game theory

• Game theory


  The study of how people behave in strategic situations
• Strategic decisions


  Decisions in which each person, in deciding what actions to take, must consider how others might respond to that action
• Game Theory Definition


  The study of strategic decision making. More formally, it is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers
• Game Theory is used to analyze how firms interact but has many other applications
• If the market is composed by a small number of firms

  Each firm must act strategically
• If one firm increases production

  The market supply increases and the price has to drop to reach an equilibrium
• Some Applications of Game Theory

  • The study of oligopolies (industries containing only a few firms)
  • The study of cartels; e.g. OPEC
  • The study of externalities; e.g. using a common resource such as a fishery
  • The study of military strategies
• Other Applications of Game Theory

  • National Defense-Terrorism and Cold War
  • Movie Release Dates and Program Scheduling
  • Auctions
  • Sports-Cards, Cycling, and race car driving
  • Politics-positions taken and $$/time spent on campaigning
  • Nanny Monitoring
  • Group of Birds Feeding
  • Mating Habits
• Game


  A situation where the participants' payoffs depend not only on their decisions, but also on their rivals' decisions
• Strategic Interactions


  My optimal decisions will depend on what others do in the game
• Four elements to describe a game

  • Players
  • Rules: when each player moves, what are the possible moves, what is known to each player before moving
  • Outcomes of the moves
  • Payoffs of each possible outcome: how much money each player receive for any specific outcome
• Types of Games


  • Complete (symmetric) info
  • One-shot games
  • Repeated games
  • Incomplete (asymmetric) info
  • Simultaneous-move games
  • Sequential-move games
  • Simultaneous & sequential-moves games
• Two-Player Game


  A game with just two players
• We will study only games in which there are two players, each of whom can choose between only two strategies
• If B plays Right then A's best reply is Down


  This improves A's payoff from 1 to 2
• If A plays Up then B's best reply is Left


  If B plays Left then A's best reply is Up
• Dominant Strategy


  A strategy that gives higher payoffs no matter what the opponent does
• Dominated Strategy


  A strategy is dominated if there exists another strategy that is dominant
• Nash Equilibrium


  The decisions of the players are a Nash Equilibrium if no individual prefers a different choice. In other words, each player is choosing the best strategy, given the strategies chosen by the other players
• In most games there are no dominant strategies for all players
• If Pure Strategies can't produce a Nash Equilibrium, Mixed Strategies can