Game Theory: The Applicability of Prudence to Nonzero-sum Gs

[merlin2007]

I have a problem set question relating to the following nonzero-sum game.


L R

U 5,3 1,1

D 1,1 4,2

Note: the L and the R should be at the heads of the columns, but for some reason the act of posting kills the spaces.


The question is "Find the Prudent (pure or mixed) strategies for each player.
von Neumann's minimax theorem states that there must be a saddlepoint in either pure or mixed strategies for every two-player zero-sum game. However, this is a non-zero sum game, and I'm uncertain about whether a prudent strategy exists, since the minimum of each row is 1 for the row player, and the minimum of each column is 1 for the column player. Are all the strategies then "prudent?"


Thanks

 

[JakeD]

Re: Game Theory: The Applicability of Prudence to Nonzero-su

I have a problem set question relating to the following nonzero-sum game.


L R

U 5,3 1,1

D 1,1 4,2

Note: the L and the R should be at the heads of the columns, but for some reason the act of posting kills the spaces.


The question is "Find the Prudent (pure or mixed) strategies for each player.
von Neumann's minimax theorem states that there must be a saddlepoint in either pure or mixed strategies for every two-player zero-sum game. However, this is a non-zero sum game, and I'm uncertain about whether a prudent strategy exists, since the minimum of each row is 1 for the row player, and the minimum of each column is 1 for the column player. Are all the strategies then "prudent?"


Thanks

By playing mixed strategies, can't the players guarantee themselves payoffs better than 1?

For spacing, use the [ code] ... [ /code] tags:

       L      R

U     5,3    1,1

D     1,1    4,2