Limits...
Rational Constraints and the Evolution of Fairness in the Ultimatum Game.

Tomlin D - PLoS ONE (2015)

Bottom Line: Under the other system, a simple, ordinal constraint was placed on the acceptance probabilities such that a given offer was at least as likely to be accepted as a smaller offer.For simulations under either system, agents' preferences and their corresponding behavior evolved over multiple generations.Populations without the ordinal constraint came to emulate maximizing economic agents, while populations with the constraint came to resemble the behavior of human players.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, University of Colorado Colorado Springs, Colorado Springs, Colorado, United States of America.

ABSTRACT
Behavior in the Ultimatum Game has been well-studied experimentally, and provides a marked contrast between the theoretical model of a self-interested economic agent and that of an actual human concerned with social norms such as fairness. How did such norms evolve, when punishing unfair behavior can be costly to the punishing agent? The work described here simulated a series of Ultimatum Games, in which populations of agents earned resources based on their preferences for proposing and accepting (or rejecting) offers of various sizes. Two different systems governing the acceptance or rejection of offers were implemented. Under one system, the probability that an agent accepted an offer of a given size was independent of the probabilities of accepting the other possible offers. Under the other system, a simple, ordinal constraint was placed on the acceptance probabilities such that a given offer was at least as likely to be accepted as a smaller offer. For simulations under either system, agents' preferences and their corresponding behavior evolved over multiple generations. Populations without the ordinal constraint came to emulate maximizing economic agents, while populations with the constraint came to resemble the behavior of human players.

No MeSH data available.


Co-evolution of offer frequencies and acceptance rates in monotonic populations with selection pressure.The lines in each panel show the mean genotype for proposers (blue line) and responders (red line) across the eleven possible offers for a population of size N = 100. The expected value of each offer, from the proposer’s perspective, is shown in green. When acceptance rates were constrained to monotonically increase over offer sizes, the highest expected value for proposers came from fair (or nearly fair) offers. As proposers and responders co-evolved, extremely high and extremely low offers ceased and proposers settled on a modal offer of 30%—the offer with the highest expected value.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4520471&req=5

pone.0134636.g003: Co-evolution of offer frequencies and acceptance rates in monotonic populations with selection pressure.The lines in each panel show the mean genotype for proposers (blue line) and responders (red line) across the eleven possible offers for a population of size N = 100. The expected value of each offer, from the proposer’s perspective, is shown in green. When acceptance rates were constrained to monotonically increase over offer sizes, the highest expected value for proposers came from fair (or nearly fair) offers. As proposers and responders co-evolved, extremely high and extremely low offers ceased and proposers settled on a modal offer of 30%—the offer with the highest expected value.

Mentions: As shown above, the imposition of monotonicity on acceptance rates not only produced acceptance rates similar to actual human behavior, but also shifted the modal proposed offer from the minimum non-zero offer of 10% (Fig 1C) to more fair offers of 30% (Fig 2C). However, the data above do not demonstrate how populations achieved this endpoint. Fig 3 depicts the evolutionary time course of proposer and responder genotypes for a single population size (N = 100). When the population was initialized, mean offers did not differ significantly across the possible offer sizes, and acceptance rates increased linearly across sizes due to the constraint of monotonicity (Fig 3A). From the proposers’ perspective, extremely low and high offers both had low expected values: the former because the likelihood of acceptance was very low, and the latter because the return to the proposer was very low. In contrast, the expected value of fairer offers was maximal. Proposers quickly evolved to avoid low and high offers in favor of fair ones (Fig 3B and 3C). Meanwhile, selection strongly favored responders that accepted fair or hyperfair offers. The probability of acceptance for low offers drifted upward as well, but there was no strong selection for this class of offers–they were not frequently proposed, and even when accepted they did not contribute much to the responders’ overall fitness (Fig 3B and 3C). The expected value for low offers from the proposer’s perspective continued to sharpen, and the genotypes for proposed offers followed suit. Upon reaching equilibrium (Fig 3E), offers of 30% accounted for more than half of all offers, with a negligible number of minimum non-zero offers being made (for evidence that the simulations indeed attained equilibrium after 500,000 generations, see S3 Fig).


