Month: October 2007

11 – The Rise of Athens (cont.)

11 – The Rise of Athens (cont.)

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 be noted that Solon established laws that were moderate in nature. Therefore, it comes as no surprise that Solon was only partially successful. Eventually, a tyranny is established in Athens by Peisistratus, but Peisistratus, according to Professor Kagan, was a special type of tyrant, one that not only upheld the new laws of Solon, but was also interested in the welfare of Athens.

11 – Evolutionary Stability: Cooperation, Mutation, and Equilibrium

11 – Evolutionary Stability: Cooperation, Mutation, and Equilibrium

We discuss evolution and game theory, and introduce the concept of evolutionary stability. We ask what kinds of strategies are evolutionarily stable, and how this idea from biology relates to concepts from economics like domination and Nash equilibrium. The informal argument relating these ideas toward at the end of his lecture contains a notation error [U(Ŝ,S’) should be U(S’,Ŝ)]. A more formal argument is provided in the supplemental notes.

10 – The Rise of Athens

10 – The Rise of Athens

In this lecture, Professor Kagan finishes up his description of the Spartan constitution. He argues that Sparta had a mixed constitution and gained great power due to alliances that the Spartans made with their neighbors. After the discussion of Sparta, Professor Kagan examines Athens and the development of the Athenian constitution. In addition, he shows how different these two poleis were. Finally, Professor Kagan discusses the emergence of the hoplite class in Athens and the failure of Cylon to make himself tyrant of Athens.

10 – Mixed Strategies in Baseball, Dating and Paying Your Taxes

10 – Mixed Strategies in Baseball, Dating and Paying Your Taxes

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 implications of the mixed equilibrium in games; in particular, we look how the equilibrium changes in the tax-compliance/auditor game as we increase the penalty for cheating on your taxes.

9 – Sparta (cont.)

9 – Sparta (cont.)

In this lecture, Professor Donald Kagan explores the development and character of Sparta. He points out that in Sparta, the ethos of the polis was present to an extraordinary degree. Then he describes how this came about. In short, Professor Kagan argues that the Spartans were able to create a distinct military culture on account of their subjugation of the inhabitants of Messenia, who were forced to carry on the work of farming while the Spartans trained for war. Finally, Professor Kagan examines the education and training of the Spartan citizen as well as the constitution of Sparta.

9 – Mixed Strategies in Theory and Tennis

9 – Mixed Strategies in Theory and Tennis

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 game of tennis.

8 – Sparta

8 – Sparta

In this lecture, Professor Donald Kagan explores the rise, fall, and significance of tyrannies in the Greek polis. He argues that the various tyrannies in the Greek world had both negative and positive aspects, which need to be appreciated. For instance, on the one hand, tyrannies promoted economic, commercial and artistic advances. On the other hand, tyrannies ruled absolutely and curbed the freedom of the polis. Finally, Professor Kagan intimates that tyrannies in many ways were a necessary step in the development of the classical polis. In short, through tyrannies, the power and influence of the aristocracy was broken and the hoplite farmer grew greater in significance.

8 – Nash Equilibrium: Location, Segregation and Randomization

8 – Nash Equilibrium: Location, Segregation and Randomization

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 decentralized randomization by the individuals themselves, “mixed strategies.” Finally, we look at rock, paper, scissors to see an example of a mixed-strategy equilibrium to a game.

The Lion, the Kiwi, and the Sacred Cow: A look at contemporary language in English Liturgies

The Lion, the Kiwi, and the Sacred Cow: A look at contemporary language in English Liturgies

Dr. Peter Davies, publisher of “Alien Rights: A Critical Examination of Contemporary English in Anglican Liturgies”, addresses the topic in this presentation and netcast.