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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.
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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.
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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.
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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.
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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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In this lecture, Professor Kagan addresses what scholars call the Homeric question. He asks: what society do Homer’s poems describe? He argues that in view of the long oral transmission of the poems, the poems of Homer probably reflect various ages from the Mycenaean world to the Dark Ages. More importantly, close scrutiny of the poems will yield historical information for the historian. In this way, one is able to reconstruct through the poems, to a certain extent, the post-Mycenaean world. Finally, Professor Kagan says a few words on the heroic ethic of the Greek world.
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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 is going to do, and then ask what is the best strategy for us to choose given those beliefs?
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In this lecture, Professor Donald Kagan explores the earliest history of Greek civilization. He demonstrates how small agricultural enclaves eventually turned into great cities of power and wealth in the Bronze Age, taking as his examples first Minoan Crete and then Mycenaean Greece. He also argues that these civilizations were closely related to the great monarchies of the ancient Near East. He points out that the Mycenaean age eventually came to an abrupt end probably through a process of warfare and migration. Reconstructing the Mycenaean age is possible through archaeological evidence and through epic poetry (Homer). Finally, he provides an account of the collapse of the Mycenaean world, and explains how in its aftermath, the Greeks were poised to start their civilization over on a new slate.
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At the start of the lecture, we introduce the “formal ingredients” of a game: the players, their strategies and their payoffs. Then we return to the main lessons from last time: not playing a dominated strategy; and putting ourselves into others’ shoes. We apply these first to defending the Roman Empire against Hannibal; and then to picking a number in the game from last time. We learn that, when you put yourself in someone else’s shoes, you should consider not only their goals, but also how sophisticated are they (are they rational?), and how much do they know about you (do they know that you are rational?). We introduce a new idea: the iterative deletion of dominated strategies. Finally, we discuss the difference between something being known and it being commonly known.
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Professor Donald Kagan explains why people should study the ancient Greeks. He argues that the Greeks are worthy of our study not only because of their vast achievements and contributions to Western civilization (such as in the fields of science, law, and politics) but also because they offer a unique perspective on humanity. To the Greeks, man was both simultaneously capable of the greatest achievements and the worst crimes; he was both great and important, but also mortal and fallible. He was a tragic figure, powerful but limited. Therefore, by studying the Greeks, one gains insight into a tension that has gripped and shaped the West and the rest of the world through its influence. In short, to study the Greeks is to study the nature of human experience.