If I understand you correctly, is the following the correct 4x4 payoff-matrix? See the following Word document.
Jack and Jill play a game. First, each flips a coin. After seeing their own coins (but not each others’), each player (separately) says either “Red” or “Black”. If they name opposite colors, then the Black-sayer gets $4 and the Red-sayer gets nothing. If both say Black, then they both get either $5 (if both flipped heads) or $10 (otherwise). If they both say Red, then they both get either nothing (if both flipped heads) or $20 (otherwise).
1. Set up the game matrix with players, strategies, and payoffs.
2. Are there any dominant strategies? Dominated strategies?
3. Write down the players' maximization problem and LaGrangian
4. What is the mixed-strategy equilibrium?
5. Is there a pure-strategy equilibrium?
I don't know what to do, I can work with a problem in which there are two colors and two people, but how to solve this when there is also two faces to a coin? Help!