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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
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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.
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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.
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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."
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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'.
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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.
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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.
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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.
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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'.
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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.
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Chapter 9 - Mixed Strategies and Nonzero -Sum
Games
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Chapter 10 - Threats, Promises, and
Commitments
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Chapter 11 - Credibility Deterrence, and
Compliance
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Chapter 12 - Incomplete and Imperfect
Information
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Chapter 13 - Whom Can You Trust - Signaling
and Screening
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Chapter 14 - Encouraging Productivity -
Incentive Schemes
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Chapter 15 - The Persistence of Memory -
Repeated Games
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Chapter 16 - Does This Stuff Really Work?
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Chapter 17 - The Tragedy of the Commons
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Chapter 18 - Games in Motion - Evolutionary
Game Theory
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Chapter 19 - Game Theory and Economics -
Oligopolies
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Chapter 20 - Voting - Determining the Will of
the People
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Chapter 21 - Auctions and the Winner's Curse
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Chapter 22 - Bargaining and Cooperative Games
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Chapter 23 - Game Theory and Business -
Co-petition
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Chapter 24 - All the World's a Game
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Definitions - The author provides a very
useful list of definitions used in discussions of game theory. Here are a few.
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