5' Combining simultaneous and sequential moves'

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5. Combining simultaneous and sequential moves.

• In this section we shall learn
• How the tools used to analyze sequential games
  can be used on simultaneous games and vice versa.
• How to understand games that involve both
  sequential and simultaneous moves.
• How a switch from simultaneous to sequential (or
  vice versa) moves may be used by a player to gain
  an advantage.

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Combining simultaneous and sequential moves.

• Many games involve both simultaneous and
  sequential moves.
• The use of game trees (extensive form) and payoff
  matrices (strategic form) are interchangeable.

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Combining simultaneous and sequential moves.From
extensive form to strategic form

• Recall the senate race game.
• The key to converting this from extensive to
  sequential form is to recognize that Gary has two
  types of strategy.
• Simply play in or out.
• Play a contingent strategy. For example If
  Arnold plays ads I play out.

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Combining simultaneous and sequential moves.From
extensive form to strategic form
Strategies. In, In - always enter. In, Out
enter if ads, dont enter otherwise. Out, In
enter if no ads, dont enter otherwise. Out,
Out Never enter.
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Combining simultaneous and sequential movesFrom
strategic form to extensive form

• To convert from strategic to extensive form
  representation requires the use of information
  sets.
• Consider the chicken game

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Combining simultaneous and sequential moves.From
strategic form to extensive form.
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Combining simultaneous and sequential
moves.Games with both sequential and
simultaneous moves.

• Product development and pricing game.
• Consider a game in which two firms are deciding
  on their future product lines.
• Each must first choose whether to develop and
  produce one of two similar goods, a fancy
  expensive to manufacture high-tech model, or a
  cheaply produced low-tech version.
• Their decisions are unknown to each other up
  until the point the new models are unveiled.
• Once the models are unveiled each must then
  choose a pricing strategy. For simplicity they
  may choose a high or low priced for each model.

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Combining simultaneous and sequential
moves.Games with both sequential and
simultaneous moves.
Product development and pricing game. Game tree.
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Combining simultaneous and sequential
moves.Games with both sequential and
simultaneous moves.

• Product development and pricing game.
• The players first play a simultaneous product
  development game.
• They then play simultaneously play the pricing
  game.
• But the two games occur sequentially and thus
  the solution requires the use of backwards
  induction.

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Combining simultaneous and sequential
moves.Games with both sequential and
simultaneous moves.

• Rules Change.
• Switching from a sequential move to a
  simultaneous move game.
• Sometimes this switch can be used as a strategy.
• Consider the senate race game as in simultaneous
  form.

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Combining simultaneous and sequential
moves.Games with both sequential and
simultaneous moves.
Senate race game in simultaneous form. We see
that no ads is a dominant strategy for Arnold.
Hence Gary chooses in. In the sequential version
Arnold chose ads and Gary stayed out.
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Combining simultaneous and sequential
moves.Games with both sequential and
simultaneous moves.

• Subgame perfection.
• Suppose that gateway could commit to playing
  Foreign. The equilibrium would be U,U,F. But
  the commitment is not credible.
• Where the U, U node to be reached Gateway would
  play U.
• At each node the players will maximize.
• The continuations of the game from each node must
  be equilibria.
• This implies that the subgame perfect equilibrium
  is F,U,U.