Stochastic evolutionary dynamics of trust games with asymmetric parameters
Open accessAbstract
Trusting in others and reciprocating that trust with trustworthy actions are crucial to successful and prosperous societies. The trust game has been widely used to quantitatively study trust and trustworthiness, involving a sequential exchange between an investor and a trustee. Deterministic evolutionary game theory predicts no trust and no trustworthiness, whereas the behavioral experiments with the one-shot anonymous trust game show that people substantially trust and respond trustworthily. To explain these discrepancies, previous works often turn to additional mechanisms, which are borrowed from other games such as the prisoner's dilemma. Although these mechanisms lead to the evolution of trust and trustworthiness to an extent, the optimal or the most common strategy often involves no trustworthiness. In this paper, we study the impact of asymmetric demographic parameters (e.g., different population sizes) on game dynamics of the trust game. We show that, in a weak-mutation limit, stochastic evolutionary dynamics with the asymmetric parameters can lead to the evolution of high trust and high trustworthiness without any additional mechanisms in well-mixed finite populations. Even full trust and near full trustworthiness can be the most common strategies. These results are qualitatively different from those of the previous works. Our results thereby demonstrate rich evolutionary dynamics of the asymmetric trust game.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Previous studies on enhancing trust are usually carried out in the framework of one-shot interaction.
“Although there were attempts for enhancing the level of trust from different aspects, we notice that these studies are usually carried out in the framework of one-shot interaction, to our knowledge [8, 9, 16, 24, 26].”
From Conditional investment strategy in evolutionary trust games with repeated group interactions (2022) · cites this paper as [26]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Smith, J., & Price, G. R. (1973) · Nature · doi:10.1038/246015a0 · Cited by 6,423 · see citing works
Five Rules for the Evolution of Cooperation
Nowak, M. A. (2006) · Science · doi:10.1126/science.1133755 · Cited by 5,894 · see citing works
Trust, Reciprocity, and Social History
Berg, J., Dickhaut, J., & McCabe, K. (1995) · Games and Economic Behavior · doi:10.1006/game.1995.1027 · Cited by 5,548 · see citing works
Evolutionary Games and Population Dynamics
Hofbauer, J., & Sigmund, K. (1998) · doi:10.1017/cbo9781139173179 · Cited by 5,502 · cited 2× · see citing works
“[9] J.”
BackgroundEvolutionary stable strategies and game dynamics
Taylor, P., & Jonker, L. (1978) · Mathematical Biosciences · doi:10.1016/0025-5564(78)90077-9 · Cited by 3,543 · see citing works
Szabó, G., & Fáth, G. (2007) · Physics Reports · doi:10.1016/j.physrep.2007.04.004 · Cited by 2,928 · see citing works
Evolution of indirect reciprocity by image scoring
Nowak, M. A., & Sigmund, K. (1998) · Nature · doi:10.1038/31225 · Cited by 2,700 · see citing works
Evolutionary Dynamics: Exploring the Equations of Life
NOWAK, M. A. (2006) · doi:10.2307/j.ctvjghw98 · Cited by 2,438 · cited 2× · see citing works
“The frequency-independent selection in the two-population model allows us to use the well-known formula for fixation probability under the Moran process [27].”
Statistical physics of human cooperation
Perc, M., Jordan, J., Rand, D. G., Wang, Z., Boccaletti, S., & Szolnoki, A. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.05.004 · Cited by 1,572 · cited 2× · see citing works
“[4] M.”
BackgroundEvolutionary dynamics on graphs
Aiden, E. L., Hauert, C., & Nowak, M. A. (2005) · Nature · doi:10.1038/nature03204 · Cited by 1,351 · see citing works
Getting to Know You: Reputation and Trust in a Two-Person Economic Exchange
King-Casas, B., Tomlin, D., Anen, C., Camerer, C. F., Quartz, S. R., & Montague, P. R. (2005) · Science · doi:10.1126/science.1108062 · Cited by 1,345 · see citing works
Johnson, N. D., & Mislin, A. A. (2011) · Journal of Economic Psychology · doi:10.1016/j.joep.2011.05.007 · Cited by 967 · see citing works
The statistical processes of evolutionary theory.
