What would you like to understand?

To calculate the probability $p$ for Player 1's mixed strategy, you must determine the value of $p$ that makes Player 2 completely indifferent between choosing their pure strategies, Right (R) and Left (L). This is done by computing Player 2's expected payoff for each of their pure strategies as a function of $p$, setting those two expected payoffs equal to each other, and solving the resulting linear equation for $p$.

Conditions: The game is a finite normal-form game with a 2x2 payoff matrix.; Player 1 chooses R with probability $p$ and L with probability $1-p$.; Player 2's expected payoffs from playing R and L must be calculated using Player 1's mixed strategy.; The solution for $p$ must lie in the interval $[0, 1]$ to represent a valid mixed strategy.

To calculate the probability $p$ for Player 1's mixed strategy, you must determine the value of $p$ that makes Player 2 completely indifferent between choosing their pure strategies, Right (R) and Left (L). This is done by computing Player 2's expected payoff for each of their pure strategies as a function of $p$, setting those two expected payoffs equal to each other, and solving the resulting linear equation for $p$.

Conditions: The game is a finite normal-form game with a 2x2 payoff matrix.; Player 1 chooses R with probability $p$ and L with probability $1-p$.; Player 2's expected payoffs from playing R and L must be calculated using Player 1's mixed strategy.; The solution for $p$ must lie in the interval $[0, 1]$ to represent a valid mixed strategy.