Game Theory: Mean Field

Mean-field game theory studies settings with very many players where each player's payoff depends on their own action and on the aggregate distribution of others' actions — not on any single opponent. The "mean field" is the population average; individuals best-respond to that. It's used in finance (crowded trades, asset prices), congestion (traffic, servers), and platform markets. Equilibrium is a fixed point: the distribution that results when everyone best-responds to that same distribution. For founders, the lens applies to markets and platforms where "what everyone does" matters more than "what any one rival does" — e.g. adoption curves, industry capacity, or sentiment.

Model the payoff as a function of your action and the aggregate (e.g. total supply, adoption rate). Guess the equilibrium distribution; check if your best response to it reproduces it. Use the mean-field view when the number of players is large and individual identities don't matter — then optimise against the field, not against named rivals.

Mean-field games: many players; payoffs depend on own action and aggregate distribution. Equilibrium: distribution that reproduces itself under best response. Use when "the market" or "the field" matters more than any single rival — platforms, adoption, capacity.