Evolution of Fairness in the Not Quite Ultimatum Game

The Ultimatum Game (UG) is an economic game where two players (proposer and responder) decide how to split a certain amount of money. While traditional economic theories based on rational decision making predict that the proposer should make a minimal offer and the responder should accept it, human subjects tend to behave more fairly in UG. Previous studies suggested that extra information such as reputation, empathy, or spatial structure is needed for fairness to evolve in UG. Here we show that fairness can evolve without additional information if players make decisions probabilistically and may continue interactions when the offer is rejected, which we call the Not Quite Ultimatum Game (NQUG). Evolutionary simulations of NQUG showed that the probabilistic decision making contributes to the increase of proposers' offer amounts to avoid rejection, while the repetition of the game works to responders' advantage because they can wait until a good offer comes. These simple extensions greatly promote evolution of fairness in both proposers' offers and responders' acceptance thresholds.Comment: 14 pages, 3 figure

Social Preference, Incomplete Information, and the Evolution of Ultimatum Game in the Small World Networks: An Agent-Based Approach

Certain social preference models have been proposed to explain fairness behavior in experimental games. Existing bodies of research on evolutionary games, however, explain the evolution of fairness merely through the self-interest agents. This paper attempts to analyze the ultimatum game's evolution on complex networks when a number of agents display social preference. Agents' social preference is modeled in three forms: fairness consideration or maintaining a minimum acceptable money level, inequality aversion, and social welfare preference. Different from other spatial ultimatum game models, the model in this study assumes that agents have incomplete information on other agents' strategies, so the agents need to learn and develop their own strategies in this unknown environment. Genetic Algorithm Learning Classifier System algorithm is employed to address the agents' learning issue. Simulation results reveal that raising the minimum acceptable level or including fairness consideration in a game does not always promote fairness level in ultimatum games in a complex network. If the minimum acceptable money level is high and not all agents possess a social preference, the fairness level attained may be considerably lower. However, the inequality aversion social preference has negligible effect on the results of evolutionary ultimatum games in a complex network. Social welfare preference promotes the fairness level in the ultimatum game. This paper demonstrates that agents' social preference is an important factor in the spatial ultimatum game, and different social preferences create different effects on fairness emergence in the spatial ultimatum game.Spatial Ultimatum Game, Complex Network, Social Preference, Agent Based Modeling

“Economic man” in cross-cultural perspective: Behavioral experiments in 15 small-scale societies

Researchers from across the social sciences have found consistent deviations from the predictions of the canonical model of self-interest in hundreds of experiments from around the world. This research, however, cannot determine whether the uniformity results from universal patterns of human behavior or from the limited cultural variation available among the university students used in virtually all prior experimental work. To address this, we undertook a cross-cultural study of behavior in ultimatum, public goods, and dictator games in a range of small-scale societies exhibiting a wide variety of economic and cultural conditions. We found, first, that the canonical model – based on self-interest – fails in all of the societies studied. Second, our data reveal substantially more behavioral variability across social groups than has been found in previous research. Third, group-level differences in economic organization and the structure of social interactions explain a substantial portion of the behavioral variation across societies: the higher the degree of market integration and the higher the payoffs to cooperation in everyday life, the greater the level of prosociality expressed in experimental games. Fourth, the available individual-level economic and demographic variables do not consistently explain game behavior, either within or across groups. Fifth, in many cases experimental play appears to reflect the common interactional patterns of everyday life

