Problem Set 1, MIEG (Part II), Winter Term, 2016
1. Carefully observe the game tree below and find if there is any contradiction(s) to the standard conventions of game theory. How many subgames and information sets are there in this game. What happens if instead of player 1 some other player, say player 3, starts the game.
2. Analyse each of the following game trees below :-
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Now, for each game tree above compute:
(i) All pure strategy SPNE
(ii) A pure strategy Nash equilibrium which is not a SPNE.
(iii) A mixed strategy SPNE.
3. Alpha(A) and Beta(B) have been facebook friends for a long time. They decide to go on a date. They have two options: quick lunch at Pizza Hut, or movie at PVR.A first chooses where to go. B doesn’t automatically know where A went, but she can learn without any cost. She can see A0s FB update to know where he went or she can ignore it consciously (i.e. without knowing where A went, B first chooses between Learn (without any cost) and Not-Learn); if she chooses Learn, then she knows where A went and then decides where to go; otherwise she chooses where to go without learning where A went. The payoffs depend only on where each player goes. A prefers PVR, and B prefers Pizza Hut. A player gets 3 out of his/her preferred date option, 1 out of his/her less preferred date option, and 0 if they end up at different places. All these are common knowledge. Find a SPNE of this game.
Compare it with the case when B doesn’t have option of not knowing about A0s action i.e.
she knows for sure where A went. Does it seem (counter) intuitive.
Note: Special emphasis should be given to writing the strategies precisely.
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