Some Basic Game Theory

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Some Basic Game Theory
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Games and Economic Situations

• To consider this set of ideas, we need to examine
  how and where it arises
• Basic situation where there is interaction
  between individuals (agents)
• Persons
• Firms
• Other
• Cooperation vs. Non-cooperation

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Strategic Behavior

• Cooperative interactions
• What is necessary for this to be true?
• Potential gains for both parties
• Generally, a means to communicate
• Generally, some means to form binding agreements
• What about situations absent these elements?
• What about strategic behavior is this
  cooperative or non-cooperative?

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Non-Cooperative Situations

• This is where game theory (or more precisely,
  non-cooperative game theory comes into play)
• That is, when players cannot communicate or form
  binding agreements when they have the incentive
  to act strategically
• Develop a basic set of principles

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Basic Principles of Game Theory

• Type of game
• Static
• Dynamic
• Information
• Complete (Common Knowledge)
• Incomplete
• Three Elements
• Players or agents
• Actions or Strategies
• Payoffs

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Basic Principles

• Illustrates presence of basic elements of
  economics
• Rationality
• Self interested behavior (optimization)
• equilibrium

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Games

• Types of games we consider
• Static
• Play is simultaneous
• 2 or more players
• Constant or Fixed payoffs
• Normal form (usually shown as a payoff matrix)
• Complete information
• Presumption is that rational players will
  optimize Best Response
• What does simultaneous play imply?

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Games

• Dynamic Games
• Play is sequential
• 2 or more players
• Constant payoffs
• Extensive form
• Complete or Incomplete Information
• What does sequential play imply?

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Static Games

• Rational play of the game
• Player acts rationally in their own self
  interest, which produces an optimal outcome for
  them, under the circumstances
• Note that this does not imply that higher payoffs
  could not be obtained
• Inability to form binding agreements

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How Should You Play a Game?

• Rational Play
• Choose actions that are optimal for youBest
  Response
• Types of strategies
• Dominant strategy vs. Dominated Strategy
• Playing the best response
• This depends as we will see, on what the other
  player chooses/has chosen

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Approaches to Play

• Elimination of Dominated Strategies
• Examples
• Playing a Dominant Strategy
• The Prisoners Dilemma
• Mutual Best Response
• Nash Equilibrium
• Multiple Equilibria

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Dynamic Games

• Sequence of plays and choices available to
  players
• How to play Backward Induction
• Nash Equilibria
• Refinement of Nash Equilibrium Subgame
  perfection