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Respond to the question: Solution with a saddle point?

 09/12/2000 09:27 AM by Walter;
I didn't say you can't use linear algebra to find a pure strategy NE. I said that it is easier to check for them first (at least for me it is easier to do it when the game is simple), and also it gives me reference of how many NE in mixed strategies I have to find. Remember that in non-degenerate games there is an odd number of NE (in pure strategies and mixed strategies).

Anyway, if you want to stick to the algebra, do it. If you find that Q is greater than or equal to 1, that means that you may have a pure strategy NE (you still have to check the other player's best response). If Q<1, you may have a mixed strategy NE (again, still check the other player's strategy and payoffs).

When games are bigger (more strategies, more players, etc.) algebra may be messy. I would check for dominated strategies first to reduce the game, check for NE in pure strategies to see whether I need to check for NE in mixed, etc. Example, suppose a 2-player game. If a player has a dominant strategy, then there is only one NE in pure str.. Why to spend time doing algebra?

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 09/10/2000 07:44 AM by KR Simpson; Solution...
Thanks Walter. What doesn't make sense to me is why I cannot use linear algebra to determine that there is a pure strategy. In other words, why I don't get t=1, and 1-t=0. There are other pure strategy games where I don't get t=7/5 [View full text and thread]

 09/04/2000 09:11 AM by Walter;
Let me repeat the game COL L R ROW U 3 5 D 1 -2 The numbers are player ROW's payoffs, since COL's payoffs are the negative of those (or some other number such that the sum of the utilities is [View full text and thread]

 09/02/2000 01:59 PM by KR Simpson; Solution with a saddle point...
I am trying to solve the zero-sum game: 3, 5 1, -2 Ignoring for the moment that this game has a saddle point, how can I solve using linear algebra? If I assign the column player fractional times Q and (1-Q), I should get Q=1, as [View full text and thread]