# 博弈论-经管之家官网！

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Jerry can hide in the bedroom, the den or the kitchen. Tom can search in one and only one of these locations. If he searches where Jerry is hiding, he catches Jerry. Otherwise Jerry escapes. If Jerry is caught, Tom's utility is 1 and Jerry's is 0. If Jerry gets arMay, Tom's utility is 0 and Jerry's is 1.

(a) Draw the game tree for the case when Tom can see where Jerry hides before searching. Explain why Tom has 27 strategies to choose from while Jerry has only 3. What are the subgame perfect equilibria?

(b) Draw the game tree for the case when Jerry can see where Tom searches before hiding. How many possible strategies does each player have? Write down 4 different pure-strategy subgame perfect equilibria. How many pure-strategy subgame perfect equilibria are there?

(c) Draw a game tree for the case where the players make their decisions in ignorance of the other's choice. Write down the strategic form. Does this game have a mixed-strategy equilibrium?

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