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Doves and hawks
Imagine a world with only 2 kind of creatures: doves and hawks. Doves are very peaceful. When 2 doves meet they help each other and share their food. Not so with the hawks. They are very agressive. When a dove meets a hawk the dove hands over its food to the hawk as it doesn't want to fight. So it loses a little energy while the hawk wins some energy. However when a hawk meets a hawk a fight breaks out. You decide if the losing hawk lives on and how much energy he loses and how much energy the winning hawk receives. If enough energy is there a new animal is born and if an animal's energy level gets too low it dies. Play around with different values and see which animal wins as a species.
Of course in the real world no animal is as peaceful or as aggressive as the dove and hawk in this example. Each individual is a bit different and of course there are many other aspects e.g. availability of food, illnesses etc. that have a strong influence of the real outcome which is not in the model at all. Still I found it to be fascinating stuff to play around with the simulation as I got many results that were totally unexpected to me.
Let's talk a bit more about the results. The question here is: which strategy is evolutionarily stable? That is, under what conditions will either the Hawk or Dove strategy dominate a population?
Usually you will find both hawks and doves. In an evolutionary sense, there is a balance point where the number of Hawks and Doves in the population is stable. This balance depends on the relationship between the value of the energy won and the cost of injury (the negative energy or even loss of life).
In the Hawk-Dove game, if the cost of fighting (loss of life, negative energy) is high relative to the value of positive energy won, doves will have a higher payoff and dominate the population. In this scenario doves, who avoid fighting, do better in encounters because they don't risk death or a huge loss of energy.
When two doves meet, they share peacefully, and each gets a payoff of half the energy. But if a Hawk meets a Dove, the Hawk wins and takes the full energy, leaving the Dove with nothing (0). However the hawk is also facing the risk of death or a high loss of energy, so if it's too high, the hawk's strategy becomes less viable in the long run.
On the other hand, if the positive energy won is much higher than the cost (loss of life unlikely, only small amount of negative enery), hawks are more likely to dominate.
In this case, fighting is not particularly costly and the value of the energy won is high enough to justify the risk. Hawks, who are aggressive and fight for their food, tend to win in confrontations against doves, who avoid conflict.
When two Hawks meet, they both risk a small loss of energy but only a small or no risk of death but they still gain the food(albeit at a reduced payoff of due to the cost of injury (negative energy). Since the value of the food is relatively high, the risk of negative energy is worth it. The payoff is lower than if a hawk meets a dove, but still profitable compared to avoiding conflict entirely.
In many real-world populations, a mixed strategy often arises, where both hawks and doves coexist at an equilibrium point. In real populations, a mix of Hawks and Doves can be stable because the success of each strategy is influenced by how common each is in the population.
In nature, this balance can lead to fascinating dynamics, like how animals may signal their intentions to avoid escalation, or how some species alternate between being aggressive and passive depending on the context (such as size, strength, or social status).
I first came across the description of the dove-hawk game in the book "Liars and Outliars" by Bruce Schneier (p. 28ff).
It was originally proposed by J. Maynard Smith and G.R. Price in their paper "The logic of Animal Conflict" to model conflict and aggression in animals..
It directly models agonistic (conflict-related) behavior in animals. For example, many species of animals exhibit ritualized displays where individuals "compete" for resources (like mates or territory) without actually fighting to the death. For instance:
Male deer engage in ritualized antler battles. They signal strength and dominance, but only to the point where the loser is likely to retreat, avoiding injury.
Cicadas or lions may have similar patterns of escalating conflict that involve costly battles or the risk of injury.
The game reflects these trade-offs in real-world animal contests, where organisms must decide between fighting aggressively (hawk) and avoiding conflict (dove) based on the costs of fighting and the value of the resource.
The Hawk-Dove game is just one of many well-known games in evolutionary game theory. There are several other games that model different types of interactions between individuals, often involving trade-offs between cooperation and competition. Some of these games also model social behaviors and strategies that can evolve in populations.
As Matrix: with V = positive energy, C= cost or negative energy
| hawk | dove |
| hawk | (V-C)/2, (V-C)/2 | V, 0 |
| dove | 0, V | V/2, V/2 |
Prisoner's Dilemma
The Prisoner's Dilemma is probably the most famous game in evolutionary game theory. It models situations where two individuals (often called "players") can either cooperate or defect (betray the other).
