4/12/2013 Game Theory

by Brandon Taylor

          What do engagement rings, the Princess Bride, steam engines, and spider battles have in common? They can all be explained through game theory. In the second half of the twentieth century, game theory helped make breakthroughs in various disciplines, including economics, biology, computer science, and philosophy. It sheds light on such fundamental notions as morality, coordination, cooperation, signaling, and credibility.

• Intuitive strategies (coming forthwith)
• Definition of game
• Large numbers assumption
• Definition of utility (for our purposes)
• Utility models
• Self regarding vs. altruisitic
• Perfect information
• Components of a game
• Normal form games
• Dominating strategies/dominated strategies
• Strong
• Weak
• Nash equilibrium (yes, as in A Beautiful Mind)
• Examples
• Prisoner's Dilemma (Cooperation game)
• Tragedy of the fishers
• Karma
• Afterlife
• Societal punishments
• Caveman (Coordination game)
• Focal points
• New York example
• Steam engine example
• Mixed Nash equilibrium
• Soccer game
• Caveman example
• Extensive form game
• Nature's move
• Unknown move
• Backwards Induction
• Burning bridges
• Subgames
• Subgame reduction
• Subgame perfect equilibrium'
• Signaling games
• Engagement ring
• Credibility
• Changing the game: strategies for establishing credibility
• Coming forthwith
• Repeated games
• Finitely repeated prisoner's dilemma
• Infinitely repeated games
• Certain probability of ending at each round
• Decaying returns
• Tit for tat
• Public Choice Theory
• Voting
• Giving the wrong directions
• Sortition

List of Interesting Applications:
Business School

Keyboards

Steam engines vs. combustion engines

Tragedy of the fishers

Burning bridges

Alarm clock

Lemons (warranty)

Auctions

Business collusion

Biological Examples (genetic altruism)

New York example

Weight loss example

Giving/taking money (cultural relativity)*

Engagement rings

More coming forthwith

Discussion Questions:

What the disadvantages of this kind of utility model?

How can society achieve cooperation and coordination?

What are the advantages of this kind of very quantitative model of human behavior?

What are the disadvantages?

Do societies differ in their utility models? Their game strategies?

Bonus: Wikipedia to the rescue

Game theory has been put to several uses in philosophy. Responding to two papers by W.V.O. Quine (1960, 1967), Lewis (1969) used game theory to develop a philosophical account of convention. In so doing, he provided the first analysis of common knowledge and employed it in analyzing play in coordination games. In addition, he first suggested that one can understand meaning in terms of signaling games. This later suggestion has been pursued by several philosophers since Lewis (Skyrms (1996), Grim, Kokalis, and Alai-Tafti et al. (2004)). Following Lewis (1969) game-theoretic account of conventions, Edna Ullmann-Margalit (1977) and Bicchieri (2006) have developed theories of social norms that define them as Nash equilibria that result from transforming a mixed-motive game into a coordination game.[24][25]

Game theory has also challenged philosophers to think in terms of interactive epistemology: what it means for a collective to have common beliefs or knowledge, and what are the consequences of this knowledge for the social outcomes resulting from agents' interactions. Philosophers who have worked in this area include Bicchieri (1989, 1993),[26] Skyrms (1990),[27] and Stalnaker (1999).[28]

In ethics, some[who?] authors have attempted to pursue the project, begun by Thomas Hobbes, of deriving morality from self-interest. Since games like the prisoner's dilemma present an apparent conflict between morality and self-interest, explaining why cooperation is required by self-interest is an important component of this project. This general strategy is a component of the general social contract view in political philosophy (for examples, see Gauthier (1986) and Kavka (1986).[29]

Other authors have attempted to use evolutionary game theory in order to explain the emergence of human attitudes about morality and corresponding animal behaviors. These authors look at several games including the prisoner's dilemma, stag hunt, and the Nash bargaining game as providing an explanation for the emergence of attitudes about morality (see, e.g., Skyrms (1996, 2004) and Sober and Wilson (1999)).

Some assumptions used in some parts of game theory have been challenged in philosophy; for example, psychological egoism states that rationality reduces to self-interest—a claim debated among philosophers. (see Psychological egoism#Criticisms)