In a population playing the Hawk-Dove game, Hawks are currently very rare. Almost every interaction a Hawk has is with a Dove, so Hawks win the resource easily each time. What happens to Hawk frequency over subsequent generations?
AHawks remain rare — they are already at the stable equilibrium frequency
BHawks increase in frequency because they currently have higher fitness than Doves in this population composition
CDoves increase because cooperation is better for the group's long-term survival
DFrequency stays constant because natural selection does not act on behavioral strategies
When Hawks are rare, they almost always encounter Doves and win the resource without injury. Their fitness is therefore high relative to Doves, who must share resources with other Doves. Natural selection favors the high-fitness type, so Hawks increase in frequency. This continues until Hawks become common enough that they frequently encounter each other — suffering injury costs — and their average fitness drops to match Doves' average fitness. The equilibrium is reached not at pure Hawk or pure Dove, but at the frequency where both strategies have equal average fitness. This frequency-dependence is the key insight.
Question 2 Multiple Choice
Which of the following best describes an evolutionarily stable strategy (ESS)?
AThe strategy that maximizes the average fitness of the entire population
BThe strategy that gives the individual the highest possible payoff, regardless of what others do
CA strategy that, once it becomes common in the population, cannot be successfully invaded by a rare mutant using a different strategy
DAny strategy that allows the individual to survive and reproduce at least once
An ESS is defined by its stability against invasion, not by optimality. If a population is playing an ESS and a rare mutant with a different strategy appears, the mutant will have lower fitness than the resident strategy and be eliminated by natural selection. Crucially, the ESS need not maximize individual payoff (a lone Dove in a Hawk population does badly) or group welfare (ritualized display is the ESS even though all-out fighting might be better for some individuals). It is the strategy that is self-reinforcing: once common, it resists displacement.
Question 3 True / False
In evolutionary game theory, the fitness value of a strategy can change as the frequency of that strategy in the population changes.
TTrue
FFalse
Answer: True
This is the defining feature of evolutionary game theory — fitness is frequency-dependent. A Hawk strategy is highly fit when Hawks are rare (easy wins against Doves) but less fit when Hawks are common (frequent costly fights). A Dove strategy has moderate but stable fitness. The payoff to any strategy depends on what strategies it is likely to encounter, which depends on population composition. This is fundamentally different from simple natural selection models where a trait has a fixed fitness advantage or disadvantage independent of its frequency.
Question 4 True / False
An evolutionarily stable strategy is generally the strategy that maximizes the reproductive output of the group as a whole.
TTrue
FFalse
Answer: False
An ESS is stable against invasion, not collectively optimal. Classic examples illustrate the gap: in the Prisoner's Dilemma, mutual defection is evolutionarily stable in a single-interaction context even though mutual cooperation would produce higher fitness for everyone. Male peacock tails are an ESS (honest signaling) that imposes enormous individual costs and serves no group benefit. The tragedy of many ESS outcomes is exactly that individually stable strategies can produce collectively suboptimal results — a key theme in understanding arms races, overexploitation, and the evolution of altruism.
Question 5 Short Answer
Why does evolutionary game theory require considering strategy frequencies in the population, rather than simply asking which trait has higher fitness?
Think about your answer, then reveal below.
Model answer: In evolutionary game theory, the fitness of a strategy is not a fixed property — it depends on what other strategies it encounters, and what it encounters depends on the frequencies of strategies in the population. This is frequency-dependent selection. A Hawks-only population suffers high injury costs; a Doves-only population is vulnerable to invasion by Hawks. Neither pure state is stable. The fitness of each strategy changes as its frequency changes, and the population evolves toward the equilibrium frequency where strategies have equal fitness. Simple fitness comparisons assume payoffs are constant, which fails whenever organisms interact and the outcomes of those interactions determine fitness.
This insight applies far beyond the Hawk-Dove game: it explains why cooperation can evolve (tit-for-tat is stable in iterated games), why costly signals are honest (only high-quality individuals can afford them), and why many biological equilibria involve mixed strategies or polymorphisms rather than the fixation of a single 'optimal' type.