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Class 007

Game Theory

Popularized by movies such as "A Beautiful Mind", game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Beyond what we call 'games' in common language, such as chess, poker, soccer, etc., it includes the modeling of conflict among nations, political campaigns, competition among firms, and trading behavior in markets such as the NYSE. That's where this class comes in...

 

If you haven't watched the movie "A Beautiful Mind", you should. It is about John Nash (played by Russell Crowe) who won the Nobel Prize in economics for his foundational contributions to game theory. Nash put some structure around how players in a "game" can optimize their outcomes (if the movie is to be fully believed, this insight struck him when he realized that if all his friends hit on the most pretty girl, he should hit on the second-most pretty one--you saw the clip in class). In this tutorial, we use the classic "prisoner's dilemma" to highlight this concept.

 

Game theory is mainly concerned with predicting the outcome of games of strategy in which the participants (for example two or more businesses competing in a market) have incomplete information about the others' intentions. It's a way to divine the future--or, at least, companies that spend a bunch of money on research employing game theory hope to be able to predict the future.

Game theory analysis has direct relevance to the study of the conduct and behavior of firms in oligopolistic markets – for example the decisions that firms must take over pricing and levels of production, and also how much money to invest in research and development spending.

Costly research projects represent a risk for any business – but if one firm invests in R&D, can a rival firm decide not to follow? They might lose the competitive edge in the market and suffer a long term decline in market share and profitability.

The dominant strategy for both firms is probably to go ahead with R&D spending. If they do not and the other firm does, then their profits fall and they lose market share. However, there are only a limited number of patents available to be won and if all of the leading firms in a market spend heavily on R&D, this may ultimately yield a lower total rate of return than if only one firm opts to proceed.

The Prisoners’ Dilemma
The classic example used in every single Econ class in the world. That is not an overstatement. If you want an A in this class or to pass an AP Econ Exam you'd better make a point of knowing
The Prisoners' Dilemma.

  • The classic example of game theory is The Prisoners’ Dilemma, a situation where two prisoners are being questioned over their guilt or innocence of a crime.
  • They have a simple choice, either to confess to the crime (thereby implicating their accomplice) and accept the consequences, or to deny all involvement and hope that their partner does likewise.

Confess or keep quiet? The Prisoner’s Dilemma is a classic example of basic game theory in action!

  • The “pay-off” is measured in terms of years in prison arising from their choices and this is summarized in the table below.
  • No communication is permitted between the two suspects – in other words, each must make an independent decision, but clearly they will take into account the likely behavior of the other when under-interrogation.

Nash Equilibrium
A Nash Equilibrium is an idea in game theory – it describes any situation where all of the participants in a game are pursuing their best possible strategy given the strategies of all of the other participants.

In a Nash Equilibrium, the outcome of a game that occurs is when player A takes the best possible action given the action of player B, and player B takes the best possible action given the action of player A.

If we assume that each player cares only about minimizing his or her own time in jail, then the prisoner's dilemma forms a non-zero-sum game in which two players may each either cooperate with or defect from (betray) the other player. In this game, as in most game theory, the only concern of each individual player (prisoner) is maximizing his or her own payoff, without any concern for the other player's payoff. The unique equilibrium for this game is a Pareto-suboptimal solution, that is, rational choice leads the two players to both play defect, even though each player's individual reward would be greater if they both played cooperatively.

In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. No matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal.

Here's an infographic that applies game theory to terrorism and smuggling:

 

Did you know?

Game Theory remains at the cutting edge of economic theory, with game theorists winning the Noble Prize in Economics in 1994, 1996, 2005, 2007 and 2012. For his path-breaking dissertation that revolutionized economics and many other disciplines, John Nash won the Nobel in 1994, along with game theorists John Harsanyi and Reinhard Selten.

 

 

 

 

Success comes in cans,
failure in can'ts.
- Author Unknown

 

Opportunity is always knocking. The problem is that most people have the self-doubt station in their head turned up way too loud to hear it.
- Brian Vaszily

 

Opportunity dances with those who are already on the dance floor.
- Jackson Brown

 

People often say that motivation doesn't last. Well, neither does bathing - that's why we recommend it daily.
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Life is not about how fast you run, or how high you climb, but how well you bounce.
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Game theory and Nash equilibrium Microeconomics Khan Academy

Dilbert - Search Results for game theory