# Game theory: value of a game

1. Feb 26, 2006

### mathlete

The problem:
"Player I can choose l or r at the first move in a game G. If he chooses l, a chance move selects L with probability p, or R with probability 1-p. If L is chosen, the game ends with a loss. If R is chosen, a subgame identical in structure to G is played. If player I chooses r, then a chance move selects L with probability q or R with probability 1-q. If L is chosen, the game ends in a win. If R is chosen, a subgame is played that is identical to G except that the outcomes win and loss are interchanged together with the roles of players I and II"

*whew*

Now the question is... if the value of the game is v, show that v=q+(1-q)(1-v)

Now the game tree is so complicated... I really have no idea how to get the value of the game. Is there any easy way to do this that i'm missing?

2. Feb 26, 2006

### Hurkyl

Staff Emeritus
I don't understand the statement of the game.

What happens when player I picks l', and R' gets chosen? Is it now player II's turn? Does "win" always mean a win for player I? et cetera.

If I sat down and tried to teach this game to someone else so we could play, I'd have no idea what the rules are.

Anyways, the analysis should be straightforward.

What is the expected value of the game if player I picks l'?
What is the expected value of the game if player I picks r'?
What is the expected value of the game if player I picks optimally?

Last edited: Feb 26, 2006
3. Feb 27, 2006

### neurocomp2003

are L,R the nodes and l,r are the branches??

4. Oct 11, 2009