Nash equilibrium
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This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
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Professor Sylvia Ceyer discusses the nature of chemical equilibrium as it relates to free energy, the reaction quotient, and the relationship between K and Q. The meaning of K is further clarified and the external effects on K are identified, from adding and removing reagents to changes associated with the Principle of Le Chatelier.
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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 impli...more
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We first discuss Zermelo's theorem: that games like tic-tac-toe or chess have a solution. That is, either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win. The proof is by induction. Then we formally define and informally discuss both perfect information and strategies in such games. This allows us to find Nash equilibria in sequential games. But we fin...more
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This course attempts to explain the role and the importance of the financial system in the global economy. Rather than separating off the financial world from the rest of the economy, financial equilibrium is studied as an extension of economic equilibrium. The course also gives a picture of the kind of thinking and analysis done by hedge funds.
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This course deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions.
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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 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
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Stoichiometry of chemical reactions, quantum mechanical description of atoms, the elements and periodic table, chemical bonding, real and ideal gases, thermochemistry, introduction to thermodynamics and equilibrium, acid-base and solubility equilibria, introduction to oxidation-reduction reactions.
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Life history covers three main classes of traits in organisms: age and size at maturity, number and size of offspring, and lifespan and reproductive investment. Organisms must make tradeoffs among these traits that typically cause them to come to evolutionary equilibrium at intermediate values. Life history traits are evolutionary solutions to the ecological problems of the risk of mortality and the acquisition of food, and they are expres...more
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Until now we have ignored risk aversion. The Bernoulli brothers were the first to suggest a tractable way of representing risk aversion. They pointed out that an explanation of the St. Petersburg paradox might be that people care about expected utility instead of expected income, where utility is some concave function, such as the logarithm. One of the most famous and important models in financial economics is the Capital Asset Pricing Mod...more
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Professor Sylvia Ceyer discuses titrations involving a strong acid and a strong base. Defining the point and equivalence and the end point. The lecture continues with a focus on calculating points on a pH curve, specifically calculating pH before the equivalence point, calculating volume of HCl needed to reach equivalence point, and calculating pH after the equivalence point. Finally, Professor Ceyer discusses characteristics of titratio...more
