Two people have 10 dollars to divide between themselves. They use the following procedure

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 named (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 named 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 receives 5 dollars. Determine the best response of each player to each of the other players' actions, plot them in a diagram and thus find the nash equilibrium

I need to know HOW the answer was gotten also, not just an answer.

Guideline:

uses formula Ai(c+Aj-Ai) where Ai is i's effort level, Aj is the other individuals effort level, and c>o is a constant

Players: two individuals
Actions Each players' set of actions is the set of effort levels (nonnegative numbers)

Preferences Player i's preferences are represented by the payoff function Ai(c +Aj-Ai)

Given Aj, individual i's payoff is a quadratic function of Ai that is zero when Ai=o and when Ai = c + Aj, and reaches a maximum in between. The symmetry of quadratic functions implies that the best response of each individual i to Aj is

Bi (Aj) = 1/2 (c+Aj)

If you know calculus you get same conclusion by setting the derivative of player i's payoff with respect to Ai equal to zero.

ANY HELP AT ALL SOOOOOOOO MUCH APPRECIATED

eric. Nothing posted.

If you are trying to copy and paste, I suggest you simply type it in. Also, I suggest you look at what you have posted after you have done so to see what is there.

nope, that's what i meant to type, dunno wat u mean

the prime factorization of 9 and 21

To find the Nash equilibrium in this scenario, we need to determine the best response of each player to each of the other player's actions.

Let's consider the actions available to each player as the set of effort levels, which are nonnegative numbers. Let's denote the effort level of Player 1 as A and the effort level of Player 2 as B.

According to the given preferences, Player i's payoff is represented by the function Ai(c + Aj - Ai), where Ai is Player i's effort level, Aj is the other player's effort level, and c > 0 is a constant.

First, let's analyze Player 1's best response to Player 2's effort level (B). To find the best response, we need to maximize Player 1's payoff function with respect to A.

Taking the derivative of Player 1's payoff function with respect to A and setting it equal to zero, we can find the maximum point. So, let's differentiate Ai(c + Aj - Ai) with respect to A:

d(A1(c + A2 - A1))/dA1 = c + A2 - 2A1

Setting this equal to zero and solving for A1:

c + A2 - 2A1 = 0
A1 = (c + A2)/2

This implies that Player 1's best response to Player 2's effort level (B) is given by:

B1(B) = (c + B)/2

Now, let's analyze Player 2's best response to Player 1's effort level (A). Using a similar approach, we can find the best response of Player 2.

Taking the derivative of Player 2's payoff function with respect to B and setting it equal to zero, we can find the maximum point:

d(A2(c + A1 - A2))/dB2 = c + A1 - 2A2

Setting this equal to zero and solving for A2:

c + A1 - 2A2 = 0
A2 = (c + A1)/2

This implies that Player 2's best response to Player 1's effort level (A) is given by:

B2(A) = (c + A)/2

In summary, the best response of each player to the other player's effort level can be determined using the formulas:

B1(B) = (c + B)/2
B2(A) = (c + A)/2

To find the Nash equilibrium, we need to find the effort levels (A, B) for which neither player can gain by unilaterally deviating from their chosen effort level. This occurs when each player's effort level is the best response to the other player's effort level.

So, in the Nash equilibrium, we have:

A = B1(B) = (c + B)/2
B = B2(A) = (c + A)/2

Solving these equations simultaneously will give us the Nash equilibrium effort levels (A, B). By plotting these equations on a graph, we can determine the Nash equilibrium point(s) where the two lines representing the best responses intersect.