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Scott P. Stevens


The Great Courses, Chantilly, VA., 2008, 412 pgs., bibliography, biographical notes, timeline This is both a video lecture and transcript book of 24 lectures and chapters


Reviewer comments

The author uses many examples both of experiments in game theory and from real life situations. The text -transcript - is worth reading, but some times the author (lecturer) is showing an illustration on screen that does not appear in the text, so the reader is left wondering a bit. The subject matter progresses from simple games that are easy to understand to more and more complex games that are explained by more and more complex theory. At the conclusion of each lecture (chapter) Dr Stevens proposes some questions that test the reader's understanding of the material.

The author focuses on the games themselves, but the reader also can understaned why games such as these are 'played' in the real world. The 'games' are actually exercises in strategy - strategi thinking - and as Dr. McCloskey so aptly couined the term the purpose of the 'players' is to achieve 'betterment', either for themselves or for their group. Dr. Stevens describes 'zero-sum' games - those closed games in which if one side wins the other looses. He also describes open games - those that in addition to the former also it is possible for both sides to either win or loose. His explaination of these games is particularly ineresting - how two or more competetors can conclude that by employing the correct strategies all might win and otherwise, the incorrect strategties will cause all to loose. This is particularly the case in some strategies related to potential nuclear war.


Chapter 1 - The World of Game Theory

Dr. Stevens starts right out with a game for the viewer (reader) to play. It is a simple computer game involving a $100 prize and 100 players each in a different location. Each has a button to activate. Each player has two options - 1 to deduct $2.00 from each other player, which also reduces whatever loss is coming from the other players' action. Or 2, to not click. He then discusses the results of each option and the ethics of each choice. This is just an example and he shows several. These are just that, examples. He writes: 'game theory is the study of strategic interactions among rational players." He points out that this involves not only learning which actions would result in the most favorable outcome for the player, but also which games themselves would result in a loss so should not be played. He describes how game theory relates to making choices in many daily situations and to the payoffs that might result from employing different strategies.


Chapter 2 - The Nature of the Game

In this chapter the author increases the complexity of the scenarios and of the various strategies each player may choose. Among his examples he uses chess. For these games he states that: "A player's payoff represents how much he or she likes the outcome of the game." He distinguishes between 'finite games' and others. He defines 'strategy' in game theory, "it specifies how a player will react in every situation, even situations that will not come to pass when the game is actually played. "Consider the proposition that what you choose to do often depends on the consequences that would result if you chose to do something else - in other words, your choice is dependent upon events that never occur."


Chapter 3 - The Real Life Chessboard - Sequential Games

He defines this as games in which the events evolve over time. And the players learn at least something about what the opposing players are doing. Games in which the players do not know anything about what the other players are doing are termed 'simultaneous games.'. Some sequential games include the situation in which one player moves, then the other. These games then can be studied to learn if that gives a 'first player advantage'. He quotes an example from a book by Avianash Dixit and Barry Nalebuff titled Thinking Strategically. The moves in a sequential game are recorded -depicted - in a 'game tree'. This shows branches as the number of choices and counter choices increase. He uses an example of hypothetical competition between Airbus and Boeing. Then he moves to an extensive discussion of the "Nash Equilibrium'.


Chapter 4 - Life's Little Games - The 2 x 2 Classic Games

A 2 x 2 game is a simultaneous game - that is a game in which each player does not know the other's move - not necessairly that the moves are simultaneous in time. And 2 x 2 means that there are two players and each has only 2 moves that complete the game. The author discusses 4 examples - 1 the coordination game - 2 the battle of the sexes - 3 chicken - and 4 prisoner's dilemma.


Chapter 5 - Guessing Right - Simultaneous Move Games

This idea depicts a scenario in which both sides have several options and each side knows that the other knows those options, but not which one the opponent will actually select. Each then tries to 'second guess' the other in choosing the option that the other fails to choose. These games can be an example of a 'zero-sum game' - one of perfect competition in which if one side wins the other must loose. He explains that such games are useful for modeling situations in which in real life the players lack communication (thus knowledge) of what the other is doing. He uses as example the Battle of the Bismark Sea during WWII.
And these games also involve the concept of 'dominant strategy' - For this concept he uses a easier to understand example from business. The concept is that each player has multiple potential strategies and none know what strategies their opponents will choose. The player then tests each of his possible strategies against each of the opoonent's possible strategies to find the likely outcome. The resulting potential outcomes will vary. One or possibly more strategies will produce better outcomes than any other no matter which strategy the opponent may select. This is the 'dominant' strategy. A rational player will always choose his dominant strategy. Our player, tests not only his potential strategies but also all the oponent's potential strategies. He finds the opponent's 'dominant' strategy and can presume the opponent will use it. The next step, then, is to chouse his own strategy that at least is dominant agaisst that opposing strategy. These strategies for each side may be depicted in a matrix. The analysis enables the player to eliminate strategies that clearly won't work. The author then concludes. "Any cell in the matrix eliminated (by this study) is guaranteed not to be a Mash equilibrum and if only one cell remains that is a nash equilibrum.
He continues with more elaborate examples from from real world situations reqiring selecting from options and reaching decisions. Some times there is no dominant strategy. He describes another tactic "best-response method" in which each player attempts at least to find what his best strategy can be. The result may be a Nash equilibrium in which both players chose the combination of their strategies with the opponent's which result in the best outcome for both.


