(Dividing money) Two people have $10 to divide between themselves. They use the following process…

(Dividing money) Two people have $10 to divide between themselves. They use the following process to divide the money. Each person names a number of dollars (a nonnegative integer), at most equal to 10. If the sum of the amounts that the people name is at most 10 then each person receives the amount of money she names (and the remainder is destroyed). If the sum of the amounts that the people name exceeds 10 and the amounts named are different then the person who names the smaller amount receives that amount and the other person receives the remaining money. If the sum of the amounts that the people name exceeds 10 and the amounts named are the same then each person receives $5. Determine the best response of each player to each of the other player’s actions, plot them in a diagram like Figure 36.2, and thus find the Nash equilibria of the game. A diagram like Figure 36.2 is a convenient representation of the players’ best response functions also in a game in which each player’s set of actions is an interval of numbers, as the next example illustrates.