econs424_spring2018_homework_1_all_files.pdf

econs424_spring2018_homework_1_all_files.pdf - EconS 424...

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1 EconS 424 Strategy and Game Theory Homework #1 – Answer Key Exercise 1 From extensive form to normal form representation Consider the following extensive form game Player 2 Player 2 Player 1 H L a r M Player 2 a r a r 10 0 0 0 5 5 0 0 0 10 0 0 a) Which are the strategies for player 1? Three strategies S 1 ={H,M,L} b) What are the strategies for player 2? Now the second mover can condition his move to the first player’s action, since he is able to observe it (unlike in the prisoners’ dilemma game). Hence, S 2 ={ aaa, aar, arr, rrr, rra, raa, ara, rar } where each of them represents a complete plan of action that specifies what to do in the event that player 1 chooses H, in the event that player 1 chooses M and in the case that he chooses L, respectively. c) Take your results from a) and b) and construct a matrix representing its normal form game representation. If you take the about three strategies for player 1, and the above eight strategies for player 2, we have the following normal form game.
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