We investigate the one-dimensional dynamics of alternatives of the Axelrod model (ξ(t)), where t is the time, with k binary features and confidence parameter ε = 0, 1,…, k. Simultaneously, the simple Axelrod model is also critically examined. Specifically, for small and large ε, simulations suggest that the convergent model (ξ(t)) is emulated by a corresponding attractive model (η(t)) with the same parameters (conditional on bounded confidence). (η(t)) is more mathematically tractable than (ξ(t)), and (...) the very definitions of the two qualitative behaviors of cyclic particle systems (fluctuation and fixation) are applicable in special cases. Moreover, we observe a complementarity: for not too small k and equation image, (η(t)) fixates (each site has a final type independent of the possibly infinite size of the lattice), whereas (ξ(t)) fluctuates (each site changes type at arbitrarily larger times t as the size of the lattice increases). (shrink)

Les modèles basés sur des agents en interactions, constituent des systèmes sociaux complexes, qui peuvent être simulés par informatiques. Ils se répandent dans les sciences économiques et sociales - comme dans la plupart des sciences des systèmes complexes. Des énigmes épistémologiques (ré)apparaissent. On a souvent opposé modèles et investigations empiriques : d’un côté, on considère les sciences empiriques fondées sur une observation méthodique (enquêtes, expériences) tandis que de l’autre, on conçoit les approches théoriques et la modélisation comme s’appuyant sur une (...) approche conceptuelle ou hypothético-déductive. la simulation a de son coté souvent été comparée à une forme d’expérience ou à une méthode intermédiaire entre la théorie et l’expérience. Tesfatsion a parlé de « laboratoire computationnel » comme d’une manière d’étudier « les comportements des systèmes complexes au moyen d’expériences sous contrôle qu’on peut répéter (réplicable)» et Axelrod a proclamé que la simulation serait « une troisième manière de pratiquer la science dans les sciences sociales », entre l’induction et la déduction. Nous introduisons de nouveaux concepts épistémologiques afin de montrer dans quelle mesure les auteurs ont raison lorsqu'ils se concentrent sur une signification empirique, instrumentale ou conceptuelle de leur modèle ou simulation. La première partie du chapitre discute plus particulièrement de l'épistémologie des modèles économiques à partir des travaux d’Hausman, Guala, Mäki, Sugden, Schelling etc. pour expliquer les divergences entre modèles et simulations. En distinguant entre modèles et simulations, comme entre entre types de modèles, types de simulations informatiques et types d'empiricité obtenue par une simulation, la seconde partie donne la possibilité de comprendre plus précisément - et ensuite de justifier - la diversité des positions épistémologiques présentées dans la première partie. En utilisant les notion de sous-symbolisation (due à Smolensky) et, de hiérarchie dénotationnelle (due à Goodman), une attention particulière est accordée à la multiplicité des pouvoirs dénotationnels des symboles en jeu dans les modèles complexes et les simulations informatiques. Selon cette grille d'analyse, on peut déterminer, dans chaque cas particulier son statut épistémique et la crédibilité qui peut y être associée. -/- Ce chapitre est une traduction (par Gilles Campagnolo) réviséee et augmentée par les auteurs de : Agent-Based Models and Simulations in Economics and Social Sciences: From Conceptual Exploration to Distinct Ways of Experimenting, Journal of Artificial Societies and Social Simulation 13 (1) 5 DOI: 10.18564/jasss.1532. (shrink)

This paper discusses critically what simulation models of the evolution ofcooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” and the modeling tradition it has inspired. Hardly any of the many simulation models of the evolution of cooperation in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this (...) research design was fundamentally flawed, because it is not possible to draw general empirical conclusions from theoretical simulations. At best such simulations can claim to prove logical possibilities, i.e. they prove that certain phenomena are possible as the consequence of the modeling assumptions built into the simulation, but not that they are possible or can be expected to occur in reality I suggest several requirements under which proofs of logical possibilities can nevertheless be considered useful. Sadly, most Axelrod-style simulations do not meet these requirements. I contrast this with Schelling’s neighborhood segregation model, thecore mechanism of which can be retraced empirically. (shrink)

