9 – Mixed Strategies in Theory and Tennis

9 – Mixed Strategies in Theory and Tennis

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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 game of tennis.

8 – Sparta

8 – Sparta

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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

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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

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

7 – The Greek “Renaissance” – Colonization and Tyranny (cont.)

7 – The Greek “Renaissance” – Colonization and Tyranny (cont.)

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In this lecture, Professor Donald Kagan explores the rise of Greek colonies. He argues that the rise of new colonies was primarily due to the need for new farmland, although he acknowledges several other important reasons. He also shows where the Greeks colonized and explains that the process of founding a new colony probably took place within the dynamics of a polis. Finally, he offers a few important outcomes of this colonizing impulse.

7 – Nash Equilibrium: Shopping, Standing and Voting on a Line

7 – Nash Equilibrium: Shopping, Standing and Voting on a Line

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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 is voters that are spread along a line. This time, however, we do not allow candidates to choose positions: they can only choose whether or not to enter the election. We play this “candidate-voter game” in the class, and we start to analyze both as a lesson about the notion of equilibrium and a lesson about politics.

6 – The Greek “Renaissance” – Colonization and Tyranny

6 – The Greek “Renaissance” – Colonization and Tyranny

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In this lecture, Professor Donald Kagan discusses the emergence of a new style of warfare among the Greeks, the hoplite phalanx. After discussing the panoply of the hoplite solider and the method of fighting, he argues that this style of fighting came about early in the life of the polis. In addition, he shows that the phalanx was almost invincible on the field. At the lecture’s conclusion, he answers several questions from students about hoplite warfare in the Greek world.

6 – Nash Equilibrium: Dating and Cournot

6 – Nash Equilibrium: Dating and Cournot

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We apply the notion of Nash Equilibrium, first, to some more coordination games; in particular, the Battle of the Sexes. Then we analyze the classic Cournot model of imperfect competition between firms. We consider the difficulties in colluding in such settings, and we discuss the welfare consequences of the Cournot equilibrium as compared to monopoly and perfect competition.

5 – The Rise of the Polis (cont.)

5 – The Rise of the Polis (cont.)

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In this lecture, Professor Donald Kagan tells the story of the emergence of the polis from the Dark Ages. He shows that by the time of the poet Hesiod, there is already a polis in place. He describes the importance of the polis in the Greek world and explains that it was much more than a mere place of habitation; it was a place where there was justice, law, community, and a set of cultural values that held Greeks together. Finally, Professor Kagan argues, following the lead of Victor David Hanson, that the polis came to be chiefly through the emergence of a new man: the hoplite farmer.