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Modelling Two-Person Interactions Within and Between Cultural Groups
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The groups with which we associate influence our actions. This is often the case even when they are not deliberately organised but rather based on social categories, such as sex and skin colour, or cultural homogeneity, such as common language or customs. Group membership can cause widespread phenomena such as ingroup favouritism, polarisation of opinion and competition. Previous experiments have shown that these effects can be triggered by even completely arbitrary distinctions between groups. This thesis uses mathematical models to investigate under what circumstances these phenomena can arise.

Using a game theoretical approach, the first three papers address the evolution of ingroup favouritism. Previous models have focused on the prisoners’ dilemma, interactions where the socially optimal behaviour is to co-operate, but where it is in the individual’s self-interest not to. The results presented here suggest that co-ordination problems may have been more important than those of co-operation in the evolution of an ingroup bias. In particular, this applies to common goals that require trust. It is also demonstrated in a behavioural experiment that such trust is most common within groups, but that it can emerge between groups through group reputation.

The fourth paper focuses on a model on how cultural groups in contact can develop common norms, rather than polarise into different norm groups, by assuming a confirmation bias. The model is empirically tested on demographic and linguistic data from Mauritian Creole, a natural language developed from the mixing of parent languages.

In the fifth paper, the group is defined by common preferences (e.g. for pop songs), which are transmitted in a random copying model. The competitive success of the groups, with respect to their size, is recorded on a toplist, the turnover rate of which is derived.

In the final paper, people match up in pairs between groups according to their preferences, and all stable matchings are found under a specific assumption of bounded rationality, when people’s individual behaviour may be affected by the consequences for fellow group members.

Place, publisher, year, edition, pages
Västerås: Mälardalen University , 2013.
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 136
Keyword [en]
Mathematical modelling, cultural evolution
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-16500ISBN: 978-91-7485-100-7 (print)OAI: oai:DiVA.org:mdh-16500DiVA: diva2:579004
Public defence
2013-02-22, Lambda, Mälardalens högskola, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2012-12-19 Created: 2012-12-10 Last updated: 2015-11-13Bibliographically approved
List of papers
1. Pitfalls in Spatial Modelling of Ethnocentrism: A Simulation Analysis of the Model of Hammond and Axelrod
Open this publication in new window or tab >>Pitfalls in Spatial Modelling of Ethnocentrism: A Simulation Analysis of the Model of Hammond and Axelrod
2013 (English)In: JASSS: Journal of Artificial Societies and Social Simulation, ISSN 1460-7425, Vol. 16, no 3Article in journal (Refereed) Published
Abstract [en]

Ethnocentrism refers to the tendency to behave differently towards strangers based only on whether they belong to the ingroup or the outgroup. It is a widespread phenomenon that can be triggered by arbitrary cues, but the origins of which is not clearly understood. In a recent simulation model by Hammond and Axelrod, an ingroup bias evolves in the prisoners’ dilemma game. However, it will be argued here that the model does little to advance our understanding of ethnocentrism. The model assumes a spatial structure in which agents interact only with their immediate neighbourhood, populated mostly by clones, and the marker becomes an approximate cue of whether the partner is one. It will be shown that agents with an ingroup bias are successful compared to unconditional cooperators since they only exclude non-clones, but are outcompeted by less error-prone kin identifiers. Thus, the results of the simulations can be explained by a simple form of kin selection. These findings illustrate how spatial assumptions can alter a model to the extent that it no longer describes the phenomenon under study.

Keyword
Agent-Based Modelling, Ethnocentrism, Prisoners’ Dilemma, Spatial Interactions, Validation
National Category
Other Mathematics Social Sciences Interdisciplinary
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-16502 (URN)000324544700002 ()2-s2.0-84879725654 (Scopus ID)
Available from: 2012-12-10 Created: 2012-12-10 Last updated: 2015-03-25Bibliographically approved
2. What Strategic Structures Support the Evolution of Ethnocentrism?
Open this publication in new window or tab >>What Strategic Structures Support the Evolution of Ethnocentrism?
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Game theory deals with the impact of strategic structure on interactions. It is of course not known what strategic structures (i.e., games) dominated interactions in the evolutionary past of humans. Evolutionary models often uncritically assume some game, typically some kind of the prisoners’ dilemma, to investigate the effects of some other feature of the model. Here, another approach is suggested: What can be said about the likely strategic structure of interactions, given the features of human evolved psychology? The feature considered in this paper is ethnocentrism (also known as ingroup bias), which refers to the tendency to behave differently to different strangers simply depending on whether they seem to belong to the ingroup or the outgroup. Analysis and simulations of simple evolutionary models indicate that only some strategic structures are conducive to the evolution of ethnocentrism. In particular, this class does not contain the prisoners’ dilemma, but it does contain anti-coordination and coordination games, with socially optimal strategies being more frequent in ingroup interactions in the latter, especially if the other strategy is risk dominant, which applies to a class of games known as the stag hunt. This indicates that the strategic structure of coordination games, such as the stag hunt, and anti-coordination games, such as hawk-dove, may have been more common than games of cooperation and defection in human’s evolutionary past.