People experiencing similar conditions may make different decisions, and their belief systems provide insight about these differences. An example of high‐stakes decision‐making within a complex social context is the Arab Spring, in which large numbers of people decided to protest and even larger numbers decided to stay at home. This study uses qualitative analyses of interview narratives and social media addressing individual decisions to develop a computational model tracing the cognitive decision‐making process. The model builds on work by (...) Abelson and Carroll (1965), Schank and Abelson (1977), and Axelrod (1976) to systematically trace the inferences connecting beliefs to decisions. The findings show that protest decisions were often based on positive emotions such as pride, hope, courage, and solidarity, triggered by beliefs about successful protest and self‐sacrifice. By contrast, decisions to stay at home were triggered by beliefs about safety, state approval, and living conditions. As one participant said, “When I heard about the revolution in Tunisia, my heart was filled with solidarity for the people.” In the words of a non‐participant: “When people are killed, we must be careful. There are more important things than protest: safety and stability.” This study of individual explanations about events identifies the role of emotions in high‐stakes decision‐making within complex social environments. (shrink)

This paper is intended as a critical examination of the question of when and under what conditions the use of computer simulations is beneficial to scientific explanations. This objective is pursued in two steps: First, I try to establish clear criteria that simulations must meet in order to be explanatory. Basically, a simulation has explanatory power only if it includes all causally relevant factors of a given empirical configuration and if the simulation delivers stable results within the measurement inaccuracies of (...) the input parameters. -/- In the second step, I examine a few examples of Axelrod-style simulations as they have been used to understand the evolution of cooperation (Axelrod, Schüßler). These simulations do not meet the criteria for explanatory validity and it can be shown, as I believe, that they lead us astray from the scientific problems they have been addressed to solve. (shrink)

Louis Marinoff [1990] criticizes Axelrod and Hamilton's [1981] use of the concept of an evolutionarily stable strategy, and claims to find an inconsistency between their theory for repeated Prisoner's Dilemma games and empirical results. Marinoff seeks to resolve the inconsistency by arguing that Axelrod and Hamilton's model is ill conceived: he purports to prove, contra Axelrod and Hamilton, that no evolutionarily stable strategy exists in the repeated Prisoner's Dilemma. But his argument is flawed, and moreover, Marinoff (...) gives no good reason for thinking the claimed discrepancy between thory and empirical results exists. (shrink)

Axelrod (The evolution of cooperation, 1984) and others explain how cooperation can emerge in repeated 2-person prisoner’s dilemmas. But in public good games with anonymous contributions, we expect a breakdown of cooperation because direct reciprocity fails. However, if agents are situated in a social network determining which agents interact, and if they can influence the network, then cooperation can be a viable strategy. Social networks are modelled as graphs. Agents play public good games with their neighbours. After each game, (...) they can terminate connections to others, and new connections are created. Cooperative agents do well because they manage to cluster with cooperators and avoid defectors. Computer simulations demonstrate that group formation and exclusion are powerful mechanisms to promote cooperation in dilemma situations. This explains why social dilemmas can often be solved if agents can choose with whom they interact. (shrink)

The iterated Prisoner’s Dilemma has become the standard model for the evolution of cooperative behavior within a community of egoistic agents, frequently cited for implications in both sociology and biology. Due primarily to the work of Axelrod (1980a, 198Ob, 1984, 1985), a strategy of tit for tat (TFT) has established a reputation as being particularly robust. Nowak and Sigmund (1992) have shown, however, that in a world of stochastic error or imperfect communication, it is not TFT that finally (...) triumphs in an ecological model based on population percentages (Axelrod and Hamilton 1981), but ‘generous tit for tat’ (GTFT), which repays cooperation with a probability of cooperation approaching 1 but forgives defection with a probability of l/3. In this paper, we consider a spatialized instantiation of the stochastic Prisoner’s Dilemma, using two-dimensional cellular automata (Wolfram, 1984, 1986; Gutowitz, 1990) to model the spatial dynamics of populations of competing strategies. The surprising result is that in the spatial model it is not GIFT but still more generous strategies that are favored. The optimal strategy within this spatial ecology appears to be a form of ‘bending over backwards’, which returns cooperation for defection with a probability of 2/3 - a rate twice as generous as GTFT. (shrink)

