//This code calculates the
//quantal response equilibria 
//for a crisis model with audience costs
//10.15.11

clear all

set more off
version 11.1
clear all
set mem 500m
set obs 2500
// parameters of the model

global max=10
global d=-0.3
global war_a=0.2
global war_b=0.2

//code

gen y=_n
gen lambda= ($max/2500)*y
gen A_backs_down= 1/(1+exp(lambda*($war_a -$d)))
gen B_backs_down= 1/(1+exp(lambda*(A_backs_down+(1-A_backs_down)*$war_b)))
gen A_status_quo=1 /(1+exp(lambda*(B_backs_down+(1-B_backs_down)*(A_backs_down*$d+(1-A_backs_down)*$war_a))))


twoway line A_backs_down  lambda || line B_backs_down  lambda || line A_status_quo  lambda   ||,  ytitle( "probabilities") xtitle( "lambda" )title( "QRE probabilities",span  ) subtitle("when labmda=0 model predicts perfect randomization,""as lambda increases model approaches NE") note("Model parameters: domestic audience cost=$d, cost of war for A=$war_a, cost of war for B=$war_b")