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We develop a simple model of bargaining, starting from an ultimatum game (one person makes the other a take it or leave it offer), and building up to alternating offer bargaining (where players can make counter-offers). On the way, we introduce discounting: a dollar tomorrow is worth less than a dollar today. We learn that, if players are equally patient, if offers can be in rapid succession, and if each side knows how much the game is worth to the other side, then the first offer is for an equal split of the pie and this offer is accepted. But this result depends on those assumptions; for example, bargaining power may depend on wealth.

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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.

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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.

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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.