time and space complexity analysis
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We apply the main idea from last time, iterative deletion of dominated strategies, to analyze an election where candidates can choose their policy positions. We then consider how good is this classic model as a description of the real political process, and how we might build on it to improve it. Toward the end of the class, we introduce a new idea to get us beyond iterative deletion. We think about our beliefs about what the other player ...more
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In this lecture, Professor Kagan traces the development of Athens. He argues that Athens, like other poleis, undergoes political and social turmoil due to the rise of the hoplite farmer. This unrest is first seen in the attempted coup d'état of Cylon and the Law of Draco. Professor Kagan also points out that in response to these developments, Solon was made sole archon of Athens to establish peace in a time of unrest. It should also ...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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This class is an introduction to the evolutionary analysis of human emotions, how they work, why they exist, and what they communicate. In particular, this lecture discusses three interesting case studies, that of happiness (e.g., smiling), fear and the emotions we feel towards our relatives. Finally, this lecture ends with a brief discussion of babies' emotional responses to their caregivers.
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Professor Kleiner explores the architecture of the western provinces of the Roman Empire, focusing on sites in what are now North Italy, France, Spain, and Croatia. Her major objective is to characterize "Romanization," the way in which the Romans provide amenities to their new colonies while, at the same time, transforming them into miniature versions of the city of Rome. Professor Kleiner discusses the urban design of two Augustan towns ...more
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Part 1 - This Land is My Land: The philosopher John Locke believes that individuals have certain rights—to life, liberty, and property—which were given to us as human beings in the “the state of nature,” a time before government and laws were created. According to Locke, our natural rights are governed by the law of nature, known by reason, which says that we can neither give them up nor take them away from anyone else. Part 2 - Consen...more
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We discuss auctions. We first distinguish two extremes: common values and private values. We hold a common value auction in class and discover the winner's curse, the winner tends to overpay. We discuss why this occurs and how to avoid it: you should bid as if you knew that your bid would win; that is, as if you knew your initial estimate of the common value was the highest. This leads you to bid much below your initial estimate. Then we d...more
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We continue the idea (from last time) of playing a best response to what we believe others will do. More particularly, we develop the idea that you should not play a strategy that is not a best response for any belief about others' choices. We use this idea to analyze taking a penalty kick in soccer. Then we use it to analyze a profit-sharing partnership. Toward the end, we introduce a new notion: Nash Equilibrium.
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Professor Blight narrates the momentous events of 1857, 1858, and 1859. The lecture opens with an analysis of the famous Lincoln-Douglas debates of 1858. Next, Blight analyzes the Dred Scott decision and discusses what it meant for northerners--particularly African Americans--to live in "the land of the Dred Scott decision." The lecture then shifts to John Brown. Professor Blight begins by discussing the way that John Brown has been rememb...more
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Bias/variance Tradeoff, Empirical Risk Minimization (ERM), The Union Bound, Hoeffding Inequality, Uniform Convergence - The Case of Finite H, Sample Complexity Bound, Error Bound, Uniform Convergence Theorem & Corollary
