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Respond to the question: Finding number of Subgame perfect Nash e?

12/09/2006 09:25 AM by name withheld; Finding number of Pure Strategy Subgame Perfect NE
From the payoff matrix, we can find there exist two stage pure strategy NE. They are (T,L) and (M,C) with payoff (13,13) and (5,5) respectively. The stage game plays twice. Certainly, for any Subgame Perfect NE, at the last stage (second stage) the players must play a stage NE. That means at the second stage the equilibrium is either (T,L) or (M,C). Certainly, playing stage NE at each stage is always Subgame Perfect NE. Thus, there are at least four pure strategy Subgame Perfect NE.

Moreover, since (T,L) has payoff (13,13) larger than the payoff (5,5) from (M,C), at the first stage, with appropriate discount factor, players can enforce some of non-stage NE profile through a threat as following: if the opponent does not follow the non-stage NE profile, then he will play (M,C) instead of (T,L) and his opponent will lose 8 at the second stage. For instance, 1st stage (B,R) and 2nd stage (T,L) is a Subgame Perfect NE if discount fact is greater than or equal to 0.5. You may check all other pure strategy profiles in the payoff matrix.

If discount factor is approaching one, you may find that there exist 7 pure strategy Subgame Perfect NE. If discount factor is approaching zero, you may find that there exist 4 pure strategy Subgame Perfect NE. [Manage messages]

11/20/2006 11:41 PM by name withheld; Finding number of Subgame perfect Nash eq.
Consider the following stage game, which is to be played twice in succession (this is a repeated game with T=2.) How many pure strategy subgame perfect equilibria are there? Normal Form: Player 1 strategy set: {T, M, B} Player 2 [View full text and thread]