You and your friend will divide $4. You have agreed to use the following procedure. Each of you will name a number of dollars, either $0, $1, $2, $3, or $4. You will choose your numbers simultaneously. If the sum of the amounts is less than or equal to $4, then each of you receives the amount you named and the rest of the money is thrown away. If the sum of the amounts is greater than $4 and the amounts named are different, then the person who named the smaller amount receives that amount and the other person receives the remaining money. If the sum of the amounts is greater than $4 and the amounts named are the same, then each receives $2. (a)Draw the payoff matrix of this game. Let “you” be the row player and “your friend” be the column player. (b) Derive the best reply functions of all players. (c) Find the Nash equilibrium (or all of the equilibria) of this game using the best reply functions you found in part (a).
You and your friend will divide $4. You have agreed to use the following procedure.
Each of you will name a number of dollars, either $0, $1, $2, $3, or $4. You will choose
your numbers simultaneously. If the sum of the amounts is less than or equal to $4, then
each of you receives the amount you named and the rest of the money is thrown away.
If the sum of the amounts is greater than $4 and the amounts named are different, then
the person who named the smaller amount receives that amount and the other person
receives the remaining money. If the sum of the amounts is greater than $4 and the
amounts named are the same, then each receives $2.
(a)Draw the payoff matrix of this game. Let “you” be the row player and “your
friend” be the column player.
(b) Derive the best reply functions of all players.
(c) Find the Nash equilibrium (or all of the equilibria) of this game using the
best reply functions you found in part (a).
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