Nash equilibrium
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We apply the notion of Nash Equilibrium, first, to some more coordination games; in particular, the Battle of the Sexes. Then we analyze the classic Cournot model of imperfect competition between firms. We consider the difficulties in colluding in such settings, and we discuss the welfare consequences of the Cournot equilibrium as compared to monopoly and perfect competition.
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We first complete our discussion of the candidate-voter model showing, in particular, that, in equilibrium, two candidates cannot be too far apart. Then we play and analyze Schelling's location game. We discuss how segregation can occur in society even if no one desires it. We also learn that seemingly irrelevant details of a model can matter. We consider randomizations first by a central authority (such as in a bussing policy), and then d...more
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We first consider the alternative "Bertrand" model of imperfect competition between two firms in which the firms set prices rather than setting quantities. Then we consider a richer model in which firms still set prices but in which the goods they produce are not identical. We model the firms as stores that are on either end of a long road or line. Customers live along this line. Then we return to models of strategic politics in which it i...more
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In this lecture, Professor Diamond continues a review of the nervous system and covers the eye and the ear. She begins by diagramming the eye, and she differentiates between the eye itself and its accessory structures, including the bony orbit, the eyebrow and eyelids, and the conjunctiva. She describes how tarsal glands in the eyes function. Then, Professor Diamond moves on to the subject of the ear. She touches on the three divisions...more
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In order for Social Security to work, people have to believe there's some possibility that the world will last forever, so that each old generation will have a young generation to support it. The overlapping generations model, invented by Allais and Samuelson but here augmented with land, represents such a situation. Financial equilibrium can again be reduced to general equilibrium. At first glance it would seem that the model requires a s...more
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Professor Sylvia Ceyer begins by adding and subtracting half-cell reactions (a continuation of her prior lecture on oxidation/reduction). The Nernst Equation is introduced, which can be used to determine the equilibrium reduction potential of a half cell in an electrochemical cell.
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After mentioning some legal implications of chirality, the discussion of configuration concludes using esomeprazole as an example of three general methods for producing single enantiomers. Conformational isomerism is more subtle because isomers differ only by rotation about single bonds, which requires careful physico-chemical consideration of energies and their relation to equilibrium and rate constants. Conformations have their own notat...more
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Philosophers and theologians have railed against interest for thousands of years. But that is because they didn't understand what causes interest. Irving Fisher built a model of financial equilibrium on top of general equilibrium (GE) by introducing time and assets into the GE model. He saw that trade between apples today and apples next year is completely analogous to trade between apples and oranges today. Similarly he saw that in a worl...more
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Using theoretically quasi-static and/or reversible processes to stay pretty much at equilibrium.
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Equilibrium reactions and constants.
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In business or personal relationships, promises and threats of good and bad behavior tomorrow may provide good incentives for good behavior today, but, to work, these promises and threats must be credible. In particular, they must come from equilibrium behavior tomorrow, and hence form part of a subgame perfect equilibrium today. We find that the grim strategy forms such an equilibrium provided that we are patient and the game has a high p...more
