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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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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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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This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.
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We first play and then analyze wars of attrition; the games that afflict trench warfare, strikes, and businesses in some competitive settings. We find long and damaging fights can occur in class in these games even when the prizes are small in relation to the accumulated costs. These could be caused by irrationality or by players' having other goals like pride or reputation. But we argue that long, costly fights should be expected in these...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
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The form of medicine that arose in fifth-century Greece, associated with the name of Hippocrates and later popularized by Galen, marked a major innovation in the treatment of disease. Unlike supernatural theories of disease, Hippocrates' method involved seeking the causes of illness in natural factors. This method rested upon an analogy between the order of the universe and the composition of the body's "humors." Health, on this view, was ...more
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Continuing the discussion of Lewis structures and chemical forces from the previous lecture, Professor McBride introduces the double-well potential of the ozone molecule and its structural equilibrium. The inability for inverse-square force laws to account for stable arrangements of charged particles is prescribed by Earnshaw's Theorem, which may be visualized by means of lines of force. J.J. Thomson circumvented Earnshaw's prohibition on ...more
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After discussing the classic determination of the heat of atomization of graphite by Chupka and Inghram, the values of bond dissociation energies, and the utility of average bond energies, the lecture focuses on understanding equilibrium and rate processes through statistical mechanics. The Boltzmann factor favors minimal energy in order to provide the largest number of different arrangements of "bits" of energy. The slippery concept of di...more
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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