In this paper, I discuss the problems of ``order in social situations'' using a computer simulation of iterated N -person prisoners' dilemma game. It has been claimed that, in the case of the 2 -person prisoners' dilemma, repetition of games and the reciprocal use of the ``tit-for-tat'' strategy promote the possibility of cooperation. However, in cases of N -person prisoners' dilemma where N is greater than 2, the logic does not work effectively. The most essential problem is so called ``sanctioning (...) problems''. In this paper, firstly, I discuss the ``sanctioning problems'' which were introduced by Axelrod and Keohane in 1986. Based on the model formalized by Axelrod, I propose a new model, in which I added a mechanism of players' payoff changes in the Axelrod's model. I call this mechanism norm-internalization and call our model `` norm-internalization game ''. Second, by using the model, I investigated the relationship between agents' norm-internalization (payoff-alternation) and the possibilities of cooperation. The results of computer simulation indicated that unequal distribution of cooperating norm and uniform distribution of sanctioning norm are more effective in establishing cooperation. I discuss the mathematical features and the implications of the results on social science. (shrink)

Norms provide a valuable mechanism for establishing coherent cooperative behaviour in decentralised systems in which there is no central authority. One of the most influential formulations of norm emergence was proposed by Axelrod :1095–1111, 1986). This paper provides an empirical analysis of aspects of Axelrod’s approach, by exploring some of the key assumptions made in previous evaluations of the model. We explore the dynamics of norm emergence and the occurrence of norm collapse when applying the model (...) over extended durations. It is this phenomenon of norm collapse that can motivate the emergence of a central authority to enforce laws and so preserve the norms, rather than relying on individuals to punish defection. Our findings identify characteristics that significantly influence norm establishment using Axelrod’s formulation, but are likely to be of importance for norm establishment more generally. Moreover, Axelrod’s model suffers from significant limitations in assuming that private strategies of individuals are available to others, and that agents are omniscient in being aware of all norm violations and punishments. Because this is an unreasonable expectation, the approach does not lend itself to modelling real-world systems such as online networks or electronic markets. In response, the paper proposes alternatives to Axelrod’s model, by replacing the evolutionary approach, enabling agents to learn, and by restricting the metapunishment of agents to cases where the original defection is observed, in order to be able to apply the model to real-world domains. This work can also help explain the formation of a “social contract” to legitimate enforcement by a central authority. (shrink)

In A Darwinian left Peter Singer aims to reconcile Darwinian theory with left wing politics, using evolutionary game theory and in particular a model proposed by Robert Axelrod, which shows that cooperation can be an evolutionarily successful strategy. In this paper I will show that whilst Axelrod’s model can give support to a kind of left wing politics, it is not the kind that Singer himself envisages. In fact, it is shown that there are insurmountable problems (...) for the idea of increasing Axelrodian cooperation within a welfare state. My surprising conclusion will be that a Darwinian left worthy of the name would be anarchistic. Ó 2005 Elsevier Ltd. All rights reserved. (shrink)

We extend previous work on cooperation to some related questions regarding the evolution of simple forms of communication. The evolution of cooperation within the iterated Prisoner's Dilemma has been shown to follow different patterns, with significantly different outcomes, depending on whether the features of the model are classically perfect or stochastically imperfect (Axelrod 1980a, 1980b, 1984, 1985; Axelrod and Hamilton, 1981; Nowak and Sigmund, 1990, 1992; Sigmund 1993). Our results here show that the same holds for communication. (...) Within a simple model, the evolution of communication seems to require a stochastically imperfect world. (shrink)

This paper tries to answer the question why the epistemic value of so many social simulations is questionable. I consider the epistemic value of a social simulation as questionable if it contributes neither directly nor indirectly to the understanding of empirical reality. To examine this question, two classical social simulations are analyzed with respect to their possible epistemic justification: Schelling’s neighborhood segregation model and Axelrod’s reiterated Prisoner’s Dilemma simulations of the evolution of cooperation. It is argued that Schelling’s (...) simulation is useful because it can be related to empirical reality, while Axelrod’s simulations and those of his followers cannot and thus that their scientific value remains doubtful. I relate this findingto the background beliefs of modelers about the superiority of the modeling method as expressed in Joshua Epstein’s keynote address “Why model?”. (shrink)

