Why are all Nash equilibrium not Subgame perfect?

For the second normal-form game, the Nash equilibrium of the subgame is (A, X). For the entire game Nash equilibria (DA, Y) and (DB, Y) are not subgame perfect equilibria because the move of Player 2 does not constitute a Nash Equilibrium.

Is every Nash equilibrium Subgame perfect?

If an equilibrium is subgame-perfect, then not only is the equilibrium a Nash equilibrium itself, but also for every subgame of the original game, the strategies of the SPE are a Nash equilibrium for the subgame. So, all SPEs are Nash equilibria, but not all Nash equilibria are subgame-perfect.

How many subgames are there?

The whole game can be pictured in extensive form. There are five subgames.

What is considered a subgame?

In game theory, a subgame is a subset of any game that includes an initial node (which has to be independent from any information set) and all its successor nodes. A subgame-perfect equilibrium is an equilibrium not only overall, but also for each subgame, while Nash equilibria can be calculated for each subgame.

How do you find subgames?

In an extensive form game with perfect information, let x be a node of the tree that is not an end node. The part of the game tree consisting of all nodes that can be reached from x is called a subgame. Each game is a subgame of itself. A subgame on a strictly smaller set of nodes is called a proper subgame.

How do you count sub games?

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.

Can there be multiple SPNE?

More videos on YouTube This lecture shows how games can sometimes have multiple subgame perfect equilibria. 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.

How do you identify a sub game?