Scenario: Imagine two criminals are caught and interrogated separately. Each has two choices:
Cooperate with the other (stay silent).
Defect (betray the other).
Payoffs:
If both cooperate, they both get a moderate sentence (e.g., 1 year in prison each).
If one defects and the other cooperates, the defector goes free (0 years), and the cooperator gets the full punishment (e.g., 5 years).
If both defect, they both get a somewhat harsh sentence (e.g., 3 years each).
As Matrix:
| player1 | player2 |
| player1 | -1,-1 | -5, 0 |
| player2 | 0, -5 | -3,-3 |
In this game, defecting is the dominant strategy because it gives a higher payoff no matter what the other player does. However, if everyone defects, they both end up worse off than if they had cooperated.
The Prisoner's Dilemma is often used to explain how cooperation can evolve in a population, even though defection is individually rational. The game is foundational in the study of cooperative behaviors in biology, economics, and sociology.
It was originally formulated as a thought experiment in game theory by Albert W. Tucker in 1950.
While it was not initially inspired by specific biological observations, the Prisoner's Dilemma is frequently used to model cooperation and defection in nature. Many evolutionary strategies in animals resemble this dilemma, especially in cooperative behaviors:
Altruistic behaviors in animals, like warning calls in meerkats or helping behavior in eusocial insects (e.g., bees or ants), can be modeled as a version of the Prisoner's Dilemma.
Parental care or food sharing in many species involves trade-offs where individuals might benefit more from defecting (selfish behavior) but cooperation leads to greater long-term survival benefits for the group.
Cooperation in primates: Studies of primates, such as chimpanzees, often reveal cooperative grooming or coalition-building among individuals. But the risk of defection (betraying or cheating) is always present, mirroring the dilemma in nature.
While not directly observed as a single "game," cooperative and competitive strategies in nature often resemble this structure, especially in reciprocal altruism.
Stag Hunt
The Stag Hunt game is another classic model for cooperation, but it differs from the Prisoner's Dilemma in the way the payoff structure works.
Scenario: Two hunters can either hunt a stag (which requires cooperation) or hunt a hare (which can be done alone).
If both hunters cooperate to hunt the stag, they get a big reward (the stag).
If one hunter defects and hunts a hare while the other hunts the stag, the hare-hunter gets a smaller reward, while the stag-hunter gets nothing.
If both hunters defect and hunt hares, they both get a smaller reward.
As Matrix:
| Stag (player2) | Hare (player2) |
| Stag (player1) | 3,3 | 0, 2 |
| Hare (player1) | 2, 0 | 2,2 |
The Stag Hunt has two Nash equilibria: both cooperate and hunt the stag, or both defect and hunt hares.
The Stag Hunt illustrates the tension between cooperation and safety: hunting a hare is a safe, guaranteed option, while hunting the stag requires trust and coordination. The game models how cooperation might emerge in situations where the benefit of cooperation is high, but failure to cooperate can lead to poor outcomes.
The Stag Hunt was formulated by philosopher Jean-Jacques Rousseau in 1755 as a metaphor for cooperation in society, but it was later formalized into game theory by Brian Skyrms in the 1990s.
It models situations in which cooperation is essential for achieving the best outcome but comes with the risk of one party not cooperating.
This game mirrors the hunt-based behaviors observed in species that hunt in groups. For example:
Wolf packs hunt large prey like deer or elk. Success requires cooperation, but if one wolf defects (doesn't pull its weight), the hunt fails.
Humans historically hunted in groups for large game (like mammoths), requiring coordinated cooperation. If one person defects and hunts smaller game (like a hare), the group may not get the payoff of a successful stag hunt.
Many species, especially those that hunt in packs or groups, exhibit cooperation in high-stakes contexts where mutual trust is needed for success.
Chicken Game
The Chicken Game is often used to model situations where two individuals are engaged in a dangerous contest, and the one who "backs down" (or "chickens out") loses, but the one who doesn't back down risks a worse outcome (such as a crash).
Scenario: Two cars drive toward each other on a collision course. The driver who swerves is the "chicken," but if neither driver swerves, they both crash.
If one swerves and the other doesn't, the one who didn't swerve wins (gets a large payoff), and the one who swerved gets a smaller payoff.
If neither swerves, they crash and both get a very low payoff (or a "negative" payoff, representing the cost of the crash).