National Category
Other Mathematics Social Sciences Interdisciplinary
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-16503 (URN)
Available from: 2012-12-19 Created: 2012-12-10 Last updated: 2013-01-17Bibliographically approved
3. Trusting You Trusting Me: The Importance of Beliefs about Trust in the Stag Hunt/Assurance Game
Open this publication in new window or tab >>Trusting You Trusting Me: The Importance of Beliefs about Trust in the Stag Hunt/Assurance Game
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In the coordination game known as the stag hunt or the assurance game, players face a choice between a risk-free strategy and a risky strategy that pays higher if chosen also by the other player. Such games are commonly described as trust problems because the risky strategy is a rational choice only if one expects the other player to choose it. Here we argue that the stag hunt ought to be about trust only in an indirect and recursive waywhere beliefs about trust are more important than actual trust. On the basis of an established trust questionnaire we categorised 323 participants as having either high or low trust. They then played series of stag hunt games with varying amounts of information (either none, or private or common) about trust levels of involved parties. In line with our predictions, a player’s strategy choice was not strongly predicted by his or her trust level unless the latter was common knowledge. In other words, a high (low) truster Ego is more likely to play the risky (risk-free) strategy if Ego knows that Alter knows Ego’s trust level, emphasising the importance of beliefs about trust.

National Category
Applied Psychology Other Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-16504 (URN)
Available from: 2012-12-19 Created: 2012-12-10 Last updated: 2014-01-10Bibliographically approved
4. Modelling the Evolution of Creoles
Open this publication in new window or tab >>Modelling the Evolution of Creoles
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Various theories have been proposed regarding the origin of creole languages. Describing a process where only the end result is documented involves dealing with several methodological difficulties. In this paper we try to deal with some of the issues by using a novel mathematical model together with detailed empirical data on the origin and structure of Mauritian Creole. Our main focus is on whetherMauritian Creole may have been created only from a mutual desire to communicate, without a target language or prestige bias. Our conclusions are affirmative. With a confirmation bias towards learning from successful communication, the model predicts Mauritian Creole better than any of the input languages, including the lexifier French, thus providing a compelling and specific hypothetical model of how creoles are created. The results also show that it may be possible for a creole to develop quickly after first contact, and that it was created mostly from material found in the input languages, but without inheriting their morphology.

National Category
Other Mathematics General Language Studies and Linguistics Specific Languages
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-16505 (URN)
Available from: 2012-12-19 Created: 2012-12-10 Last updated: 2013-01-17Bibliographically approved
5. Bentley's conjecture on popularity toplist turnover under random copying
Open this publication in new window or tab >>Bentley's conjecture on popularity toplist turnover under random copying
2010 (English)In: The Ramanujan journal, ISSN 1382-4090, E-ISSN 1572-9303, Vol. 23, no 1, 371-396 p.Article in journal (Refereed) Published
Abstract [en]

Bentley et al. studied the turnover rate in popularity toplists in a 'random copying' model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ √μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.

National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-11179 (URN)10.1007/s11139-010-9280-z (DOI)000284594000025 ()2-s2.0-78649677346 (Scopus ID)
Note

MERO

Available from: 2010-12-01 Created: 2010-12-01 Last updated: 2014-06-23Bibliographically approved
6. The assignment game with negative externalities and bounded rationality
Open this publication in new window or tab >>The assignment game with negative externalities and bounded rationality
2011 (English)In: International Game Theory Review, ISSN 0219-1989, Vol. 13, no 4, 443-459 p.Article in journal (Refereed) Published
Abstract [en]

We introduce negative externalities in the form of ill will among the players of the classic two-sided assignment game of Shapley and Shubik, by letting each player's utility be negatively correlated with the payoff of all the players in his group. The new game is very complex, but under a certain assumption of bounded rationality we derive a straightforward notion of stable outcomes as certain conjectural equilibria. We prove that several well-known properties of the set of stable outcomes in the assignment game carry over to this new game. © 2011 World Scientific Publishing Company.

Keyword
assignment game, bounded rationality, negative externalities, social preferences, stable outcome, Two-sided matching
National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-15717 (URN)10.1142/S0219198911003088 (DOI)2-s2.0-84862228222 (Scopus ID)
Available from: 2012-10-24 Created: 2012-10-24 Last updated: 2015-11-19Bibliographically approved

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