Sequential Games and Backward Induction

What this topic is

A sequential game is one where the players move in a visible order rather than at the same moment: you set a price and they see it, you make an offer and they answer, you enter a market and the incumbent reacts. Backward induction is the method for solving it. You start at the very last decision anyone has to make, work out what that person will do, replace that branch with the outcome it produces, and then step back one move and repeat. When you reach the top, you have the whole path.

Why it matters

Almost every threat made in commerce is a claim about a future decision — we will fight, we will walk, we will sue, we will build. Backward induction is the only systematic way to check whether the person making the threat would still want to carry it out at the moment it came due. Threats that fail that test are free to make and worthless to rely on, and the entire market for commitment devices exists because of it. It also settles the question people argue about most: whether moving first is an advantage, which turns out to depend entirely on the structure and is often the reverse of what intuition says.

Who should learn it

Anyone negotiating in rounds, anyone deciding whether to enter a market held by a larger incumbent, and anyone structuring an investment in stages who needs to know what the next stage will look like from inside it.

What you will understand

• How to lay out a decision as a tree and solve it from the last node backwards, with real numbers attached
• Why most competitive threats are not credible, and precisely what has to change to make one credible
• When moving first genuinely helps and when it hands the advantage to whoever moves second
• The documented conditions under which backward induction predicts badly, and what to use instead when they hold

Prerequisites

• Price Discovery and How Information Gets Into a Price
• Price Discrimination in Three Degrees

Common misconception

"Whoever moves first has the advantage." Sometimes, and for a specific reason: moving first only helps when the move cannot be undone, because the whole benefit is that it changes what the second player will want to do. A first move that is reversible carries no information and no constraint, and the second mover keeps the advantage of choosing with full knowledge. In many settings — pricing in a market where costs are falling, technology bets, entering a category before the demand is proven — the second mover is structurally better off, and the phrase first-mover advantage has been doing damage to capital-allocation decisions for decades.