Wednesday
April 23, 2014

Homework Help: math

Posted by eric on Sunday, September 9, 2007 at 11:20pm.

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

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