Games with Stages

This lecture introduces games that take place over multiple stages.

Takeaway Points

  1. An extensive form game has stages if it has multiple phases. For example, if the players first play a prisoner’s dilemma and then play a stag hunt, we could say it has two stages. It could also be a prisoner’s dilemma that repeats some number of times.
  2. Payoffs from one stage do not directly affect payoffs from another stage.
  3. Players know each other’s previous moves.
  4. In the final stage (subgame), players must play a Nash equilibrium in all subgame perfect equilibria.
  5. Playing Nash equilibria in every stage is a subgame perfect equilibrium.
  6. There can be additional equilibria in which players play strategies that are not an equilibrium of the simultaneous move stage game. For example, it is possible under some conditions for players in a prisoner’s dilemma to cooperate.

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