Lecture 14: Backward Induction, Commitment, and First-Mover Advantage

What this lecture covers

This lecture returns to the Cournot quantity-competition model from earlier in the course and reworks it as a sequential game, known as the Stackelberg model, where one firm sets output first and the other responds. The class first reasons through the outcome intuitively using the best-response diagram, then confirms it with calculus.

You'll come away understanding why moving first can be an advantage in quantity competition, but only when it comes with real commitment, and why having more information can sometimes hurt a player if opponents know they have it. The lecture closes with the game of Nim, used to show that first-mover advantage depends entirely on the specific game and starting position, not on moving first in general.

Key ideas

• Stackelberg model: a version of Cournot competition where one firm chooses its quantity first and the other observes and responds.
• Strategic substitutes: a market structure where one firm producing more causes the other's best response to be less output.
• First-mover advantage: an advantage from moving first only when the mover's decision is genuinely observed and cannot be reversed, not from timing alone.
• Commitment through sunk cost: building a plant or otherwise spending money that cannot be recovered is what makes a first move credible.
• Information can hurt: if an opponent knows you will learn their plan in advance, they may change their own behavior in a way that leaves you worse off.
• No inherent value to moving first: some games, like rock-paper-scissors or the cake-cutting "I cut, you choose" rule, have a second-mover advantage or no advantage at all.

Walkthrough

Reviewing Cournot and setting up Stackelberg (0:00)

Polak recaps the simultaneous-move Cournot model, including the best-response diagram and equations for two firms choosing quantities. He then converts it into a sequential game, the Stackelberg model, where Firm 1 chooses its quantity first and Firm 2 observes it before choosing its own.

Solving Stackelberg intuitively (0:00)

Using backward induction, the class reasons that Firm 2 will simply play its old best response to whatever Firm 1 chose. Knowing this, Firm 1 should produce more than its old Cournot quantity, because doing so pushes Firm 2's output down, a case of strategic substitutes. The class works through, by polling and discussion, that Firm 1's profit rises, Firm 2's profit falls, and total output and consumer surplus both rise.

Confirming the result with calculus (0:00)

Polak grinds through the algebra: substituting Firm 2's best-response function into Firm 1's profit function, differentiating, and solving. The results, Q1 = (A-C)/2B and Q2 = (A-C)/4B, confirm the intuition developed earlier without calculus, and both quantities depart from the Cournot equilibrium exactly as predicted.

Why moving first needs real commitment (38:13)

Simply announcing a quantity first is not enough to gain an advantage, since an opponent has no reason to believe an unbacked announcement. Using an example of two newspaper firms entering a new market, Polak shows that building a plant, a sunk cost that cannot be reversed, is what makes the first move credible and forces the second firm into a genuine follower role.

Information can backfire, and first-mover advantage isn't universal (49:25)

A spy scenario illustrates that if a firm knows its rival has a spy in its boardroom, it can deliberately let its true plan leak, effectively becoming the first mover and forcing the rival, despite having more information, into a worse outcome. Polak warns against treating "first-mover advantage" as a universal rule: games like rock-paper-scissors reward the second mover, and the "I cut, you choose" method for splitting a cake has neither a first- nor second-mover advantage.

The game of Nim (55:53)

The class plays Nim, where two players alternately remove items from one of two piles and the player who takes the last item wins. Volunteers reveal the winning tactic: equalize the piles if they are uneven. This means the initial position, not the act of moving first, determines whether there is a first- or second-mover advantage.

Before you watch

• Review the Cournot model and best-response diagrams from earlier in the course, since this lecture builds directly on them without re-deriving the basics.
• Lecture 13's ideas of backward induction and commitment carry over directly to how sunk costs create credible first moves here.

Check your understanding

1. Why does Firm 1 produce more in the Stackelberg model than it did under simultaneous Cournot competition?
2. What makes an announcement of future output different from an actual commitment, and why does that difference matter for first-mover advantage?
3. How can having a spy in a rival's boardroom end up hurting the firm with the spy?
4. In the game of Nim, what determines whether the first or second player has the advantage?