There are two players, and each one has a die with six sides from $1$ to $6$. The probability of each side landing is equal. Now, the two players roll their dice, and they only know the number of their own die. They will propose prices in turn, until one of them doesn't provide a higher price. The winner will get the money equal to the sum of these two dice minus the price they provided.
What is the optimal strategy for playing this game?