The Evolution of Fairness

PSC 120Jeff Schank

Fairness• People engage in fair exchanges of resources even when it

would benefit them more to act unfairly

• Non-human primates exhibit patterns offair behavior similar to humans

• Vampire bats often share blood meals with unlucky bats

• Juvenile animals often learn to play fairly with each other, which may promote fair behavior as adults

• Fairness does not obviously benefit the individual, and therein lies the mystery of its evolution

Do People Behave Fairly?

• Let’s do our own study!

Ultimatum Game (UG)

• A little more of a game: First player (Proposer) proposes a split of a resource and the second player (Responder) accepts or rejects the offer

• If the Responder accepts the offer, the resource is split as proposed; otherwise both players receive nothing

• Self-Interested Solution: Proposer offers the least amount possible and the Responder accepts any positive amount

• What people do: Often split it evenly, on average give 40% to the second player

The Dictator Game (DG)

• Hardly a game: the first player simply decides how to divide a resource with a second player

• Self-interested Solution: Keep it all

• What people do: Often split it evenly, on average give 28% to the second player

How Could Fairness Evolve?

• Empathy, Benevolence? • Darwin: “It is extremely doubtful whether the offspring of the more

sympathetic and benevolent parents, or of those who were the most faithful to their comrades, would be reared in greater numbers than the children of selfish and treacherous parents belonging to the same tribe”

• But, “A tribe including many members who, from possessing in a high degree the spirit of patriotism, fidelity, obedience, courage, and sympathy, were always ready to aid one another, and to sacrifice themselves for the common good, would be victorious over most other tribes; and this would be natural selection.”

• One interpretation of the common good is that by fairly distributing risk and resources within a group, more individuals have the opportunity to survive and reproduce

Group Resources

• Consider two groups of agents playing the DG• In one group, all are completely fair and in the

other, all are completely selfish• If, on a round of play, each agent randomly

play another in the group, the expected payoff for each? – Is the same

• What about the variance? – Is not the same

Variance in Resources

The Problem

• Different degrees of fairness generate differences in within-group variance in resources

• Group selection requires between-group variance in fitness

• Can within-group variance in resources be converted into between group-variance in fitness?

A Simple Model

• Consider the same two groups as before with exactly the same properties (e.g., age, etc.)

• On each round, they play for RG resources

• Assume that each agent needs kRG resources to reproduce

• Fair agents must play 2k rounds to reproduce• However, selfish agents reproduce in x = k + r

rounds with probability

Timing of Reproduction: Fair vs. Selfish

An Agent-Based Model

• Mobility (important for engaging other agents in space)

• Aggregation (a basic condition for social behaviour)

• Lifespan • Resources required for reproduction • Reproduction and heritability (including a

mechanism for introducing variation)• Parental investment

Deci

sions

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Simulation Conditions

• Multilevel selection• Individual-only selection (agent swaps)• Group-only selection• Parameter Sweeps– Population density– Resource cap– Parental Investment

Example

Best Fit

DG UG, p UG, q0%

10%

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50%

EmpiricalBest fit

Fairness Games

Offe

r/Ac

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DG UG, p UG, q0%

10%

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50%

Empirical

Best fit

Fairness Games

Offe

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Multilevel Individual-only

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lts: M

ultil

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xam

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Groups-only Selection Simulation

Conclusions

• Fairness evolved when agents aggregated into groups and when population density was low

• It is consistent with any mechanism that reduces within-group variance in resources

• Maybe a previously unrecognized mechanism for the evolution of cooperation

• Does it generalize to cultural and economic groups?