On this page there is a game with a payoff matrix that’s about a third of the way down the page. Can I solve this in excel? Perhaps graphically? Action A is obviously dominated by action C for player 2, but I can’t for the life of my remember how to get the given choice percentages.
You can do it graphically. First of all, drop action A - player 2 will never choose it as it is dominated by C. Then add 20 to the numbers in the matrix to get rid of negative numbers (this will only affect the value of the game, not the distribution of probabilities).
You can then draw up two axes. The horizontal axis is numbered 0 to 100 and indicates the probability, percentagewise, of player 1 choosing action 1. The vertical axis indicates player 1’s payoff.
For the first graph, we shall assume that player 2 is always choosing action B.
In this case, if player 1 always chooses action 1 (probability on horizontal axis: 100 %), his average payoff is 10 (remember that we added 20!). Mark the point (100; 10). If player 1 always chooses action 2 (probability on horizontal axis: 0 %), his average payoff will be 40. Mark the point (0; 40) and draw a line connecting the two points. Then you do it likewise under the assumption that player 2 is always choosing option C - marking and connecting two points. The two graphs should intersect at a point where 1’s probability for choosing option 1 is 57 %.
Thanks. How would you go about solving this if action A was not dominated by C. Lets say that action A resulted in 10 points no matter what player 1 chose. Would I need to use a different method, or could the graphical method work with some tweaking?