ECON600lect9 - ECON 600 Lecture 9: Strategic Commitment...

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ECON 600 Lecture 9: Strategic Commitment We’ve already discussed strategic commitment in a couple of different contexts, but now we are going to be more specific and rigorous about it. The key point to understand about strategic commitment is this: it sometimes makes sense to restrict your own choices, because doing so will affect the behavior of others . I. Some Prior Examples Revisited “Market Segmentation” was one example we discussed of a game with multiple equilibria. It looked like this: Crunchy Creamy Crunchy 3, 3 8, 5 Creamy 5, 8 2, 2 As represented, this is a simultaneous game. There are two NE: {Crunchy, Creamy} and {Creamy, Crunchy}. Without having more information about the history of the game, the reputations of the firms, and so on, there’s not much more we can say. But now, let’s suppose one of the firms is able to move first. It can build its peanut-butter factory before the other firm, buying capital equipment and other inputs that are specific to the type of peanut butter it will make. Assume that it is either impossible or very costly to reverse these commitments. Then the game looks like this: The bold lines designate the subgame perfect equilibrium. In that equilibrium, firm 1 chooses Crunchy, and firm 2 chooses Creamy in response to Crunchy. (It is also part of firm 2’s strategy’s that it would choose Crunchy in response to Creamy, but that aspect of firm 2’s strategy will never be relevant.) In other words, firm 1’s ability to commit gives it a first-mover advantage, allowing it to choose the more favorable of the one-shot game’s two equilibria. We could apply the same reasoning to show that, in the Battle of the Sexes game, the partner who can move first – and commit to her choice! – can select the equilibrium that 1 2 2 Crunchy Crunchy Crunchy Creamy Creamy Creamy 3 3 2 2 8 5 5 8
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is more favorable to her. (The equilibrium that is better for the first mover is the only subgame perfect equilibrium.) And we could apply the same reasoning once more to get a similar result in the Chicken game. Once again, the first mover gets an advantage if she can commit herself to sticking with her choice. In all of these games, a commitment enables a first-mover to choose one of two possible equilibria. Now let’s look at the Mad Bomber game again. In the original version of the game, the first choice was yours (pay or not pay) and the second was the bomber’s (bomb or not bomb). Given any choice by you, it was always in his interest not to bomb; that is, he had a dominant strategy of not bombing. But now suppose the bomber has the first move: he can choose to push a button on a robot, irrevocably committing the robot to explode if you don’t pay. What happens then? The game looks like this: The bold lines show the subgame perfect equilibrium. [NOTE: To make this game comparable to the simpler version, I have violated the usual convention of having the first payoff in each pair be the payoff of the first player. Here, the first player is the
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ECON600lect9 - ECON 600 Lecture 9: Strategic Commitment...

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