In each period, the two players move simultaneously, knowing the entire

history of past actions. In answering the following questions, be cold blooded and not one of those psalm$-$singing uninformed defeatists:

a$.$ Find a strategy profile and restrictions on parameters such that the strat$-$ egy profile is a SPNE and entails neither country using poison gas; that is$,$ t h e e q u i l i b r i u m o u t c o m e p a t h i s g tc $0$ a n d g th $0$ f o r a l l t $1,2,3,....$

b$.$ Find a strategy profile and restrictions on parameters such that the strat$-$ egy profile is a SPNE and entails both countries using poison gas; that is$,$ theequilibriumoutcomepathisgtc $0$andgth $0$forallt$1,2,3,....$

c$.$ Find a strategy profile and restrictions on parameters such that the strategy profile is a SPNE and entails Churchill using gas but Hitler not using gas; that is$,$ the equilibrium outcome path is gtc $0$ and gth $0$ for all t $1,2,3,....$