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.

5 – Nash Equilibrium: Bad Fashion and Bank Runs

5 – Nash Equilibrium: Bad Fashion and Bank Runs

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We first define formally the new concept from last time: Nash equilibrium. Then we discuss why we might be interested in Nash equilibrium and how we might find Nash equilibrium in various games. As an example, we play a class investment game to illustrate that there can be many equilibria in social settings, and that societies can fail to coordinate at all or may coordinate on a bad equilibrium. We argue that coordination problems are common in the real world. Finally, we discuss why in such coordination problems–unlike in prisoners’ dilemmas–simply communicating may be a remedy.

4 – The Rise of the Polis

4 – The Rise of the Polis

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In this lecture, Professor Donald Kagan offers a sketch of the Greek heroic code of ethics. He shows that in this community, arête (manly virtue) and honor are extremely important and even worth dying for, as the case of Achilles makes clear. In addition, Professor Kagan shows how this society eventually produced a new phenomenon, the rise of the polis. The discussion ends with a strong emphasis on the importance of the polis in Greek history.