Administrative Stuff

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Administrative Stuff

• Enrollment
• HW 1

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Where are we?

• Theories in Political Science
• Induction
• Deduction

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The Spatial Model

• One of the biggest successes of rational choice
  as an approach
• Brief recap
• Coolest part of Median Voter Theory
• Robustness!

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Violations of MVT Assumptions

• Rules of the game
• More parties
• Primaries
• Distribution of voters not Normal

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Violations of MVT Assumptions II

• Preferences
• Parties care about policies/ideology
• Abstention

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Violations of MVT Assumptions III

• Information
• Parties know the median voter
• Voters know where the parties are

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Spatial Model as an EXAMPLE of a Game

• The spatial model weve shown you is an example
  of a game
• Why a game?
• There are multiple players, and their best
  strategies DEPEND on the strategies of the
  others.
• For example Chess

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Game Theory

• Game theory is a specific tool within rational
  choice
• Game theory is meant to help us solve the
  infinite regress problem
• If I know that you know that I know that you
  know, but you dont know that I know that..

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Spatial Model Redux

• What HAVENT we shown you yet?
• We have much more formal tools to analyze these
  games

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Spatial Model as a SEQUENCE of Moves

• This structure is called a game tree
• Now What?

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Rollback Equilibrium

• AKA backwards induction
• When there are sequential moves, we can trace
  back what would happen if we made a particular
  move
• How to do this in practice?

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How to find Rollback Equilibria

• Start at the last decision
• What would the player do?
• Back up, and ask the same question
• How many times?
• EVERY time somebody could make a decision, you
  figure out what the best decision would have been

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What IS a Rollback Equilibrium?

• A Nash equilibrium in game theory means a SET
  of STRATEGIES such that NO player could
  UNILATERALLY IMPROVE their PAYOFFS
• Wow, thats a whole heck of a lot of bolded
  words. What do they mean?

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Terms

• SET
• The point of game theory is to tell us what all
  the players will do. An equilibrium solution
  MUST tell us what ALL players will do
• STRATEGY
• A strategy in game theory is like instructions.
  It is a complete set of instructions for what a
  player would do in every circumstance, even if
  that circumstance probably wont happen.

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Terms 2, the Saga Continues

• PAYOFFS
• The value each player assigns to each outcome
• (A, B)..A is player 1s payoff, B is player 2s
  payoff
• More is better
• UNILATERALLY IMPROVE
• Assume that one player is certainly going to do
  something. Would the other player be better off
  changing their move.

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Back to the Spatial Model

• Youd thought Id forgotten it, didnt you?

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Example 2

• Deterrence game

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Example 3

• Bargaining game

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Making your OWN game