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Lecture 6 - Economics 101 UCLA Fall 2010 Jernej Copic...

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Economics 101, UCLA Fall 2010 Jernej Copic Lecture 6, 10/16/10. Notes on the equilibrium principle and Pareto e ciency; For a moment our story changed to a direct commentary. 1. The equilibrium principle. We have seen examples of equilibria of various games. Before moving on, let’s formulate a general way to state that a “social situation” is in equilibrium, call this the equilibrium principle. An equilibrium situation is one in which no individual can benefit by changing his/her own behavior given available information. This principle applies entirely generally, not only in games but also in other models of social interaction (later we will see that in the context of general equilibrium), as long as economic individuals are able to decide what is the best thing to do given their objective (aka utility function). In other words, none of the economic individuals could benefit by unilaterally acting di ff erently than they do. Important! Of course it could still be that everyone together could benefit if they could somehow coordinate their behavior. Unfortunately, there is no guarantee that such joint coordination would be in equilibrium - for example, in the game of a study group (aka prisoners’ dilemma) both players would benefit if they could somehow agree to play the strategy where each studies. But such agreement would not be in equilibrium, as each would have an incentive to change his own behavior to not studying. For a second, let’s just focus on the last part of this principle: “given available information.” Remember for instance the sequential game between Jeremiah and No1. There, when No1 decides his action, he has no particular information. Jeremiah, however, when it is his turn to take his action, knows what No1 did. Thus, in that case “available information” for Jeremiah would be the history, or in what situation he finds himself is what No1 did (remember that Jeremiah’s strategy specifies what he does for every possible situation or history - in our narration, that was embodied in the instruction set that Jeremiah gives to Clodoveo). In a model of a simultaneous-move game, none of the players has any particular information on which to base his decision, so we can then simply disregard the last part of the principle. If we take a mixed equilibrium of a game, as we have seen in the example of the coordination game, then none of the players could benefit by changing their behavior. That is because in the mixed equilibrium, each player is indi ff erent between both of his actions 1
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so it would make no di ff erence for him if instead of flipping a coin between the actions, he took either one for certain (and it would for the same reason make no di ff erence to him if he played them with di ff erent probabilities - the only problem is that then the other player would no longer be indi ff erent so that would not be an equilibrium situation). In any case, none of the players can benefit by changing his/her own behavior.
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