Rational Constraints and the Evolution of Fairness in the Ultimatum Game.

Tomlin D - PLoS ONE (2015)

Co-evolution of offer frequencies and acceptance rates in monotonic populations with selection pressure.The lines in each panel show the mean genotype for proposers (blue line) and responders (red line) across the eleven possible offers for a population of size N = 100. The expected value of each offer, from the proposer’s perspective, is shown in green. When acceptance rates were constrained to monotonically increase over offer sizes, the highest expected value for proposers came from fair (or nearly fair) offers. As proposers and responders co-evolved, extremely high and extremely low offers ceased and proposers settled on a modal offer of 30%—the offer with the highest expected value.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4520471&req=5

pone.0134636.g003: Co-evolution of offer frequencies and acceptance rates in monotonic populations with selection pressure.The lines in each panel show the mean genotype for proposers (blue line) and responders (red line) across the eleven possible offers for a population of size N = 100. The expected value of each offer, from the proposer’s perspective, is shown in green. When acceptance rates were constrained to monotonically increase over offer sizes, the highest expected value for proposers came from fair (or nearly fair) offers. As proposers and responders co-evolved, extremely high and extremely low offers ceased and proposers settled on a modal offer of 30%—the offer with the highest expected value.
Mentions: As shown above, the imposition of monotonicity on acceptance rates not only produced acceptance rates similar to actual human behavior, but also shifted the modal proposed offer from the minimum non-zero offer of 10% (Fig 1C) to more fair offers of 30% (Fig 2C). However, the data above do not demonstrate how populations achieved this endpoint. Fig 3 depicts the evolutionary time course of proposer and responder genotypes for a single population size (N = 100). When the population was initialized, mean offers did not differ significantly across the possible offer sizes, and acceptance rates increased linearly across sizes due to the constraint of monotonicity (Fig 3A). From the proposers’ perspective, extremely low and high offers both had low expected values: the former because the likelihood of acceptance was very low, and the latter because the return to the proposer was very low. In contrast, the expected value of fairer offers was maximal. Proposers quickly evolved to avoid low and high offers in favor of fair ones (Fig 3B and 3C). Meanwhile, selection strongly favored responders that accepted fair or hyperfair offers. The probability of acceptance for low offers drifted upward as well, but there was no strong selection for this class of offers–they were not frequently proposed, and even when accepted they did not contribute much to the responders’ overall fitness (Fig 3B and 3C). The expected value for low offers from the proposer’s perspective continued to sharpen, and the genotypes for proposed offers followed suit. Upon reaching equilibrium (Fig 3E), offers of 30% accounted for more than half of all offers, with a negligible number of minimum non-zero offers being made (for evidence that the simulations indeed attained equilibrium after 500,000 generations, see S3 Fig).

Bottom Line: Under the other system, a simple, ordinal constraint was placed on the acceptance probabilities such that a given offer was at least as likely to be accepted as a smaller offer.For simulations under either system, agents' preferences and their corresponding behavior evolved over multiple generations.Populations without the ordinal constraint came to emulate maximizing economic agents, while populations with the constraint came to resemble the behavior of human players.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, University of Colorado Colorado Springs, Colorado Springs, Colorado, United States of America.

ABSTRACT
Behavior in the Ultimatum Game has been well-studied experimentally, and provides a marked contrast between the theoretical model of a self-interested economic agent and that of an actual human concerned with social norms such as fairness. How did such norms evolve, when punishing unfair behavior can be costly to the punishing agent? The work described here simulated a series of Ultimatum Games, in which populations of agents earned resources based on their preferences for proposing and accepting (or rejecting) offers of various sizes. Two different systems governing the acceptance or rejection of offers were implemented. Under one system, the probability that an agent accepted an offer of a given size was independent of the probabilities of accepting the other possible offers. Under the other system, a simple, ordinal constraint was placed on the acceptance probabilities such that a given offer was at least as likely to be accepted as a smaller offer. For simulations under either system, agents' preferences and their corresponding behavior evolved over multiple generations. Populations without the ordinal constraint came to emulate maximizing economic agents, while populations with the constraint came to resemble the behavior of human players.

No MeSH data available.