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The ultimatum game has been a prominent paradigm in studying the evolution of fairness. It predicts that responders should accept any nonzero offer and proposers should offer the smallest possible amount according to orthodox game theory.…

Computer Science and Game Theory · Computer Science 2019-02-13 Yanling Zhang , Jian Liu , Aming Li

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…

Physics and Society · Physics 2017-04-06 Genki Ichinose , Hiroki Sayama

Repeated interactions are ubiquitous and known to promote social behaviour. While research often focuses on cooperation in the Prisoner's Dilemma, experimental evidence suggests repeated interactions also foster fairness. This study…

Adaptation and Self-Organizing Systems · Physics 2026-04-07 Prosanta Mandal , Arunava Patra , Sagar Chakraborty

Experiments on the ultimatum game have revealed that humans are remarkably fond of fair play. When asked to share an amount of money, unfair offers are rare and their acceptance rate small. While empathy and spatiality may lead to the…

Physics and Society · Physics 2012-08-20 Attila Szolnoki , Matjaz Perc , Gyorgy Szabo

Spatial structure has a profound effect on the outcome of evolutionary games. In the ultimatum game, it leads to the dominance of much fairer players than those predicted to evolve in well-mixed settings. Here we show that spatiality leads…

Physics and Society · Physics 2012-11-09 Attila Szolnoki , Matjaz Perc , Gyorgy Szabo

In the Ultimatum Game (UG) one player, named "proposer", has to decide how to allocate a certain amount of money between herself and a "responder". If the offer is greater than or equal to the responder's minimum acceptable offer (MAO),…

Physics and Society · Physics 2018-04-04 Valerio Capraro

Behavioral experiments on the ultimatum game (UG) reveal that we humans prefer fair acts, which contradicts the prediction made in orthodox Economics. Existing explanations, however, are mostly attributed to exogenous factors within the…

Machine Learning · Computer Science 2026-02-04 Guozhong Zheng , Jiqiang Zhang , Xin Ou , Shengfeng Deng , Li Chen

Behavioral experiments on the Ultimatum Game have shown that we human beings have remarkable preference in fair play, contradicting the predictions by the game theory. Most of the existing models seeking for explanations, however, strictly…

Populations and Evolution · Quantitative Biology 2022-12-07 Guozhong Zheng , Jiqiang Zhang , Rizhou Liang , Lin Ma , Li Chen

From social contracts to climate agreements, individuals engage in groups that must collectively reach decisions with varying levels of equality and fairness. These dilemmas also pervade Distributed Artificial Intelligence, in domains such…

Darwin's theory of evolution - as introduced in game theory by Maynard Smith - is not the only important evolutionary aspect in a evolutionary dynamics, since complex interdependencies, competition, and growth should be modeled by, for…

Physics and Society · Physics 2016-02-17 Roberto da Silva , Pablo A. Valverde , Luis C. Lamb

A non-zero-sum 3-person coalition game is presented, to study the evolution of complexity and diversity in cooperation, where the population dynamics of players with strategies is given according to their scores in the iterated game and…

adap-org · Physics 2015-06-30 Eizo Akiyama , Kunihiko Kaneko

We consider a version of the ultimatum game which simultaneously combines reactive and Darwinian aspects with offers in [0,1]. By reactive aspects, we consider the effects that lead the player to change their offer given the previous…

Physics and Society · Physics 2019-10-02 Roberto da Silva , Pablo Valverde , Luis C. Lamb

Recently, reputation-based indirect reciprocity has been widely applied to the study on fairness behavior. Previous works mainly investigate indirect reciprocity by considering compulsory participation. While in reality, individuals may…

Computer Science and Game Theory · Computer Science 2023-12-21 Yanling Zhang , Yin Li , Xiaojie Chen , Guangming Xie

The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the…

Optimization and Control · Mathematics 2024-08-06 Hana Krakovská , Rudolf Hanel , Mark Broom

Indirect reciprocity is a mechanism for cooperation in social dilemma situations, in which an individual is motivated to help another to acquire a good reputation and receive help from others afterwards. Ingroup favoritism is another aspect…

Physics and Society · Physics 2012-11-20 Mitsuhiro Nakamura , Naoki Masuda

Asymmetric evolutionary games, such as the Ultimatum Game, provide keys to understanding the emergence of fairness in social species. Building on this framework, we explore the evolution of social value systems and the operational role that…

Physics and Society · Physics 2025-05-13 Hana Krakovská , Rudolf Hanel

We address the problem of how cooperative (altruistic-like) behavior arises in natural and social systems by analyzing an ultimatum game in complex networks. Specifically, three types of players are considered: (a) empathetic, whose…

Physics and Society · Physics 2009-12-18 Roberta Sinatra , Jaime Iranzo , Jesús Gómez-Gardeñes , Luis M. Floría , Vito Latora , Yamir Moreno

Understanding the evolution of human social systems requires flexible formalisms for the emergence of institutions. Although game theory is normally used to model interactions individually, larger spaces of games can be helpful for modeling…

Physics and Society · Physics 2021-08-12 Seth Frey , Curtis Atkisson

This paper explores the use of Generative Pre-trained Transformers (GPT) in strategic game experiments, specifically the ultimatum game and the prisoner's dilemma. I designed prompts and architectures to enable GPT to understand the game…

General Economics · Economics 2023-12-12 Fulin Guo

Fairness in hybrid societies hinges on a simple choice: should AI be a generous host or a strict gatekeeper? Moving beyond symmetric models, we show that asymmetric social structures--like those in hiring, regulation, and negotiation--AI…

Multiagent Systems · Computer Science 2026-02-24 Zhao Song , Theodor Cimpeanu , Chen Shen , The Anh Han
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