Science and physics
Equilibrium
A state where opposing processes balance so nothing changes on net; push it and it pushes back, but balanced is not the same as good.
Henry Louis Le Chatelier's principle in chemistry; John Nash's equilibrium points in game theory (1950).
A chemical reaction at equilibrium has not stopped. The forward and reverse reactions run at equal rates, so the concentrations hold steady. Le Chatelier's principle says what happens when you disturb that: if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change. Raise the pressure on a gas reaction and it shifts towards the side with fewer molecules; add more of a reactant and it consumes some of it. The same word covers mechanics (forces summing to zero) and economics (a price at which the quantity supplied equals the quantity demanded). In each case the defining feature is a balance of flows that restores itself after a small push.
Nash's two-page paper of January 1950 extended the idea to strategy. An equilibrium point is a choice of strategy for each player such that no player can improve their payoff by changing only their own strategy, given what the others are doing, and Nash proved that every finite game has at least one. Ecology has the same shape: predator and prey numbers settle where births balance deaths, and a cull of predators is followed by a prey boom and then a predator recovery. Equilibria are useful because they say where a system will sit if left alone and which way it will lean when pushed, which is the question behind most pricing, capacity and policy decisions.
Two cautions. First, equilibrium is not optimum. The prisoner's dilemma has a single Nash equilibrium in which both players confess, and both do worse than if neither had; an equilibrium is a resting point, and the resting point can be bad for everyone in it. Second, many systems of interest are nowhere near equilibrium and never will be: a living cell, a growing company, a market during a crash, a codebase under active development. They are held away from balance by a continual flow of energy, money or effort, and treating them as settled gives confident, wrong predictions. Ask first whether the flows have had time to balance, and only then where the balance point is.
Example
John Nash's paper 'Equilibrium points in n-person games' appeared in the Proceedings of the National Academy of Sciences, volume 36, issue 1, in January 1950, and runs to two pages (48 and 49). In it Nash defined an equilibrium point as a set of strategies, one per player, from which no player gains by changing their own strategy alone, and proved that every finite game has at least one. The Stanford Encyclopedia of Philosophy's entry on game theory credits that paper with doing most to extend von Neumann and Morgenstern's work, and uses the prisoner's dilemma to show that the equilibrium it defines can leave every player worse off than another reachable outcome.
Where it applies
When a metric has stopped moving, ask which two flows are balancing and which one you can change: hires against attrition, bug inflow against fixes, requests against capacity. In a multi-agent or marketplace system, look for the equilibrium users will actually settle into under your rules, not the behaviour you hope for; if it is a bad one, change the payoffs rather than pleading.
Think about it
Which number in your work is stable, and is it stable because things are good or because two bad things are cancelling out?
Applied it to something real? Log it.
Test yourselfWhy can a Nash equilibrium be bad for everyone in it?
It only requires that no player gains by changing alone. In the prisoner's dilemma both confess and both do worse than mutual silence, but neither can improve by switching on their own.
Related models
- Supply and demandPrice settles where what sellers will offer meets what buyers will take; hold it anywhere else and a shortage or a glut does the adjusting instead.
- Feedback loopsA system's output feeds back into its input: balancing loops hold a level steady, reinforcing loops make change grow on itself.
- Stocks and flowsA stock is what has accumulated; flows are the rates that change it. The stock moves only as fast as inflow minus outflow.
- Critical mass and tipping pointsBelow a threshold a chain reaction fizzles; above it the same process feeds itself, and the change between the two is sudden.