Terrence and Philip are debating over how to split a dollar.Both Terence and Philip

题目

Terrence and Philip are debating over how to split a dollar.Both Terence and Philip
simultaneously yell out their shares which we will denote by sT and sP .The rules that
apply are simple.
x0f If the sum of sT and sP is greater than $1,both players get zero.
x0f If the sum of sT and sP is less than or equal to $1,they both get the share they
call.
(a) Define the set of players (N),the set of strategies (S),and the pay-off function(u),of this game.
(b) Find and represent graphically the best-response function for Terence and Philip.
(c) Find all ) pure-strategy Nash equilibria of the game.

答案

参与人players N={T,P}
策略strategies S={St,Sp}
反应函数pay-off function
Ut=St 当(St+Sp1)
Up=Sp 当(St+Sp1)
所有的纳什均衡是
St+Sp=1
此时Ut=St Up=Sp