I can answer questions if anyone needs clarification! I just don't know where to start with this one. So far game theory has been really fun (I've already mastered mixed strategy equilibria), but this new Bayesian equilibria just confuse me. I originally thought this was just an iterative Prisoner's Dilemma game, but I guess I was wrong. Plus my TA's sick so I can't get any help.
Here's the question:
Suppose there are two countries that are making a simultaneous choice between accepting a peace deal that gives each a payoff of 1/2 and fighting a war, whose outcome is uncertain. If both countries accept then they get the settlement payoff, but any country can choose to start a war.
The outcome of a war is determined by the countries' types. Each country can be a weak, moderate, or strong type. In a war strong types beat weak and moderate ones, moderate ones beat weak ones, and weak ones always lose. When countries of the same strength meet, each wins with probability 1/2.
Also each country has private information, in particular they know their own strength but think that the opponent is equally likely to be weak, moderate, or strong. Finally, suppose the cost of war for all countries is c = 1/6 (c = cost), the strong type fights in equilibrium and the weak type does not in both countries. Does the moderate type of country fight or accept a settlement in equilibrium? Explain your answer.
Thanks!
P.S. I think by "simultaneous choice" the question means that the two countries don't know what the other is doing.
Here's the question:
Suppose there are two countries that are making a simultaneous choice between accepting a peace deal that gives each a payoff of 1/2 and fighting a war, whose outcome is uncertain. If both countries accept then they get the settlement payoff, but any country can choose to start a war.
The outcome of a war is determined by the countries' types. Each country can be a weak, moderate, or strong type. In a war strong types beat weak and moderate ones, moderate ones beat weak ones, and weak ones always lose. When countries of the same strength meet, each wins with probability 1/2.
Also each country has private information, in particular they know their own strength but think that the opponent is equally likely to be weak, moderate, or strong. Finally, suppose the cost of war for all countries is c = 1/6 (c = cost), the strong type fights in equilibrium and the weak type does not in both countries. Does the moderate type of country fight or accept a settlement in equilibrium? Explain your answer.
Thanks!
P.S. I think by "simultaneous choice" the question means that the two countries don't know what the other is doing.
