Month: October 2007

16 – Backward Induction: Reputation and Duels

16 – Backward Induction: Reputation and Duels

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In the first half of the lecture, we consider the chain-store paradox. We discuss how to build the idea of reputation into game theory; in particular, in setting like this where a threat or promise would otherwise not be credible. The key idea is that players may not be completely certain about other players’ payoffs or even their rationality. In the second half of the lecture, we stage a duel, a game of pre-emption. The key strategic question in such games is when; in this case, when to fire. We use two ideas from earlier lectures, dominance and backward induction, to analyze the game. Finally we discuss two biases found in Americans: overconfidence and over-valuing being pro-active.

15 – Athenian Democracy

15 – Athenian Democracy

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In this lecture, Professor Kagan describes the mechanics of the Delian League and its transformation into the Athenian empire. This transformation caused Athens to rival Sparta as an equal in power and prestige. He also argues that this process took place rather smoothly due to the good relations between Sparta and Athens. Professor Kagan argues that Cimon the Athenian generally played an important part in this development. Finally, Professor Kagan begins to describe the workings of Athenian democracy by comparing it with modern American democracy.

15 – Backward Induction: Chess, Strategies, and Credible Threats

15 – Backward Induction: Chess, Strategies, and Credible Threats

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We first discuss Zermelo’s theorem: that games like tic-tac-toe or chess have a solution. That is, either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win. The proof is by induction. Then we formally define and informally discuss both perfect information and strategies in such games. This allows us to find Nash equilibria in sequential games. But we find that some Nash equilibria are inconsistent with backward induction. In particular, we discuss an example that involves a threat that is believed in an equilibrium but does not seem credible.

14 – The Athenian Empire (cont.)

14 – The Athenian Empire (cont.)

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In this lecture, Professor Donald Kagan examines the developments that took place after the Greek victory over the Persians in 479 BC. He argues that even after the Greek victories, there was great fear amongst the Greeks that the Persians would return to seek revenge. For this reason, many of the Greek poleis, especially the islands, looked to Athens to lead this league, which later became the Delian League. Athens, according to Professor Kagan, accepted this responsibility, since it too feared a Persian invasion, but Sparta was content to retreat into the Peloponesus. Finally, Professor Kagan intimates that this league would eventually turn into the Athenian empire.

14 – Backward Induction: Commitment, Spies, and First-Mover Advantages

14 – Backward Induction: Commitment, Spies, and First-Mover Advantages

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We first apply our big idea–backward induction–to analyze quantity competition between firms when play is sequential, the Stackelberg model. We do this twice: first using intuition and then using calculus. We learn that this game has a first-mover advantage, and that it comes commitment and from information in the game rather than the timing per se. We notice that in some games having more information can hurt you if other players know you will have that information and hence alter their behavior. Finally, we show that, contrary to myth, many games do not have first-mover advantages.

13 – The Athenian Empire

13 – The Athenian Empire

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In this lecture, Professor Kagan traces the development and the power of the Persian empire. He also shows how the Persian empire and the Greek world eventually came into conflict through a few incidents concerning Ionian Greeks in Asia Minor, which eventually turned into the Persian Wars. Professor Kagan ends this lecture with a description of the events of the battle of Marathon in which the Athenians defeated the Persians.

13 – Sequential Games: Moral Hazard, Incentives, and Hungry Lions

13 – Sequential Games: Moral Hazard, Incentives, and Hungry Lions

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We consider games in which players move sequentially rather than simultaneously, starting with a game involving a borrower and a lender. We analyze the game using “backward induction.” The game features moral hazard: the borrower will not repay a large loan. We discuss possible remedies for this kind of problem. One remedy involves incentive design: writing contracts that give the borrower an incentive to repay. Another involves commitment strategies; in this case providing collateral. We consider other commitment strategies such as burning boats. But the key lesson of the day is the idea of backward induction.

12 – The Persian Wars

12 – The Persian Wars

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In this lecture, Professor Kagan examines in detail the development, growing pains, and emergence of Athenian democracy. He argues that the tyranny under the Peisistratids led to the development of the idea of self-government among the Athenians, which Cleisthenes used to develop Athens in a more democratic direction. One of the ways Cleisthenes was able to accomplish this was to diminish the power of the aristocracy by reordering and restructuring the tribes and giving greater power to the assembly. Finally, Professor Kagan says a word on the Athenian practice of ostracism as a political tool to protect a fledgling democracy.

12 – Evolutionary Stability: Social Convention, Aggression, and Cycles

12 – Evolutionary Stability: Social Convention, Aggression, and Cycles

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We apply the idea of evolutionary stability to consider the evolution of social conventions. Then we consider games that involve aggressive (Hawk) and passive (Dove) strategies, finding that sometimes, evolutionary populations are mixed. We discuss how such games can help us to predict how behavior might vary across settings. Finally, we consider a game in which there is no evolutionary stable population and discuss an example from nature.