by Mr. Philip Wilderman PhD
Published 2 years ago
Updated 1 year ago
The subgame perfect equilibria are computed as follows. First compute a Nash equilibrium of the subgame, then fixing the equilibrium actions as they are (in this subgame), and taking the equilibrium payoffs in this subgame as the payoffs for entering the subgame, compute a Nash equilibrium in the remaining game.
What is a subgame perfect equilibrium?
A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that at any point in the game, the players' behavior from that point onward should represent a Nash equilibrium of the continuation game (i.e. of the subgame), no matter what happened before.
How do you find the perfect equilibrium of a finite game?
A common method for determining subgame perfect equilibria in the case of a finite game is backward induction. Here one first considers the last actions of the game and determines which actions the final mover should take in each possible circumstance to maximize his/her utility.
Why is the Nash equilibrium (UA/X) a subgame perfect?
The Nash equilibrium (UA, X) is subgame perfect because it incorporates the subgame Nash equilibrium (A, X) as part of its strategy. To solve this game, first find the Nash Equilibria by mutual best response of Subgame 1.
What is subgame perfection?
Subgame perfection generalizes this notion to general dynamic games: Definition 11.1 A Nash equilibrium is said to be subgame perfect if an only if it is a Nash equilibrium in every subgame of the game. A subgame must be a well-defined game when it is considered separately. That is,
What is the difference between Nash and Subgame Perfect Equilibrium?
The key difference between subgame perfect equilibrium and Nash equilibrium is that subgame perfect equilibrium require that all threats are credible. Consequently, the study of subgame perfect equilibrium is the study of credible threats. Subgame perfect equilibria are a subset of Nash equilibria. That is, a subgame perfect equilibrium is ...
What are Nash Equilibria strategies?
Strategies from Nash equilibria allow players to take actions that they would not actually want to do when it is time for them to implement those actions.
Is a Nash equilibrium a subgame perfect equilibrium?
Subgame perfect equilibria are a subset of Nash equilibria. That is, a subgame perfect equilibrium is a Nash equilibrium. But a Nash equilibrium may or may not be a subgame perfect equilibrium. Back to Game Theory 101.
How to construct a non-subgame perfect NE?
Adding to @soslow's answer: once you have an SPE, it should be easy to construct a non-subgame-perfect NE by modifying the off-equilibrium actions in such a way that 1) the players have no incentive to deviate to those actions and 2) the action profile is not a NE in any subgame.
Is there a pure strategy nash equilibrium?
In a game theory textbook there is something similar to the table below where there is one pure strategy nash equilibrium and multiple mixed strategy nash equilibria. It is a simultaneous game with the payoffs presented below.
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Subgame Perfect Equilibrium Subgame Perfect Equilibrium Note that a strategy speci es a strategy for any subgame. For any strategy s i 2S i, denote the continuation strategy after h …
