In my attempts to learn the foundations, I was given the following game in a mock interview:
Two players each roll a d6, and are not able to see each other's rolls. The player with the higher value wins \$1. After the players roll their dice, each player may either pay \$0.25 to increase their individual roll by 2 or keep their roll. What is the optimal strategy and payout? Consider the cases for which i) nothing happens when both players roll the same number, and ii) the players keep rerolling (for free) until different numbers appear.
What is the best strategy here? Is it important for both players to have the same strategy for Nash/symmetric equilibrium (not sure what the terminology I should be using is)? What should my considerations be in calculating the expected value? Please help prod me to attempt deriving the strategy, thanks!