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ECO290E Game Theory

Lecture 1: Introduction and Motivation

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What is Game Theory?

 

Game theory is a field of Mathematics,

analyzing strategically inter-dependent

situations (or strategic situations) in which the

outcome of your actions depends also on the

actions of others.

Are mathematical models helpful?

Is strategic thinking really important?

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Are Mathematical Models Helpful?

Physical phenomena - Natural Science

  Follow consistent patters, i.e., natural laws

  We cannot ask objects for the reason behind the event.

Mathematical models are necessary.

Economic (Social) phenomena - Social Science

  Each person acts anyway she wants.

  She can explain why she took a specific action.

No mathematical model is needed (?)

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Two Alternative Approaches

  Institutional knowledge: Look into the “facts”.

Superficial knowledge alone cannot explain economic movement.

  Economic Theory: Look for the “laws” behind facts.

Q: What’s the fundamental economic law? A: Each person acts for her own interest.

  Preferences need not be selfish, or materially based.

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Traditional Economics 

  Traditionally, economics focused (almost) only on the ideal market economy, called

“perfectly competitive market.”

  Supply and demand is the main tool.

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Is Strategic Thinking Relevant?

  In demand-supply analysis, the market outcome is

derived by the intersection of the demand curve and the supply curve.

  There is NO strategic inter-dependence in its framework.

Q: What’s the underlying assumption?

A: Each economic agent is a “price-taker.”

  Every agent (consumer, firm, etc) reacts to market prices, not (directly) to other agents’ actions.

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Need for Game Theory

Q: Can most of problems in Economics analyzed by

supply-demand? A: NO!

von Neumann and

Morgenstern (1944)

“We need essentially new mathematical theory to

solve variety of problems in social sciences.”

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Strategic Thinking: Example

Example: Google vs. Apple

  Google’s (optimal) action depends on how Google predicts the Apple’s action.

  Apple’s action depends on how Apple predicts the Google’s action.

  Google’s action depends on how Google predicts how Apple predicts the Google’s action.

  Google’s action depends on how Google predicts

how Apple predicts how Google predicts the Apple’s action.

and so on… (this is called “infinite regress”)

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Revolution by Game Theory

  Game theory can solve the problem of strategic inter-dependence by pinning down how to predict other players’ action.

  Therefore, game theory

  Provides us tools for analyzing important economic phenomena beyond market economy (with perfect competition).

  Enables us to compare different resource allocation mechanisms.

  It dramatically changed economics since 80’s!

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Fields Transformed by Game Theory

  How does economy function if market is immature or does not exist?

Economic History, Development Economics

  How does government (politician, bureaucrat) behave?

Political Economics

  What’s going on inside private companies?

Organizational Economics

  How to compare different types of market economy?

Comparative Institutional Analysis

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Discovery by vNM 

 

Any social problem can be formalized as a

“game” which consists of three elements:

  Players: relevant individuals (also called “agents”)

  Strategy: their possible choice of actions

  Payoff: their utility for each possible action profile

Q: What’s the solution of games?

Von Neumann and Morgenstern failed to

establish a general solution concept…

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A Beautiful Mind Discovered It! 

  John Nash (1950) established THE solution concept:

  In (Nash) equilibrium, no one can benefit if she unilaterally changes her action.

  The solution always exists.

  John Harsanyi and Reinhard Selten significantly extended Nash equilibrium.

  Triggered a thousands of applications of game theory.

Revolution by game theory!

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Impact of Nash 

  “Soon after Nash’s work, game-theoretic models began to be used in economic theory and political

science, and psychologists began studying how human subjects behave in experimental games.”

  “In the 1970s game theory was first used as a tool in evolutionary biology. Subsequently, game-theoretic methods have come to dominate microeconomic theory and are used also in many other fields of economics and a wide range of other social and behavioral sciences.”

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Three Fathers of Game Theory 

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Revolution Continues…

- Novel Prize for Game Theory since 1994

  1996: Mirrlees, Vickrey

  for their fundamental contributions to the economic theory of incentives under asymmetric information.

  2001: Akerlof, Spence, Stiglitz

  for their analyses of markets with asymmetric information.

  2005: Aumann, Schelling

  for having enhanced our understanding of conflict and cooperation through game-theory analysis.

  2007: Hurwicz, Maskin, Myerson

  for having laid the foundations of mechanism design theory.

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Year 2012 As Well

- Roth and Shapley for Market Design!

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Market Design: from Theory to Practice 

  Applying new insights in microeconomic theory (game theory), market design tries to (re-)design actual markets and to fix market failures.

  Experiments and simulations are used to check the performance. => Engineering

  New mechanisms proposed by economists are implemented in real world. => Practical

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Real Life Applications

  Auction Design

  Radio spectrum

  Treasury bills

  AdWords (Google)

  Matching Mechanisms

  Medical residency

  Kidney exchange

  Public school choice

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There are Many Success Stories!

  Use “Money”

  Radio spectrum

  Treasury bills

  AdWords (Google)

  No “Money”

  Medical residency

  Kidney exchange

  Public school choice

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Example: Prisoners Dilemma

 

Two suspects are charged with a joint crime,

and are held separately by the police.

 

Each prisoner is told the following (assume

that a plea bargain is allowed):

  If both confess, each receives 3 years imprisonment.

  If neither confesses, both receive 1 year.

  If one confesses and the other one does not, the former will be set free immediately (0 payoff) and the latter receives 5 years.

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Prisoners’ Dilemma: Payoff Matrix 

  Here we set payoffs as (negative of) years.

  Other numbers such that larger number shows better outcomes can express the same situations.

Player 2 Player 1

Silent Confess

Silent -1 -1

0 -5

Confess -5 0

-3 -3

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How to Use (Read) Bi-Matrices

  Any two players game (with finite number of

strategies) can be expressed as a bi-matrix, called payoff bi-matrix or payoff matrix.

  The payoffs to the two players when a particular pair of strategies is chosen are given in the appropriate cell.

  The payoff to the row player (player 1) is given first, followed by the payoff to the column player (player 2).

How can we solve this game?

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Prisoners’ Dilemma: Analysis (1) 

  If the opponent (player 2) chooses Silent,

  Playing Confess is better since 0 > -1. Player 2

Player 1

Silent Confess

Silent -1 -1

0 -5

Confess -5 0

-3 -3

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Prisoners’ Dilemma: Analysis (2) 

  If the opponent (player 2) chooses Confess,

  Playing Confess is better since -3 > -5. Player 2

Player 1

Silent Confess

Silent -1 -1

0 -5

Confess -5 0

-3 -3

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Prisoners’ Dilemma: Analysis (3) 

  (Silent, Silent) looks mutually beneficial outcomes, though

  Playing Confess is optimal regardless of other player’s choice!

  Acting optimally (Confess, Confess) rends up realizing!!

Player 2 Player 1

Silent Confess

Silent -1 -1

0 -5

Confess -5 0

-3 -3

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Further Exercises 

  List up strategically interdependent situations from daily problems you encounter.

  Survey the academic achievements made by Nobel laureates listed on slide 15.

  Check out research fields other than Economics in which game theory is used or applied.

  Find a social problem which can be described as a Prisoner’s Dilemma.

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