Moran, P. A. P. (1962) · Medical Entomology and Zoology · Cited by 776 · see citing works
Via Freedom to Coercion: The Emergence of Costly Punishment
Hauert, C., Traulsen, A., Brandt, H., Nowak, M. A., & Sigmund, K. (2007) · Science · doi:10.1126/science.1141588 · Cited by 709 · see citing works
Reputation-based partner choice promotes cooperation in social networks
Fu, F., Hauert, C., Nowak, M. A., & Wang, L. (2008) · Physical Review E · doi:10.1103/physreve.78.026117 · Cited by 682 · see citing works
On The Economics and Biology of Trust
Fehr, E. (2009) · Journal of the European Economic Association · doi:10.1162/jeea.2009.7.2-3.235 · Cited by 680 · see citing works
The Statistical Processes of Evolutionary Theory.
Pl, W., & Moran, P. A. P. (1963) · Journal of the American Statistical Association · doi:10.2307/2283297 · Cited by 647 · see citing works
Stochastic dynamics of invasion and fixation
Traulsen, A., Nowak, M. A., & Pacheco, J. M. (2006) · Physical Review E · doi:10.1103/physreve.74.011909 · Cited by 608 · see citing works
Social learning promotes institutions for governing the commons
Sigmund, K., De Silva, H., Traulsen, A., & Hauert, C. (2010) · Nature · doi:10.1038/nature09203 · Cited by 580 · see citing works
Evolutionary game dynamics in finite populations
TAYLOR, C., Fudenberg, D., SASAKI, A., & Nowak, M. A. (2004) · Bulletin of Mathematical Biology · doi:10.1016/j.bulm.2004.03.004 · Cited by 434 · see citing works
Imitation processes with small mutations
Fudenberg, D., & Imhof, L. A. (2006) · Journal of Economic Theory · doi:10.1016/j.jet.2005.04.006 · Cited by 335 · see citing works
Evolution of extortion in Iterated Prisoner’s Dilemma games
Hilbe, C., Nowak, M. A., & Sigmund, K. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1214834110 · Cited by 296 · see citing works
Evolution of cooperation in stochastic games
Hilbe, C., Šimsa, Š., Chatterjee, K., & Nowak, M. A. (2018) · Nature · doi:10.1038/s41586-018-0277-x · Cited by 277 · see citing works
Evolution of fairness in the one-shot anonymous Ultimatum Game
Rand, D. G., Tarnita, C. E., Ohtsuki, H., & Nowak, M. A. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1214167110 · Cited by 251 · see citing works
Universality of weak selection
Wu, B., Altrock, P. M., Wang, L., & Traulsen, A. (2010) · Physical Review E · doi:10.1103/physreve.82.046106 · Cited by 175 · see citing works
Reacting Differently to Adverse Ties Promotes Cooperation in Social Networks
Van Segbroeck, S., Santos, F. C., Lenaerts, T., & Pacheco, J. M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.058105 · Cited by 170 · see citing works
Evolution of trust and trustworthiness: social awareness favours personality differences
McNamara, J. M., Stephens, P. A., Dall, S. R. X., & Houston, A. I. (2008) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2008.1182 · Cited by 152 · see citing works
Defector-accelerated cooperativeness and punishment in public goods games with mutations
Helbing, D., Szolnoki, A., Perc, M., & Szabó, G. (2010) · Physical Review E · doi:10.1103/physreve.81.057104 · Cited by 148 · see citing works
Evolution as a general theoretical framework for economics and public policy
Wilson, D. S., & Gowdy, J. M. (2012) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2012.12.008 · Cited by 126 · cited 5× · see citing works
“To evolve non-zero trustworthiness as the most common strategy in the symmetric TG, previous works turned to additional mechanisms such as reputation-based interactions [17][24][25].”
