Die Johannes Kepler Universitt Linz

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Prof. Dr. Friedrich Schneider Institut für
Volkswirtschaftslehre http//www.econ.jku.at/sch
neider
Recht und Ökonomie (Law and Economics) LVA-Nr.
239.203 WS 2009/10 Mikroökonomie (Wiederholung
Teil 3)
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Outline of the section on Microeconomics

• 1 Basic concepts and tools
• Consumer theory
• Theory of the firm
• 4 Interactions of households and firms
• 5 Game theory
• 6 Pricing of assets
• 7 Welfare economics
• 8 Uncertainty

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5.1 Game Theory

• Basic objective general analysis of strategic
  interaction(s)
• Applications
• war or arms race
• political negotiations
• markets economics of imperfect competition
• legal disputes
• competitions, e. g. sports

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5.2 Payoff Matrix of a Game

• Outcome of a game (gains or losses) for any given
  pair of action/reaction by players involved
• Dominant strategy
• A bottom
• B left

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5.3 Nash-Equilibrium

• Each players choice is optimal given the other
  players choice
• Nash-Equilibrium
• if A chooses top, B will choose left
• If B chooses left, A will choose top
• thus (top, left) is a Nash-Equilibrium
• but (bottom, right) is also a Nash- Equilibrium!

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5.4 Prisoners Dilemma

• Bonny Clyde are suspected of a robbery
  questioned in separate rooms.
• There is no conclusive evidence, thus
• confession is needed for a conviction for
  robbery otherwise its only illegal possession
  of a weapon.
• No one confesses 1 year for both.
• One confessor goes free, the other will get 6
  years.
• Both confess, each gets 3 years.

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5.5 Payoff Matrix for the Prisoners Dilemma

• Unique Nash- equilibrium is for both to confess.
• Obviously it would be optimal for both to deny
  Pareto optimum!
• Applications
• cartel cheating
• arms control

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5.6 One-shot vs. Repeated Games

• Which is the correct way to play the game?
• Important finite or infinite number of rounds!
• with finite number of rounds no change in the
  outcome
• with infinite repetitions of the game if
  cooperation is best (Pareto-optimal) threat of
  non-cooperation may (will?) induce cooperation.
• Experiment use experts favourite strategies of
  P. D. in a computer simulation
• outcome simple tit-for-tat gets highest payoff!

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5.7 Sequential Games

• Thus far players acted simultaneously.
• Now suppose that one player (A) starts.
• He will choose bottom
• outcome (bottom, right)
• But B would prefer top!
• B could threaten A to choose left credibility?
• Monopolist (B) deters entry of competitor (A).

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5.8 Pure and Mixed Strategies

• Pure strategy choice is made and then maintained
  (with certainty).
• Mixed strategy the choice by each player has a
  certain probability.
• Sometimes there may be no equilibrium solution in
  pure, but only in mixed strategies.

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5.9 Applications of Game Theory (1)

• Games of coordination
• prisoners dilemma contract
• arms race disarmament agreement
• Games of competition
• assumption on probable reaction of competitor
• Games of coexistence
• biology (dove-hawk game)

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5.10 Applications of Game Theory (2)

• Games of commitment
• frog/scorpion
• kidnapper/hostage
• generations
• Bargaining games
• Nash bargaining specify properties of
  reasonable solution and show uniqueness of
  solution.
• Rubinstein bargaining analyse sequence of
  choices and solve for subgame perfect
  equilibrium (e.g. division of a given sum only
  fair offer will be acceptable social norm of
  behaviour?).

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6.1 Pricing of Assets

• An asset can be land, a company, shares in a
  corporation, a patent, an annuity,
• The asset generates income, assumed to accrue
  annually rent, dividend, interest, ...
• In principle, the value of an asset is the sum of
  the income stream, F, it generates over its life
  span, n.
• Due to time preferences, income accruing in the
  future has to be discounted at the rate r.

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6.2 Present discounted value

• We assume an income stream over a fixed period of
  time, n.
• Then the present discounted value (PDV) becomes
• PDV F1/(1r) F2/(1r)2 F3/(1r)3
  Fn/(1r)n
• For an infinite constant income stream, F, we get
• PDV F/r

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6.3 Applications of Asset Pricing

• Determine value of damages, e. g. of destroyed
  property
• Value of land in case of expropriation
• Value of life