Plate v in print

The Population

Maynard Smith; the evolutionarily stable strategy, where equilibrium is reached not by reason but by survival, and conflict proves self-limiting.

Let the strategies be not chosen but inherited, and the payoff be not satisfaction but survival, and an equilibrium still appears — the strategy that, once common, no rare rival can invade; so the resting points of the game are reached not only by minds that reason but by creatures that merely live and die.

— the argument of this plate, after John Maynard Smith, 1973

Every game so far has assumed a calculating player — Nash's optimizer, Schelling's strategist, Selten's backward-reasoning chooser. John Maynard Smith, a biologist by trade, asked a startling question: what if the players cannot reason at all? In the living world, strategies are not chosen but inherited, and they compete not for satisfaction but for survival, whose currency is offspring. Maynard Smith showed that game-theoretic equilibrium survives this stripping-away of mind entirely — that an equilibrium emerges from blind natural selection just as surely as it does from reason. The discovery vastly widened the reach of the theory, and it hands the volume a new way to think about how a cooperative strategy might take hold: not because anyone decides to cooperate, but because cooperation, in the right conditions, simply out-survives its rivals.

Maynard Smith's move was to reinterpret every element of a game in the language of evolution. The strategies are no longer options weighed by a mind but heritable behavioral programs — to fight or to flee, to share or to grab, to cooperate or to cheat — written into an organism by its inheritance. The players are the organisms carrying those programs. And the payoff is neither money nor pleasure but Darwinian fitness, the number of surviving offspring a strategy yields. With these three substitutions, the machinery of selection replaces the machinery of choice. A strategy that earns higher fitness leaves more copies of itself in the next generation and so spreads; a strategy that earns lower fitness dwindles toward extinction. The population's mixture of strategies shifts across the generations until it settles — and the resting point at which it settles is an equilibrium, reached without a single calculation, by creatures that merely live and reproduce and die.1

1. The evolutionary reinterpretation: strategies become heritable programs (fight or flee, share or cheat), players become organisms, payoff becomes Darwinian fitness — surviving offspring. Selection replaces choice. A fitter strategy leaves more copies and spreads; a less fit one dwindles. The population's mixture shifts over generations until it settles. The resting point is an equilibrium — reached with no calculation at all, by creatures that merely live, reproduce, and die.

The equilibrium concept Maynard Smith defined is the evolutionarily stable strategy, and it captures the idea of a strategy that, once established, cannot be displaced. A strategy is evolutionarily stable if, when almost the whole population already plays it, no rare mutant playing anything else can invade — that is, the established strategy earns at least as much fitness in this population as any mutant would, so the mutant cannot multiply and gain a foothold. Such a strategy is uninvadable: small deviations are selected against, and the population returns to it. The concept is a close cousin of the Nash equilibrium — indeed every evolutionarily stable strategy is a Nash equilibrium, for if some mutant could earn more it would not be held in check — but it adds a condition of stability against the ceaseless drift of mutation, asking not merely that no one could gain by deviating but that the equilibrium actively repel the deviations that biology will forever throw at it. Equilibrium becomes not just a resting point but a resilient one.2

2. The evolutionarily stable strategy: one that, once nearly universal, no rare mutant can invade — the established strategy earns at least what any mutant would, so the mutant gains no foothold. It is uninvadable; deviations are selected against. Every such strategy is a Nash equilibrium (else the mutant would not be checked), but with an added condition: stability against the constant drift of mutation. Equilibrium becomes not just a resting point but a resilient one.
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The illustration that made the idea vivid is the contest of hawk and dove. Imagine animals of one species meeting again and again to contest a resource — food, territory, a mate — and suppose each carries one of two programs. The hawk always escalates, fighting until it wins or is injured; the dove makes a display but retreats the moment its opponent escalates. Pit them against each other and the fitness payoffs emerge. A hawk meeting a dove wins the resource outright, the dove fleeing unhurt. Two doves share or settle the resource cheaply between them. But two hawks fight in earnest, and the risk of serious injury makes that encounter very costly to both. Now ask which population is stable. A population of all doves is not: a single hawk, winning every contest against the gentle doves, would multiply and spread through it. A population of all hawks is not stable either: when hawks are everywhere, the constant injurious fights grow so costly that a rare dove, by simply declining them, does better and gains ground. Stability lies between — at a mixture of hawks and doves, or a population in which each animal escalates only part of the time, where the two strategies earn exactly equal fitness and neither can invade the other.3