Strategy intervention for the evolution of fairness

Masses of experiments have shown individual preference for fairness which seems irrational. The reason behind it remains a focus for research. The effect of spite (individuals are only concerned with their own relative standing) on the evolution of fairness has attracted increasing attention from experiments, but only has been implicitly studied in one evolutionary model. The model did not involve high-offer rejections, which have been found in the form of non-monotonic rejections (rejecting offers that are too high or too low) in experiments. Here, we introduce a high offer and a non-monotonic rejection in structured populations of finite size, and use strategy intervention to explicitly study how spite influences the evolution of fairness: five strategies are in sequence added into the competition of a fair strategy and a selfish strategy. We find that spite promotes fairness, altruism inhibits fairness, and the non-monotonic rejection can cause fairness to overcome selfishness, which cannot happen without high-offer rejections. Particularly for the group-structured population with seven discrete strategies, we analytically study the effect of population size, mutation, and migration on fairness, selfishness, altruism, and spite. A larger population size cannot change the dominance of fairness, but it promotes altruism and inhibits selfishness and spite. Intermediate mutation maximizes selfishness and fairness, and minimizes spite; intermediate mutation maximizes altruism for intermediate migration and minimizes altruism otherwise. The existence of migration inhibits selfishness and fairness, and promotes altruism; sufficient migration promotes spite. Our study may provide important insights into the evolutionary origin of fairness.Comment: 15 pages, 7 figures. Comments welcom

Reciprocity - an indirect evolutionary analysis

This paper investigates strategic interaction between rational agents whose preferences evolve over time. Players face a pecuniary �game of life� comprising the ultimatum game and the dictator game. Utility may but need not be attached to the reciprocation of fair and unfair play by the opponent and equitable payoff distributions as proposed by Falk and Fischbacher (2001). Evolutionary fitness is determined solely by material success � regardless of the motives for its achievement. Agents cannot explicitly condition the social component of their preferences on whether they face the ultimatum or dictator game. Under these conditions, agents develop a strong preference for reciprocation but little interest in an equitable distribution as such. This corresponds to equitable ultimatum offers but full surplus appropriation by dictators. Adding an exogenous constraint on the possible divergence between preference for reciprocation and for an equitable distribution either makes ultimatum divisions asymmetric or dictators become generous depending on the relative frequency of ultimatum and dictator interaction.

Theories of Fairness and Reciprocity

Most economic models are based on the self-interest hypothesis that assumes that all people are exclusively motivated by their material self-interest. In recent years experimental economists have gathered overwhelming evidence that systematically refutes the self-interest hypothesis and suggests that many people are strongly motivated by concerns for fairness and reciprocity. Moreover, several theoretical papers have been written showing that the observed phenomena can be explained in a rigorous and tractable manner. These theories in turn induced a new wave of experimental research offering additional exciting insights into the nature of preferences and into the relative performance of competing theories of fairness. The purpose of this paper is to review these recent developments, to point out open questions, and to suggest avenues for future research

Emergence of communities and diversity in social networks

Communities are common in complex networks and play a significant role in the functioning of social, biological, economic, and technological systems. Despite widespread interest in detecting community structures in complex networks and exploring the effect of communities on collective dynamics, a deep understanding of the emergence and prevalence of communities in social networks is still lacking. Addressing this fundamental problem is of paramount importance in understanding, predicting, and controlling a variety of collective behaviors in society. An elusive question is how communities with common internal properties arise in social networks with great individual diversity. Here, we answer this question using the ultimatum game, which has been a paradigm for characterizing altruism and fairness. We experimentally show that stable local communities with different internal agreements emerge spontaneously and induce social diversity into networks, which is in sharp contrast to populations with random interactions. Diverse communities and social norms come from the interaction between responders with inherent heterogeneous demands and rational proposers via local connections, where the former eventually become the community leaders. This result indicates that networks are significant in the emergence and stabilization of communities and social diversity. Our experimental results also provide valuable information about strategies for developing network models and theories of evolutionary games and social dynamics.This work was supported by the National Nature Science Foundation of China under Grants 61573064, 71631002, 71401037, and 11301032; the Fundamental Research Funds for the Central Universities and Beijing Nova Programme; and the Natural Sciences and Engineering Research Council of Canada (Individual Discovery Grant). The Boston University work was supported by NSF Grants PHY-1505000, CMMI-1125290, and CHE- 1213217, and by Defense Threat Reduction Agency Grant HDTRA1-14-1-0017, and Department of Energy Contract DE-AC07-05Id14517. (61573064 - National Nature Science Foundation of China; 71631002 - National Nature Science Foundation of China; 71401037 - National Nature Science Foundation of China; 11301032 - National Nature Science Foundation of China; Fundamental Research Funds for the Central Universities and Beijing Nova Programme; Natural Sciences and Engineering Research Council of Canada (Individual Discovery Grant); PHY-1505000 - NSF; CMMI-1125290 - NSF; CHE-1213217 - NSF; HDTRA1-14-1-0017 - Defense Threat Reduction Agency; DE-AC07-05Id14517 - Department of Energy)Published versio

