Lecture 13: Sequential Games, Moral Hazard, and Commitment

What this lecture covers

This lecture opens the second half of the course by introducing sequential-move games, where one player observes another's choice before acting. Using a live classroom game where a lender puts money in a hat and a borrower can match it or keep it, Polak shows why sequential games need a different tool than the Nash equilibrium methods used earlier in the course.

You'll come away able to build a game tree, solve it by backward induction, and recognize moral hazard problems in lending, insurance, and employment relationships. The lecture also introduces incentive design and commitment as two practical ways to fix these problems, illustrated with historical and business examples, before closing with a lion-themed backward induction puzzle.

Key ideas

• Sequential move game: a game where the second mover observes the first mover's choice before acting, and the first mover knows this in advance.
• Backward induction: solving a game by starting at the last decision and working backward, assuming each player anticipates later players' best responses.
• Moral hazard: a situation where one party (the borrower) has an incentive to act against the interests of the other (the lender) once money or trust has changed hands.
• Incentive design: restructuring payoffs, such as letting a borrower keep a larger share of profits, so that following through becomes the borrower's best choice.
• Commitment strategy: deliberately removing your own options, such as posting collateral or burning ships, so that others change their behavior in your favor.
• Nodes, edges, and end nodes: the vocabulary for describing a game tree, where decision nodes belong to a player and end nodes carry payoffs.

Walkthrough

Setting up the lender-borrower game (0:02)

Polak runs a live game where a "lender" puts $0, $1, or $3 in a hat and a "borrower" can match the amount or keep it. He maps this onto a real situation: a venture capitalist deciding how much to lend an entrepreneur who can either repay or disappear with the funds. The class identifies that this differs from earlier games because moves happen in sequence and the second player observes the first player's choice.

Trees and backward induction (10:17)

The lecture introduces the game tree as the right tool for sequential games, plotting the lender's and borrower's payoffs at each branch. Solving it by backward induction shows that a rational borrower will keep a large sum rather than match it, so a rational lender only offers the small, safe amount. This underperforms the outcome both players would prefer if trust were possible, which Polak names as a moral hazard problem, drawing a parallel to insurance deductibles.

Fixing moral hazard: incentive design (29:50)

The lecture works through several remedies: keeping loans small, staged financing, and contractual restrictions, each with real-world limitations. The main fix explored in depth is incentive design: changing the payoff split, for example giving the borrower a bit more than an even match, so that repaying becomes individually rational. Polak connects this to CEO stock options, sharecropping, and piece-rate wages as historical examples of incentive contracts.

Commitment through collateral and burning boats (44:29)

Collateral works not by reassuring the lender directly, but by lowering the borrower's payoff from defaulting enough to change their behavior. Polak generalizes this into the idea of a commitment strategy and illustrates it with William the Conqueror burning his ships before the Battle of Hastings, and the doomsday device in Dr. Strangelove. Both examples show that a commitment only works if the other side knows about it.

Backward induction is the key lesson (1:01:06)

Polak stresses that backward induction is the single most important tool of the semester before closing with jargon (nodes, edges, end nodes, paths) and a live "Hungry Lion" game, where students seated in a row must decide whether to "eat" the person next to them, knowing they might then be eaten themselves. Almost no one solves it correctly on the first try, reinforcing that backward induction needs deliberate practice.

Before you watch

• Be comfortable with the Nash equilibrium and dominance concepts from the first half of the course, since backward induction builds on them.
• No prior exposure to game trees is assumed; the lecture defines nodes, edges, and paths as it goes.

Check your understanding

1. Why does the lender in the hat game only offer a small amount, even though both players would be better off with a larger loan that gets repaid?
2. How does posting collateral change a borrower's incentives without directly benefiting the lender's payoff at the collateral itself?
3. Why did burning the boats help the Norman army, given that it removed one of their own options?
4. What must be true for a commitment strategy to actually change another player's behavior?