BackgroundMethodInfluentialEmergence of Fairness in Repeated Group Interactions
Segbroeck, S. V., Pacheco, J. M., Lenaerts, T., & Santos, F. C. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.158104 · Cited by 117 · see citing works
Multiple strategies in structured populations
Tarnita, C. E., Wage, N., & Nowak, M. A. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1016008108 · Cited by 106 · see citing works
How small are small mutation rates?
Wu, B., Gokhale, C. S., Wang, L., & Traulsen, A. (2011) · Journal of Mathematical Biology · doi:10.1007/s00285-011-0430-8 · Cited by 104 · see citing works
The Trust Game in neuroscience: A short review
Tzieropoulos, H. (2013) · Social Neuroscience · doi:10.1080/17470919.2013.832375 · Cited by 80 · see citing works
Aspiration dynamics in structured population acts as if in a well-mixed one
Du, J., Wu, B., & Wang, L. (2015) · Scientific Reports · doi:10.1038/srep08014 · Cited by 68 · see citing works
Information, Irrationality and the Evolution of Trust
Manapat, M. L., Nowak, M. A., & Rand, D. G. (2012) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2012.10.018 · Cited by 62 · see citing works
Coevolution of Trustful Buyers and Cooperative Sellers in the Trust Game
Masuda, N., & Nakamura, M. (2012) · PLoS ONE · doi:10.1371/journal.pone.0044169 · Cited by 45 · see citing works
Stochastic evolutionary dynamics of bimatrix games
Ohtsuki, H. (2010) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2010.01.016 · Cited by 39 · see citing works
Finite-population evolution with rare mutations in asymmetric games
Veller, C., & Hayward, L. K. (2015) · Journal of Economic Theory · doi:10.1016/j.jet.2015.12.005 · Cited by 35 · see citing works
A Review of Theoretical and Practical Challenges of Trusted Autonomy in Big Data
Abbass, H. A., Leu, G., & Merrick, K. E. (2016) · IEEE Access · doi:10.1109/access.2016.2571058 · Cited by 35 · see citing works
Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation
Mittal, S., Mukhopadhyay, A., & Chakraborty, S. (2020) · Physical review. E · doi:10.1103/physreve.101.042410 · Cited by 35 · see citing works
Stochastic evolutionary dynamics resolve the Traveler's Dilemma
Manapat, M. L., Rand, D. G., Pawlowitsch, C., & Nowak, M. A. (2012) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2012.03.014 · Cited by 30 · see citing works
Evolutionary dynamics of public goods games with diverse contributions in finite populations
Wang, J., Wu, B., Chen, X., et al. (2010) · Physical Review E · doi:10.1103/physreve.81.056103 · Cited by 28 · see citing works
The Red Queen and King in finite populations
Veller, C., Hayward, L. K., Hilbe, C., & Nowak, M. A. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1702020114 · Cited by 26 · see citing works
Requejo, R. J., Camacho, J., Cuesta, J. A., & Arenas, À. (2012) · Physical Review E · doi:10.1103/physreve.86.026105 · Cited by 25 · see citing works
Fairness and Trust in Structured Populations
Tarnita, C. E. (2015) · Games · doi:10.3390/g6030214 · Cited by 20 · see citing works
Satisfied-defect, unsatisfied-cooperate: An evolutionary dynamics of cooperation led by aspiration
Lim, I. S., & Wittek, P. (2018) · Physical review. E · doi:10.1103/physreve.98.062113 · Cited by 17 · see citing works
The remarkable discreteness of being
Houchmandzadeh, B. (2014) · Journal of Biosciences · doi:10.1007/s12038-013-9350-7 · Cited by 4 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Higher-order interactions shape collective human behaviour
Battiston, F., Capraro, V., Karimi, F., Lehmann, S., Migliano, A. B., Sadekar, O., Sánchez, Á., & Perc, M. (2025) · Nature Human Behaviour · doi:10.1038/s41562-025-02373-5 · Cited by 99 · see citing works
Conditional investment strategy in evolutionary trust games with repeated group interactions
Liu, L., & Chen, X. (2022) · Information Sciences · doi:10.1016/j.ins.2022.07.073 · Cited by 45 · see citing works
“Along this line, many researchers have considered network structure [8, 9, 24], punishment strategy [16], asymmetric demographic parameters [26], and reputation [22], into the NTG model to explore the evolution of trust.”
