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Game with simultaneous and sequential decisions commitment problem
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=Ch7zLqxT6kU
[Scroll down for intermediate-level treatment] • This video shows three versions of a game: • assuming simultaneous decisions (or ignoring timing): analyzed in a payoff matrix • sequential game analyzed in a decision tree, in each of the two possible orders • It shows how a desired outcome may be difficult to achieve in circumstances where promises are not credible (i.e. commitment problem), and how that may be resolved in repeated interactions or by changing the order of actions. • Intermediate level (100C) • In the first part of the video we discuss the static version of the game, where decisions are simultaneous, so players don't know - when deciding - what the other will do (they don't have perfect information). Nonetheless, because Denise has a dominant strategy and as long as they have COMPLETE information (so they know each other's payoffs), Mac will be able to predict that Denise won't do her homework, and we can expect the outcome to be the Nash Equilibrium designated by the set of strategies (Home, TV). • 3:25 Next, we consider (in extensive form) the sequential version of the game where Mac decides first. [Aside: we could express this game in normal form, but Denise would now have 4 possible strategies, since she faces two possible situations and will choose between 2 actions in each case.] • We use backward induction and start with the proper subgames that involve Denise's decision. We determine she will choose TV in both, which means that the continuation values faced by Mac are (0,300) if he takes her Brickland and (100,0) if he doesn't. Thus, he will choose to keep her at home. So the only subgame perfect NE is (Home, TV TV). - notice that we have to specify what Denise will do in both possible situations she might theoretically face, not just the one that Mac chooses. • [Clarification: you might notice that I refer to a Nash Equilibrium as an outcome in some of these introductory videos: that's an oversimplification which works okay for static games but becomes problematic in dynamic games, especially at the intermediate and advanced levels.] • 5:00 Discussion of how the fact that Denise's promise to do her homework is not credible creates a problem in the sense that are not able to reach their preferred outcome. • 6:00 Using a promise as a way to alter payoffs in a way that allows them to reach the superior outcome. Formally, we would treat this as cooperation in a repeated game, where a certain punishment is specified for players who deviate from the agreement. • 7:34 Finally, the sequential game where Denise goes first. By first solving the two proper subgames, we find that Denise faces the continuation value (50,100) if she watches TV, and (150,200) if she does her homework. Thus, the subgame perfect NE is (HW, Home Brickland)
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