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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.


Final genotypes for monotonic acceptance rates.The lines in each panel show the mean genotype for each population size across the eleven possible offers. For each panel, black dots denote offer frequencies and conditional acceptance rates of human subjects, according to a meta-analysis of multiple behavioral studies. Because offers greater than 65% are rare in human studies, the rightmost dot comprises all offers of 65% or greater. (a) Frequencies of proposed offers without selection pressure. When the identities of reproducing agents were determined randomly, offer sizes were all equally frequent. (b) Rates of acceptance, conditional upon offer size, without selection pressure. When the identities of reproducing agents were determined randomly, but acceptance rates were constrained to be monotonically increasing, acceptance rates became linear with respect to offer size. (c) Frequencies of proposed offers with selection pressure. In contrast to the non-monotonic simulations, behavior shifts toward fairer offers, with modal offer sizes of 30%-40%. As in the non-monotonic simulations, larger populations tended toward lower offers than smaller populations. (d) Rates of acceptance, conditional upon offer size, with selection pressure. When the probability of reproduction was proportional to earnings, acceptance rates became non-linear with offer size, with concavity increasing with population size.
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pone.0134636.g002: Final genotypes for monotonic acceptance rates.The lines in each panel show the mean genotype for each population size across the eleven possible offers. For each panel, black dots denote offer frequencies and conditional acceptance rates of human subjects, according to a meta-analysis of multiple behavioral studies. Because offers greater than 65% are rare in human studies, the rightmost dot comprises all offers of 65% or greater. (a) Frequencies of proposed offers without selection pressure. When the identities of reproducing agents were determined randomly, offer sizes were all equally frequent. (b) Rates of acceptance, conditional upon offer size, without selection pressure. When the identities of reproducing agents were determined randomly, but acceptance rates were constrained to be monotonically increasing, acceptance rates became linear with respect to offer size. (c) Frequencies of proposed offers with selection pressure. In contrast to the non-monotonic simulations, behavior shifts toward fairer offers, with modal offer sizes of 30%-40%. As in the non-monotonic simulations, larger populations tended toward lower offers than smaller populations. (d) Rates of acceptance, conditional upon offer size, with selection pressure. When the probability of reproduction was proportional to earnings, acceptance rates became non-linear with offer size, with concavity increasing with population size.

Mentions: Fig 2 depicts the mean genotypes, after 500,000 generations, of populations of “monotonic” agents: those whose acceptance rates in the UG were constrained such that the acceptance rate for a given offer was at least as high as that for a lower offer. Panel a demonstrates that, as with the non-monotonic agents, when no selection pressure existed agents’ offers did not vary significantly across the possible offer sizes. Because of the monotonic constraint, however, panel 2b differs markedly from its counterpart in Fig 1. Here, mean acceptance rates across agents increased linearly across offer sizes, ranging from seven percent for offers of zero up to an acceptance rate of approximately 90 percent for offers of the entire resource. This linear pattern existed because the acceptance rates were randomly generated subject to the monotonic constraint, and thanks to the large number of simulations each increment in the offer size corresponds to an average increase in acceptance probability of 1 / (number of possible offers + 1), or approximately .08.


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

Tomlin D - PLoS ONE (2015)

Final genotypes for monotonic acceptance rates.The lines in each panel show the mean genotype for each population size across the eleven possible offers. For each panel, black dots denote offer frequencies and conditional acceptance rates of human subjects, according to a meta-analysis of multiple behavioral studies. Because offers greater than 65% are rare in human studies, the rightmost dot comprises all offers of 65% or greater. (a) Frequencies of proposed offers without selection pressure. When the identities of reproducing agents were determined randomly, offer sizes were all equally frequent. (b) Rates of acceptance, conditional upon offer size, without selection pressure. When the identities of reproducing agents were determined randomly, but acceptance rates were constrained to be monotonically increasing, acceptance rates became linear with respect to offer size. (c) Frequencies of proposed offers with selection pressure. In contrast to the non-monotonic simulations, behavior shifts toward fairer offers, with modal offer sizes of 30%-40%. As in the non-monotonic simulations, larger populations tended toward lower offers than smaller populations. (d) Rates of acceptance, conditional upon offer size, with selection pressure. When the probability of reproduction was proportional to earnings, acceptance rates became non-linear with offer size, with concavity increasing with population size.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4520471&req=5

pone.0134636.g002: Final genotypes for monotonic acceptance rates.The lines in each panel show the mean genotype for each population size across the eleven possible offers. For each panel, black dots denote offer frequencies and conditional acceptance rates of human subjects, according to a meta-analysis of multiple behavioral studies. Because offers greater than 65% are rare in human studies, the rightmost dot comprises all offers of 65% or greater. (a) Frequencies of proposed offers without selection pressure. When the identities of reproducing agents were determined randomly, offer sizes were all equally frequent. (b) Rates of acceptance, conditional upon offer size, without selection pressure. When the identities of reproducing agents were determined randomly, but acceptance rates were constrained to be monotonically increasing, acceptance rates became linear with respect to offer size. (c) Frequencies of proposed offers with selection pressure. In contrast to the non-monotonic simulations, behavior shifts toward fairer offers, with modal offer sizes of 30%-40%. As in the non-monotonic simulations, larger populations tended toward lower offers than smaller populations. (d) Rates of acceptance, conditional upon offer size, with selection pressure. When the probability of reproduction was proportional to earnings, acceptance rates became non-linear with offer size, with concavity increasing with population size.
Mentions: Fig 2 depicts the mean genotypes, after 500,000 generations, of populations of “monotonic” agents: those whose acceptance rates in the UG were constrained such that the acceptance rate for a given offer was at least as high as that for a lower offer. Panel a demonstrates that, as with the non-monotonic agents, when no selection pressure existed agents’ offers did not vary significantly across the possible offer sizes. Because of the monotonic constraint, however, panel 2b differs markedly from its counterpart in Fig 1. Here, mean acceptance rates across agents increased linearly across offer sizes, ranging from seven percent for offers of zero up to an acceptance rate of approximately 90 percent for offers of the entire resource. This linear pattern existed because the acceptance rates were randomly generated subject to the monotonic constraint, and thanks to the large number of simulations each increment in the offer size corresponds to an average increase in acceptance probability of 1 / (number of possible offers + 1), or approximately .08.

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.