A warrior $($W$)$ and a mage $($M$)$ are exploring a dungeon looking for monsters. Their exploration is framed as a two$-$stage game. In the first stage, they prepare to fight a monster in the next room, and both of them can do either of two actions: cast a spell $($C$)$ or draw the sword $($D$)$; actually, strong W does not like to C and lazy M prefers not to choose D$.$ Still, they choose their actions simultaneously without talking or communicating to each other in advance. Both players are fully aware of each other$$s partial payoffs for this stage, that are defined as follows: they get utility $2$ if they choose different actions, while their utility is $0$ if the actions are the same because this might make them less prepared against certain enemies. Moreover, $1$ must be subtracted from the utility of a player who chooses the less$-$favourite action. After that stage, a second stage is played where the two adventurers, while grabbing their loot, are surprised by a troll. Now, they can either run cowardly $($R$)$ or attack the troll $($A$).$ Also this action is decided independently of each other and at the same time. If they both attack, they successfully slay the troll $($payoff $5$ for both$).$ A player attacking alone gets killed by the troll $($payoff $100)$ while the other is unharmed and can easily take the treasure before running away $($payoff $10).$ If they both run, they manage to escape but they must leave the treasure behind $($payoff $0).$Find all the Nash equilibria of the two$-$stage game.