a reasonable way.

Von Neumann and Morgenstern were very conscious of this dependence, and they began the Theory of Games and Economic Behaviorby laying the groundwork for. In our discussion of Jamaican fishing in Chapter 4, we noted that when one player in a two-person zero-sum game is not a reasoning entity capable of the forethought and adaptive play which game theory assumes of players, the minimax solution concept may not apply. On the other hand, we argued that it may still be applicable, depending on the goals of the rational player in the game. In this chapter we will examine in greater detail possible ways of playing a game against Nature, an unreasoning entity whose strategic choice affects your payoff, but which has no awareness of.

If a two-person game is not zero-sum, we must write both players’ payoffs to describe the game. If we have a game in which the payoffs to the players do not add to zero, recall from Chapter 9 that the game still might be equivalent to a zero-sum game, in the sense that it could be made zero-sum by a change of utility scales.

In such a game, the interests of the two players are strictly opposed, and we can analyze it by zero-sum methods. In general, however, the interests of players in a non-zero-sum game are not strictly opposed. In 1950 Melvin Dresner and Merrill Flood at the RAND Corporation devised Game 12.1 to illustrate that a non-zero-sum game could have an equilibrium outcome which is unique, but fails to be Pareto optimal.Later, when presenting this example at a seminar at Stanford University, Albert W. Tucker told a story to go with the game (see Straffin, 1980). The players are two prisoners, arrested for a joint crime, who are being interrogated in separate rooms. The clever district attorney tells each one thatif one of them confesses and the other does not, the confessor will get a reward.

As a central part of their monumental study The Authoritarian Personalityin 1950, T. Adorno and his co-workers developed one of the prototypes of the personality inventories now so familiar to us all. The F-scale inventory was a series of statements to which subjects were to respond by writing a number from 1 (strongly disagree) to 7 (strongly agree). The statements were designed to test personality variables which, the authors argued, underlay susceptibility to authoritarian ideologies. Here are the personality variables included, together with corresponding sample items from the inventory:Conventionalism:“One should avoid doing things in public which.

In our analysis of non-zero-sum games up to this point, we have required that the players choose their strategies simultaneously and not communicate with each other beforehand. Of course, games in real life may not be like this.

In this chapter we will consider some of the things which might happen when one player can move first and make his move known to the other player, or when the players can talk to each other before they move. Commitments, threats, and promises become possible. The classic analysis of these kinds of “strategic moves” is Sendling, 1960, which I strongly recommend. The idea of an evolutionarily stable strategy (ESS), first introduced by John Maynard Smith and G. Price 1973, is a powerful explanatory idea in evolutionary biology. It is especially applicable to the study of behavior, and has found an important place in modern sociobiology.

The basic idea is this. Because individual members of a biological species have similar needs, and resources are limited, conflict situations will often arise. In these conflict situations, there are many different behavior patterns (strategies) which individuals might follow. Which ones will they choose?

Since the question involves behavior in conflict situations, a game-theoretic formulation. In our analysis of non-zero-sum games up to this point, the players have played non-cooperatively.

Each has tried to do the best possible for himself by choosing strategies or by making strategic commitments, threats or promises. In this chapter we will consider a different approach. Imagine the players sitting down together to decide what is a reasonable or fair outcome to the game, and then agreeing to implement that outcome. Alternatively, imagine that the players call in an impartial outside arbitrator to determine a reasonable and fair outcome, and agree to abide by her decision.

What principles should guide the. The management of a factory is negotiating a new contract with the union representing its workers. The union has demanded new benefits for its members: a one dollar per hour across-the-board raise, and increased pension benefits. M5025 mfp drivers for mac windows 10.

In turn, management has demanded concessions from the union. Management would like to eliminate the 10: 00 a. Coffee break, which has proven to be excessively costly as workers straggle slowly back to the assembly line, and to automate one of the assembly line checkpoints. The union opposes both demands, especially the automation, which would eliminate union jobs. The dispute has not been.

A duopolyis a situation in which two companies control the market for a certain commodity. The duopoly problem is to decide how the companies in a duopoly situation should adjust their production to maximize their profits. In this chapter we will use a simple example to compare four different “solutions” to the duopoly problem. Some of the solutions involve calculus—at least knowing how to differentiate polynomials and the fact that a maximum value of a function occurs at a point where its derivative is zero. If you know calculus, you can calculate these solutions along with me; if.

Until now, we have dealt only with games played between two players. In our modern interconnected world, such games are rare. Most important economic, social, and political games involve more than two players.

We will now turn our attention to n-person games, where nis assumed to be at least three. We will find that with three or more players, new and interesting difficulties appear.To begin our analysis, let us consider the simplest possible case, a three-person 2 X 2 X 2 zero-sum game. Game 19.1 is an example.The three players are Rose, Colin and Larry (Larry chooses. In the 1980 United States presidential election, there were three candidates: Democrat Jimmy Carter, Republican Ronald Reagan, and Independent John Anderson. In the summer before the election, polls indicated that Anderson was the first choice of 20% of the voters, with about 35% favoring Carter and 45% favoring Reagan. Since Reagan was perceived as much more conservative than Anderson, who in turn was more conservative than Carter, let us make the simplifying assumption that Reagan and Carter voters had Anderson as their second choice, and Anderson voters had Carter as their second choice.

We then have the situationIf all. In Chapter 191 mentioned that not every n-person non-constant-sum game can be analyzed in a satisfactory way using the characteristic function form. In this chapter we will look at a particularly important type of a game which cannot. Game 21.1 is a three person example.This game is symmetric for the three players, and strategy D dominates strategy C for all of them. The unique equilibrium is DDD with payoffs (—1, —1, —1). This is a Pareto inferior outcome, since CCC with payoffs (1, 1, 1) would be better for all three players.

We recognize the game as a. In an n-person Prisoner’s Dilemma game, if all players rationally pursue their own best interests, all players end up worse off than if they had all followed some individually less rational line of play. We have seen that this type of situation appears often in the course of human interactions. One surprising place it can appear is in sequential choice procedures.

In this chapter we will analyze one well-known sequential choice procedure, the professional football draft in the United States.In football, basketball and other professional sports, teams choose new players by a draft system which involves sequential choices. In this chapter we begin the search for solutions to n-person games in characteristic function form.

I should tell you at the outset that the situation is going to be at least as murky as it is for two-person non-zero-sum games. For n-person games there are a number of different useful and illuminating ideas of what a solution might be, but none of them is completely satisfactory in all situations.Suppose we have an n-person game in characteristic function form ( N, v). We will assume that the game is superadditive.

The two questions we would like to answer about such. Von Neumann and Morgenstern’s idea of a stable set (Chapter 23) was historically the first proposed solution for games in characteristic function form. It was introduced because in essential constant-sum games, no single imputation is stable: every imputation is dominated by some other imputation. However, in non-constant-sum games there may be undominated imputations, and in the early 1950’s Gillies and Shapley pointed out that the set of all undominated imputations in a game is an object worthy of study. Gillies called it the coreof the game.Definition. The coreof a game in characteristic function form is the set.