BackgroundInfluentialTo Trust or Not to Trust: Evolutionary Dynamics of an Asymmetric N-Player Trust Game
Lim, I. S., & Masuda, N. (2023) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2023.3244537 · Cited by 36 · see citing works
“The trust game (TG) is a current gold standard of formalisation for non-simultaneous interaction in social dilemma situations and has widely been used to study trust and trustworthiness [11][12][17][18][19][20][21][22][23][24].”
MethodEvolutionary dynamics of trust in the N-player trust game with individual reward and punishment
Fang, X., & Chen, X. (2021) · The European Physical Journal B · doi:10.1140/epjb/s10051-021-00185-w · Cited by 26 · see citing works
Evolution of trust in a hierarchical population with punishing investors
Sun, K., Liu, Y., Chen, X., & Szolnoki, A. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.112413 · Cited by 18 · see citing works
N -player repeated evolutionary trust game under government management
Liu, Y., Liu, L., Guo, R., & Zhang, L. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.114031 · Cited by 14 · see citing works
Lim, I. S., & Capraro, V. (2021) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2021.3133711 · Cited by 12 · see citing works
“We decided to focus on the trust game (TG) that has been widely used to formally study trust and trustworthiness in various disciplines [2], [3], [17]–[20].”
Inter-role reciprocity in evolutionary trust game on square lattices
Wang, C., Zhang, W., Wang, X., & Szolnoki, A. (2025) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0285064 · Cited by 10 · see citing works
Guo, R., Liu, L., Liu, Y., & Zhang, L. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.114078 · Cited by 11 · see citing works
Evolution of trust in structured populations
Wang, C. (2024) · Applied Mathematics and Computation · doi:10.1016/j.amc.2024.128595 · Cited by 10 · see citing works
“Examples include a simulation study on a square lattice [58], research on fixed provider and consumer roles [59, 60, 61], and further theoretical studies [62, 63, 64].”
BackgroundEvolution of trust in the N-player trust game with the margin system
Guo, R., Liu, L., Liu, Y., & Zhang, L. (2024) · Applied Mathematics and Computation · doi:10.1016/j.amc.2024.128649 · Cited by 5 · see citing works
Interpersonal trust: Asymptotic analysis of a stochastic coordination game with multi-agent learning
Meylahn, B. V., den Boer, A. V., & Mandjes, M. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0205136 · Cited by 2 · see citing works
- Authors
- Lim, I. S.
- Affiliations
- Bangor University (GB)
- Corresponding author
- Lim, Ik Soo
- ORCID
- Lim, Ik Soo
- Venue
- Physical review. E
- Publisher
- American Physical Society (APS)
- Published
- 2020-12-22
- Volume
- 102
- Issue
- 6
- Pages
- 062419-062419
- ISSN
- 2470-0045 (ISSN-L)
- 2470-0053
- OpenAlex
- W3094594818
- Cited by
- 12
- References
- 47
- Citations by year
- 2025: 2 · 2024: 3 · 2023: 3 · 2022: 2 · 2021: 2
- FWCI
- 2.34
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. E (publishedVersion)
- PubMed (publishedVersion)
- Greenwich Academic Literature Archive (University of Greenwich) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Social Sciences › Safety Research › Experimental Behavioral Economics Studies
- Social Sciences › Decision Sciences › Management Science and Operations Research › Game Theory and Applications
- Keywords
- trust game, trustworthiness, stochastic evolutionary dynamics, finite population, well-mixed populations, evolution of cooperation
- MeSH terms
- Biological Evolution, Game Theory, Humans, Stochastic Processes, Trust
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
