Subgame Perfect Equilibrium

Game Theory · Axiom Academy

LESSON Subgame Perfect Equilibrium Unit 3 - Sequential Games: Refining Nash Equilibrium to Eliminate Non-Credible Threats A subgame is a portion of a game that can be analyzed as a game in its own right. It begins at a single decision node and includes all subsequent nodes and actions. Key requirements for a subgame: Begins at a single decision node (not an information set) No information set is partially included 2. Subgame Perfect Equilibrium (SPE) A Subgame Perfect Equilibrium is a strategy profile that induces a Nash Equilibrium in every subgame of the game, including the game itself. Players play optimally not just on the equilibrium path They also play optimally at every off-equilibrium decision node No player can improve by deviating at any point in the game 3. SPE as a Refinement of Nash Equilibrium Every SPE is a Nash Equilibrium, but not every Nash Equilibrium is subgame perfect. SPE eliminates Nash equilibria that rely on non-credible threats . Why some Nash equilibria aren't subgame perfect: They may rely on threats that are irrational to execute They don't specify optimal behavior at off-equilibrium nodes They can be "sustained" by incredible punishments 4. Example: Entry Deterrence Game Consider a market entry game where an Entrant decides whether to Enter or Stay Out, and an Incumbent decides whether to Fight or Accommodate. Stay Out, (Fight or Accommodate): (0, 5)

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