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 game theory math best response function
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Posted - 09/10/2007 :  09:44:19  Show Profile

Two people have 10 dollars to divide between themselves. they use the following procedure. each person names a number of dollars (nonnegative integer), at most equal to 10. 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 are the same, each person receives 5 dollars. determine the best response of each player to each of the other players' actions and thus find the nash equilibria

I need to know how this answer is gotten, so plz show or tell me how work done

players : two individuals
actions : each players' set of actions is the set of effort levels (non negative numbers)
preferences : player i's pereferences are representede by the payoff function Ai(c+Aj-Ai)

To find the nash equilibria we can construct and analyze the players best response functions. given Aj, in dividual i's payoff is a quadratic function of Ai that is zero when Ai=0 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 u know calc, you can reach the same conclusion by setting the derivative of player i's payoff with respect to Ai equal to zero.

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