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# GAME THEORY

Problem 1. Consider a slight modiﬁcation of the Model of entry game from our lectures. Again,
there are two ﬁrms, A (a potential entrant) and B (an incumbent monopolist), involved in a game
where A moves ﬁrst. A either stays out, in which case A gets 2 and B gets 3, or enters B ’s market.
If A enters, the ﬁrms simultaneously choose between two actions: Hawk (an aggro-live action) and
Dove (a peaceful action). The payoffs in this subgame are as follows: (i) if a ﬁrm chooses Hawk and the other plays Dove, then Hawk gets 3 and Dove gets 0;
(ii) if both play Hawk, then each gets —1;
(iii) if both choose Dove, then each gets 1. For task (a) below, use the bimatrix—game representation of the game by ﬁrst listing the players’
strategies. For (b), use backde induction. In the lectures, we only covered sequential games with
perfect information, which is not the case here, as the ﬁrms decide simultaneously in the second
stage of the game (after A enters). But backward induction is analogous here: ﬁrst solve for the NE in the second-stage subgame, then use these NE results to conclude about A’s decision on whether
or not to enter. a) Find all Nash equilibria of the game. Show your work. 5 points
b) Find all subgameperfect Nash equilibria of the game. Show your work. 5 points

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