As Matrix:
| swerve (player2) | don't swerve (player2) |
| swerve (player1) | 0,0 | -10, 1 |
| don't swerve (player1) | 1, -10 | -5,-5 |
The Chicken Game has two pure strategy Nash equilibria: one player swerves and the other doesn't. The problem arises in real-world applications, where if both players hold out (don't swerve), they risk total failure (a crash).
The Chicken Game is often used to explain situations where players need to signal commitment to a course of action and avoid a costly "crash."
The Chicken Game originated in the field of game theory, particularly in the work of John Nash in the 1950s. It was used to describe conflict resolution in strategic scenarios (often related to war and international diplomacy).
While the Chicken game is more abstract, it does have analogs in nature:
Animal signaling: Many species engage in ritualized contests that resemble a "game of chicken," where the goal is to outlast an opponent without actually fighting. For instance:
Male peacocks might engage in display rituals (e.g., expanding their tail feathers), signaling their strength without direct aggression.
Territorial animals, like lions or wolves, may engage in ritualized confrontations, where neither party wants to "back down" but also fears the consequences of escalation.
The Chicken game also shows up in territorial behavior in nature, where animals will face off, but without a real intention to cause harm.
Tragedy of the Commons
This is a model used to explain overuse of shared resources.
Scenario: Imagine a common pasture where multiple herders each have cattle. If all herders act selfishly and graze as many cattle as they can, the pasture will be overgrazed and ultimately destroyed. If they cooperate and limit their grazing, the pasture can sustain them for a long time.
Payoffs:
If each herder cooperates and limits their cattle, the pasture is preserved, and everyone benefits (higher collective payoff).
If all herders defect and overgraze, they each get a short-term benefit, but the long-term outcome is that the pasture is destroyed, and everyone suffers (lower collective payoff).
The Tragedy of the Commons illustrates the challenge of managing public goods and resources. Individuals can be tempted to defect for short-term gain, but in the long run, this leads to collective disaster.
This game explains why cooperation is difficult to achieve in situations where individuals have a strong incentive to act in their own self-interest and why mechanisms like regulation or social norms are needed to avoid the tragedy.
The Tragedy of the Commons was first described by Garrett Hardin in 1968 as a social dilemma that occurs when individuals overuse a shared resource.
It is directly inspired by real-world observations in both nature and human society.
In nature, many species rely on common resources. For example, grazing herds on shared grasslands or fish stocks in the ocean.
Overgrazing is a common issue in animal populations, where individual animals are driven to consume as much as they can, leading to resource depletion (like the overuse of waterholes in deserts).
In human societies, it applies to the overuse of natural resources (like fisheries, forests, or water supplies) when individuals or groups act in their own interest, leading to long-term degradation for everyone.
War of Attrition
This game models scenarios where two individuals compete for a resource, and they gradually escalate their investment in the conflict (such as time, energy, or money).
Scenario: Two individuals compete for a resource by repeatedly "investing" (e.g., by increasing their effort or stakes in the contest). The first one to back down loses the contest, but the longer they stay in the contest, the higher the costs (such as time or energy) they incur.
Payoffs:
The individual who stays in the contest longer incurs a higher cost but also increases their chance of winning the resource.
The individual who gives up early loses the resource but avoids the cost of further investment.
Evolutionary Implications:
The War of Attrition can model animal contests for territory or mates, where individuals gradually escalate conflict until one backs down.
The strategy that tends to emerge is based on the timing of when to give up (which is often influenced by factors like resource value, individual resilience, or past experiences).
The War of Attrition game was formulated by John Maynard Smith to model competition between individuals where the winner is the one who can hold out the longest.
This game is inspired by natural conflicts where animals engage in prolonged contests that drain energy and resources, and the one that gives up first loses.
Lions or elephants often have contests over territory or mates where they compete by staying engaged in the contest until one of them retreats, signifying an end.
Mating contests in birds and reptiles often involve prolonged displays of stamina or strength (e.g., head bobbing in male lizards), where the winner is the one who can last the longest, not necessarily the one who is strongest.
The War of Attrition can also model mating displays where individuals must display strength or endurance until one gives up or backs down.
If you are interested in this topic you might want to start with wikipedia:
https://en.wikipedia.org/wiki/Evolutionary_game_theory
https://en.wikipedia.org/wiki/Evolutionary_game_theory
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