Path Dependence

Definition

Path dependence is the property of a dynamic process in which earlier outcomes shape the probability of later outcomes, so that the sequence — and sometimes the eventual long-run equilibrium — could easily have gone otherwise. Page formalizes it with urn models: outcome path dependence means what happens now depends on history; equilibrium path dependence, the stronger property, means the long-run outcome itself is undetermined at the start and gets locked in by chance early events.

In the Book

The core model is the Polya process (Chapter 14): an urn starts with one white and one gray ball; each period a ball is drawn and returned along with an extra ball of the same color, so early draws increase the odds of matching future draws — a formal model of positive feedback or "increasing returns." Page proves the process has two striking properties: any specific sequence with a given number of white outcomes is equally likely as any other with that count, and every possible long-run proportion of white-to-gray balls is equally probable — meaning after 1,000 draws, ending at 40% white is exactly as likely as ending at 2% white. He connects this to real cases: the QWERTY keyboard layout's persistence despite arguably-superior alternatives, and a firm's dilemma over which color of product to stock — since Ford's Model T ("any color... so long as it was black") and Apple's original iPhone (black, or black) both sidestepped the problem by removing consumer choice rather than gambling on which color would randomly lock in. He contrasts the Polya process with a "balancing process" (each draw is followed by a ball of the opposite color), which is outcome path-dependent moment-to-moment but always converges back to a 50/50 equilibrium — showing that path dependence in the short run does not imply path dependence in the long run.

Why It Matters

Path dependence tells you when to ask "why did X become the standard?" versus "what would have made X inevitable?" — often the honest answer is neither superiority nor design, but an early, arbitrary event amplified by positive feedback. This matters for anyone facing a first-mover decision under increasing returns (technology standards, market entry, institutional design): the model implies you cannot always predict which of several equally-viable outcomes will lock in, only that something will, which argues for delaying commitment until feedback narrows the possibilities, or removing the choice point altogether.