Below is a question from the final for my half-semester PhD game theory course. I’ve put the game tree answer right below. For the other answers, see the comment section, where I’ll put them as a comment.
Bonus question for blog readers: Will Russia invade Estonia and Latvia?
They are the modern analog of Czechoslovakia, as the Crimea is the analog of Austria, Syria the analog of Spain, the Ukraine proper the analog of Poland, and Finland the analog of the Baltic Republics. NATO is the analog of France, America the analog of the UK, and China the analog of the Soviet Union, but fortunately Russia’s army isn’t analogous to the Werhrmacht and would have to stop with Finland.
Question. Russia’s leaders are either bold or timid. President Obama puts a 70% probability on them being bold. The Russian leaders must decide whether to invade the Crimea or not. If they do, Obama must decide whether to send troops to the Ukraine or not. If he does, then Russia’s leaders must decide whether to withdraw or risk a fight. The status quo payoffs can be set at (0,0)….