Nash Equilibrium
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Le Chatelier's Principle regarding the "stressing" of reactions in equilibrium.
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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...more
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A probabilistic look at how molecules react to develop the intuition behind the equilibrium constant formula.
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We continue our discussion of mixed strategies. First we discuss the payoff to a mixed strategy, pointing out that it must be a weighed average of the payoffs to the pure strategies used in the mix. We note a consequence of this: if a mixed strategy is a best response, then all the pure strategies in the mix must themselves be best responses and hence indifferent. We use this idea to find mixed-strategy Nash equilibria in a game within a...more
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Over time, economists' justifications for why free markets are a good thing have changed. In the first few classes, we saw how under some conditions, the competitive allocation maximizes the sum of agents' utilities. When it was found that this property didn't hold generally, the idea of Pareto efficiency was developed. This class reviews two proofs that equilibrium is Pareto efficient, looking at the arguments of economists Edgeworth and...more
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We develop three different interpretations of mixed strategies in various contexts: sport, anti-terrorism strategy, dating, paying taxes and auditing taxpayers. One interpretation is that people literally randomize over their choices. Another is that your mixed strategy represents my belief about what you might do. A third is that the mixed strategy represents the proportions of people playing each pure strategy. Then we discuss some...more
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