Anomalies: Ultimatums, Dictators and Manners

Economics can be distinguished from other social sciences by the belief that most (all?) behavior can be explained by assuming that agents have stable, well-defined preferences and make rational choices consistent with those preferences in markets that (eventually) clear. An empirical result qualifies as an anomaly if it is difficult to "rationalize" or if implausible assumptions are necessary to explain it within the paradigm. This column will resume, after a long rest, the investigation of such anomalies

Learning to Reach Agreement in a Continuous Ultimatum Game

It is well-known that acting in an individually rational manner, according to the principles of classical game theory, may lead to sub-optimal solutions in a class of problems named social dilemmas. In contrast, humans generally do not have much difficulty with social dilemmas, as they are able to balance personal benefit and group benefit. As agents in multi-agent systems are regularly confronted with social dilemmas, for instance in tasks such as resource allocation, these agents may benefit from the inclusion of mechanisms thought to facilitate human fairness. Although many of such mechanisms have already been implemented in a multi-agent systems context, their application is usually limited to rather abstract social dilemmas with a discrete set of available strategies (usually two). Given that many real-world examples of social dilemmas are actually continuous in nature, we extend this previous work to more general dilemmas, in which agents operate in a continuous strategy space. The social dilemma under study here is the well-known Ultimatum Game, in which an optimal solution is achieved if agents agree on a common strategy. We investigate whether a scale-free interaction network facilitates agents to reach agreement, especially in the presence of fixed-strategy agents that represent a desired (e.g. human) outcome. Moreover, we study the influence of rewiring in the interaction network. The agents are equipped with continuous-action learning automata and play a large number of random pairwise games in order to establish a common strategy. From our experiments, we may conclude that results obtained in discrete-strategy games can be generalized to continuous-strategy games to a certain extent: a scale-free interaction network structure allows agents to achieve agreement on a common strategy, and rewiring in the interaction network greatly enhances the agents ability to reach agreement. However, it also becomes clear that some alternative mechanisms, such as reputation and volunteering, have many subtleties involved and do not have convincing beneficial effects in the continuous case

Interpersonal comparisons of utility in bargaining : Evidence from a transcontinental Ultimatum Game

Cet article présente les résultats expérimentaux d'un jeu de l'ultimatum "transcontinental" entre la France et l'Inde. Le jeu se présente comme un jeu de l'ultimatum classique mais, dans un traitement, les sujets indiens font des propositions aux sujets français et, dans un autre traitement, les sujets français proposent aux indiens. On observe que les négotiations France-> Inde ont tendance à produire des partages monétaires inégaux, en faveur des Français, alors que les négotiations Inde -> France ont tendance à produire des partages monétaires égaux.Le cadre conceptuel que nous introduisons pour expliquer ces phénomènes est un modèle standard de norme sociale de référence, modifié de manière à pouvoir tenir comte des différences d'utilitité marginale de la monnaie. Notre explication ne nécessite pas de considérer des normes culturelles différentes dans les deux pays. Elle repose simplement sur la prise en compte des pouvoirs d'achat différents de la monnaie dans les deux pays, pour les sommes effectivement en jeu dans l'interaction considérée. Nous appellons "équité locale" une telle norme, opposée à des normes "globales", qui ne négligeraient pas la richesse des joueurs en dehors du jeu. D'après nos observations, aucune considération relative au statut des participants en dehors du jeu ne semble pertinente.Comparaisons inter-personnelles d'utilité;Justice;Equité;Expérience de négociation;Jeu de l'ultimatum