In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game.
How many subgame perfect equilibria are there?
Most games have only one subgame perfect equilibrium, but not all. When players receive the same payoff for two different strategies, they are indifferent and therefore may select either. This causes multiple SPE.
What are Subgames in game theory?
In game theory, a subgame is any part (a subset) of a game that meets the following criteria (the following terms allude to a game described in extensive form): It has a single initial node that is the only member of that node’s information set (i.e. the initial node is in a singleton information set).
How do you identify sub games in game theory?
In order to find the subgame-perfect equilibrium, we must do a backwards induction, starting at the last move of the game, then proceed to the second to last move, and so on.
What is the difference between subgame perfect Nash equilibrium and Nash equilibrium of an extensive form game?
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.
What is the subgame perfect equilibrium quizlet?
A Nash equilibrium of an extensive form game is a subgame perfect equilibrium if it induces Nash equilibrium play in every subgame. Nash equilibria that do not involve any incredible threats or promises in any part of any player’s strategy are called subgame perfect.
How many subgames are in a game tree?
There are three subgames: There are two proper subgames; one beginning at node B and one beginning at node A. The game itself is a subgame.
What is Bayesian Nash equilibrium?
A Bayesian Nash equilibrium (BNE) is defined as a strategy profile that maximizes the expected payoff for each player given their beliefs and given the strategies played by the other players.
What is a singleton in game theory?
If a game has an information set with more than one member that game is said to have imperfect information. A game with perfect information is such that at any stage of the game, every player knows exactly what has taken place earlier in the game; i.e. every information set is a singleton set.
How many subgames are in game theory?
a) There are 6 proper subgames in this game.
What is subgame in economics?
A subgame perfect equilibrium is a set of strategies (one for each of the players) with the property that the strategies constitute a Nash equilibrium for every subgame of the original game. A subgame perfect equilibrium is usually found using backward induction.
