An Alternative View of Cartels: Game Theory

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An Alternative View of CartelsGame Theory

• Game Theory the study of how individuals make
  decisions when they are aware that their actions
  affect each other and when each individual takes
  this into account.
• History Introduced in 1944 by John von Neumann
  and Oskar Morgenstern in The Theory of Games and
  Economic Behavior.
• The work of von Neuman and Morgenstern was
  expanded upon by John Nash.

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Introduction to Game Theory

• A game is a situation in which a decision-maker
  must take into account the actions of other
  decision-makers. Interdependency between
  decision-makers is the essence of a game.
• In games people must make strategic decisions.
  Strategic decisions are decision that have
  implications for other people.
• Nash Equilibrium - a collection of strategies one
  for each player, such that every player's
  strategy is optimal given that the other players
  use their equilibrium strategy.

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Dominant and Dominated Strategies

• Payoff matrix a matrix that displays the
  payoffs to each player for every possible
  combination of strategies the players could
  choose.
• Dominant Strategy a strategy that is always
  strictly better than every other strategy for
  that player regardless of the strategies chosen
  by the other players.
• Dominated Strategy a strategy that is always
  strictly worse than some other strategy for that
  player regardless of the strategies chosen by the
  other players.

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Weakly Dominate Strategies

• Weakly dominant strategy - a strategy that is
  always equal to or better than every other
  strategy for that player regardless of the
  strategies chosen by the other players.
• Weakly Dominated Strategy a strategy that is
  always equal to or worse than some other strategy
  for that player regardless of the strategies
  chosen by the other players.

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Prisoners Dilemma

• Scenario Two people are arrested for a crime
• The elements of the game
• The players Prisoner One, Prisoner Two
• The strategies Confess, Dont Confess
• The payoffs
• Are on the following slide (payoffs read 1,2)
  

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Prisoners Dilemma, cont.

• Prisoner 2
• Confess Dont Confess
• Confess 4 years, 4 years 0 years, 7 years
• Prisoner 1
• Dont Confess 7 year, 0 years 2 years, 2 years
• Dominant strategy equilibrium In this game, the
  dominant strategy for each prisoner is to
  confess. So the outcome of the game is that they
  each get two years.
• This illustrates the prisoners dilemma games in
  which the equilibrium of the game is not the
  outcome the players would choose if they could
  perfectly cooperate.

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The NCAA and TelevisionRevisiting the Cartel

• Scenario Two teams need to determine how many
  games to have televised.
• The elements of the game
• The players Florida, Miami
• The strategies
• Televise Many Games, Televise Few Games

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Miami vs. Florida State

• The payoffs Payoffs read Miami, Florida State
• Florida State
• Many Few
• Many 5, 5 20, 3
• Miami
• Few 3, 20 8, 8
• Dominant strategy equilibrium In this game, the
  dominant strategy for Miami and Florida State is
  Many. So the outcome of the game is 5, 5.
• This is alternative method to illustrate the
  instability of a cartel. Each school has an
  incentive to cheat on any cartel agreement,
  producing a result neither school desires.

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Iterated Dominant Strategies

• What if a dominant strategy does not exist?
• We can still solve the game by iterating towards
  a solution.
• The solution is reached by eliminating all
  strategies that are strictly dominated.

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• Across is Michigan, Down is Michigan State

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The NCAA and Paying Athletes

• UCLA
• Spend Dont Spend
• Spend 2, 2 15, 4
• USC
• Dont Spend 4, 15 12, 12
• Dominant strategy equilibrium In this game, the
  dominant strategy for USC and UCLA is Spend on
  Athletes. So the outcome of the game is 2, 2.
• To reach the preferred outcome of 12, 12, the
  NCAA is needed to force schools not to pay its
  athletes.

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• Across is Nebraska, Down is Colorado