Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For a two person game, player one has strategies A,B,C. Inspection reveals strategy B is strictly dominated by some mixture between A and C.

How does one calculate the probabilities assigned to A and C in the dominant strategy?

share|cite|improve this question
up vote 2 down vote accepted

The way we did it in my Combinatorics and Game Theory class was to let $p$ be the probability that we chose strategy A and $1-p$ be the probability that we chose strategy C. Then we drew a graph that has two vertical "axes" and a horizontal axis connecting the two in the middle. The horizontal axis is the value of $p$, ranging from 0 to 1. On the left "axis", put a dot corresponding to the value of strategy A when $p=0$ and another dot corresponding to the value of strategy C when $p=0$. Do the same for the right "axis" but when $p=1$. Thus, you will have two lines (that may or may not intersect) that show the values of strategies A and C depending on the choice of $p$. My guess is that you want the value of $p$ such that VA($p$) and VC($p$) are equal, which corresponds to the intersection of the lines you constructed on the graph.

I hope that's what you're asking for...

share|cite|improve this answer

In general, finding an optimal strategy in a finite two-person zero-sum game reduces to a linear programming problem.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.