I've got a question to ask about the Nash Demand game from my assignment.
Sarah and Ruth find \$100 on the ground and decide to split it between them in the following manner. Each individual simultaneously and independently selects how much of the \$100 she wants to keep. Denote this value by $xi$. If $𝑥𝑆+𝑥𝑅≤100$, then each player receives the amount she desires. If $𝑥𝑆+𝑥𝑅>100$, they forfeit the \$100, and each player receives \$0. Find all of the Nash equilibria. Explain how you come to your conclusion (i.e. how you know that your answer is exhaustive.)
I think that I've solved the Pure Strategy Nash Equilibrium for this game which is basically $𝑥𝑆+𝑥𝑅=100$. But I'm wondering whether there are any Mixed Strategy Nash Equilibrium so if anyone could help me out that I would be very appreciative! :)