Chapter 6 - Practical Applications of Game Theory
In this chapter the author considers several simple examples of situations calling for strategies described in previous chapters.One of these is a 3 player contest between three members of a corporate board each of whom would like to be elected chairman in a coming election in which the three of them vote and the winner will be the one who has two out of three votes. And each of them of course prefers himself, but also has second preference for one other and definate objection to the other. A tie, that is if all three vote for themselves resulting in a result of each receiving 1 vote is decided by the chairman. The current chairman of the three (A) designates (B) as the winner of a tie, and that (C) will vote first. The student can see the complex strategy matrix this simple issue creates.

But for the student of social control this is an example of dominace in another way. The three board members by instinct presume that there MUST be a single chairman, no three party joint control is acceptable. The necessity that a social group MUST have a leader is an ancient 'brain wired' concept to avoid the alternative, which is considered chaos.|

The author provides the analysis and decisions. He uses another example of cigarette companies agrfeeing with the government to ban all advertising on TV. Surprisingly the ban actually benefits the companies by reducing their budgets for competitive advertising. Again the author discusses this from the point-of-view of strategic decisions.

But it also is an example of the phenomena we see in the real world of corporations or other interest groups that denounce expanded government intervention in economic affairs, nevertheless seeking government intervention when their strategicanalysis shows reducing competition will increase profits.

He then presents an example in which strategic analysis indicates that a player can benefit from enabling another party to have information that amounts to potential blackmail.


Chapter 7 - A Random Walk - Dealing with Chance Events

So far the examples and strategies have involved sure outcomes of whatever strategy is selected. The author now adds the complexity in situations involving chance. He describes three different examples of types of chance. One is chance outcomes for the events IN the game. A second is uncertainty about the actual structure of the game itself. A third is uncertainty about the available strategies. The author presents examples and solutions experts have developed. One of these is called the "Harsanyi approach' named after its discoverer. A situation of chance develops when each player is not limited to choosing one strategy out of several, but rather has a 'mixed strategy' situation in which he selects strategies in a random fashion and the choices have random probabilities. He presents several real examples, for instance, from TV games in which each player has various choices that have various potential outcomes and the choosing between them is random with various proportionate outcomes. He calls tis 'mixed-strategy equilibria'.


Chapter 8 - Pure Competition - Constant-Sum Games

In this chapter Dr. Stevens discusses von Neumann's minimax theorum. He also calls the minimax strategy its 'security value' Then when both opponents have the same 'security value' in the game that is both are playing its minimax strategy chaning our own during the game won't help. But if the opponents have different minimax strategies the results will not be a Nash equilibrium.
He sumarizes: "The minimax theorem says that if players are allowed to use mixed strategies, then strategies with the same security values can always be found". He provides an example from the situation of choices for penalty kicks in soccer in which the kicker asssesses the probability of the keeper choosing to move right or left or remain in position based on his assessment of the probability of what the kicker will do.
In a soccer match, of course, both kicker and keeper are processing information almost instantaneously in their head. But the author developes and leads the students through the very complex analysis required to make a decision by using increasingly elaborate, ideas ab out probability, mathmatics and matrix displays.


Chapter 9 - Mixed Strategies and Nonzero -Sum Games


Chapter 10 - Threats, Promises, and Commitments


Chapter 11 - Credibility Deterrence, and Compliance


Chapter 12 - Incomplete and Imperfect Information


Chapter 13 - Whom Can You Trust - Signaling and Screening


Chapter 14 - Encouraging Productivity - Incentive Schemes


Chapter 15 - The Persistence of Memory - Repeated Games


Chapter 16 - Does This Stuff Really Work?


Chapter 17 - The Tragedy of the Commons


Chapter 18 - Games in Motion - Evolutionary Game Theory


Chapter 19 - Game Theory and Economics - Oligopolies


Chapter 20 - Voting - Determining the Will of the People


Chapter 21 - Auctions and the Winner's Curse


Chapter 22 - Bargaining and Cooperative Games


Chapter 23 - Game Theory and Business - Co-petition


Chapter 24 - All the World's a Game


Definitions - The author provides a very useful list of definitions used in discussions of game theory. Here are a few.


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