3. Hawk and dove contest a resource. Hawk always escalates; dove displays but retreats. Hawk beats dove (dove flees unhurt); two doves share cheaply; two hawks fight, risking costly injury. All-dove is unstable — a lone hawk beats every dove and spreads. All-hawk is unstable too — amid constant injurious fights, a rare dove that declines them does better. The stable point lies between: a mixture where hawk and dove earn equal fitness and neither can invade.

The hawk-dove result explained something real that had long puzzled naturalists: why animal conflict is so often ritualized and restrained, settled by display and posture rather than by fights to the death, even when a fight to the death might secure the prize. The naive expectation, that selection should make every creature as ferocious as it can be, is simply wrong; for in a world already full of fighters, ferocity is self-defeating, its injuries outweighing its winnings, and restraint earns the higher fitness. The evolutionarily stable mixture builds a measure of peace into the population, not from any benevolence but from the cold arithmetic of survival — too much aggression, and the aggressors destroy one another. The same logic reaches far beyond animals. It illuminates stable sex ratios, the limits of cheating in a symbiosis, the persistence of both bold and cautious temperaments within a species; and it lends a precise meaning to the old intuition that markets, like ecosystems, can reach equilibrium through the differential survival of strategies — successful firms and practices spreading, failures dying away — as if the participants were rational even where no foresight guides them at all.4

4. Hawk-dove explains why real conflict is ritualized, not lethal: amid many fighters, ferocity is self-defeating, its injuries outweighing its gains, and restraint earns more. The stable mixture builds in a measure of peace, not from benevolence but from survival's arithmetic. The logic reaches past animals — to sex ratios, the limits of cheating, the mix of bold and cautious types — and grounds the intuition that markets, like ecosystems, reach equilibrium by the survival of strategies, "as if" rational with no foresight at all.

Maynard Smith's lesson is that equilibrium has two roots, not one. The classical theory reached it through reason — players calculating best responses to one another. Evolutionary game theory reaches the same kind of resting point through survival — strategies multiplying or dwindling by their fitness until only the uninvadable remain. The second root is in a sense the deeper, for it requires no mind at all, and it suggests that the strategic logic the volume has traced is woven into the fabric of life itself, not merely into the deliberations of the clever. And it hands the volume's central question a new and hopeful angle. The prisoner's dilemma warned that cooperation cannot survive among the self-interested; but if strategies compete by survival across many encounters rather than one, perhaps a cooperative strategy could arise that, once common, no defector could invade — cooperation made evolutionarily stable. Whether that is so, and under what condition it holds, is the question the flagship answers, by setting the prisoner's dilemma to be played not once but again and again. The next plate is the reciprocity.5

5. Equilibrium has two roots: reason (players calculating best responses) and survival (strategies multiplying by fitness until only the uninvadable remain). The survival root is deeper, needing no mind, and shows the strategic logic woven into life itself. It reopens the volume's question hopefully: if strategies compete across many encounters, could a cooperative strategy arise that no defector can invade — cooperation made evolutionarily stable? The flagship answers, by repeating the dilemma. Next: the reciprocity.

Maynard Smith freed game theory from the need for rational players. Reinterpret a game in the terms of evolution — strategies as inherited programs, players as organisms, payoffs as fitness — and equilibrium still appears, reached not by calculation but by selection. The evolutionarily stable strategy is the resting point: a strategy that, once common, no rare mutant can invade, a Nash equilibrium hardened against the drift of mutation. The hawk-dove game shows such an equilibrium to be a stable mixture of aggression and restraint, and explains why real conflict is so often ritualized rather than lethal — for ferocity, when everyone is ferocious, destroys itself. Equilibrium, then, has two roots, reason and survival, and the deeper of them is survival, which needs no mind. This reframing offers the volume's question a fresh hope: that a cooperative strategy, tested across many encounters, might prove uninvadable after all. To find out, one must play the dilemma again and again. The next plate is the reciprocity.