Sufficiently frequent interaction between partners has been identified by, a.o., Axelrod as a more-or-less sufficient condition for stable cooperation. The underlying argument is that rational cooperation is ensured if short-term benefits from opportunistic behavior are offset by the long-term costs of sanctions imposed on the culprit. In this paper, we develop a model for ‘embedded trust’ in which a trustee interacts with a number of trustors who may communicate via a social network with each other about the behavior (...) of the trustor. The analysis reconfirms the standard predictions about how the level of trust depends on the payoffs and shadow of the future. We provide new predictions both on between-network effects (“which network is more favorable for cooperation?”) and on within-network effects (“in what network position can you trust more?”). (shrink)

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in terms of those games. The (...) measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation . New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling . Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19 , 95–125). (shrink)

We make the case that the Prisoner’s Dilemma, notwithstanding its fame and the quantity of intellectual resources devoted to it, has largely failed to explain any phenomena of social scientific or biological interest. In the heart of the paper we examine in detail a famous purported example of Prisoner’s Dilemma empirical success, namely Axelrod’s analysis of WWI trench warfare, and argue that this success is greatly overstated. Further, we explain why this negative verdict is likely true generally and not (...) just in our case study. We also address some possible defenses of the Prisoner’s Dilemma. (shrink)

To understand the meaning of evolutionary equilibria, it is necessary to comprehend the ramifications of the evolutionary model. For instance, a full appreciation of Axelrod's The Evolution of Cooperation requires that we identify assumptions under which conditionally cooperative strategies, like Tit For Tat, are and are not evolutionarily stable. And more generally, when does stability fail? To resolve these questions we re-examine the very foundations of the evolutionary model. The results of this paper can be analytically separated (...) into three parts. The first part is conceptual: it identifies the evolutionary model's assumptions and shows how different assumptions imply different types of evolutionary stability. The second part is deductive: it establishes necessary and sufficient conditions for the types of evolutionary stability identified in the first part, and demonstrates in which games these kinds of stability can (and cannot) be attained. The third and final part is applied: it relates the general findings (which are independent of the specific payoffs of any particular evolutionary game) to the issue of the evolutionary stability of cooperation. Results on cooperation appear throughout the paper as they both exemplify and motivate the general results. These results essentially explain when cooperation is and is not stable, and why, thus shedding new light on the meaning and applicability of Axelrod's widely known claims. (shrink)

In Nabokov's Lectures on Literature, he writes: "Style and structure are the essence of a book; great ideas are hogwash." The essays in No Symbols Where None Intended: Literary Essays from Laclos to Beckett use Nabokov's stylistic approach to well-known texts (fiction, drama and criticism) as a point of departure. Notions of style and structure link the three prose pieces discussed in the text, (Beckett, Smart, and Turgenev,) to the fiction and drama of Ibsen and Strindberg. Mark Axelrod joins (...) a wide and deep conversation on writers on writing. (shrink)

The symposium included in this issue of Analyse & Kritik extends the basis of Cooperation Theory as set forth in Axelrod’s Evolution of Cooperation (1984). This essay begins with an overview of Cooperation Theory in terms of the questions it asks, its relationship to game theory and rationality, and the principal methodologies used, namely deduction and simulation. This essay then addresses the issues raised in the symposium, including the consequences of extending the original paradigm of the two person iterated (...) Prisoner’s Dilemma to take into account such factors as nonsimultaneous play, the ability to offer hostages for performance, social networks of interaction, information sharing that can support reputations, learning behavior, envy, misunderstanding, and an option to exit. The essay places the contributions of this symposium in the context of previous research on these and related issues. (shrink)

Wie ist Kooperation möglich in einer Welt von Egoisten, in der es keine zentrale Autorität gibt? Axelrod entwickelt aus der Spieltheorie - auf der Basis des "Gefangenendilemmas" - eine verblüffende Lösung. Nicht die raffinierteste, auch nicht die aggressivste, nicht die sanfteste Strategie sichert langfristig Erfolg, sondern die grundsätzlich wohlwollende, aber stets vergeltungsbereite: TIT FOR TAT, "wie Du mir, so ich Dir". Axelrod schließt daraus, dass in der globalen arbeitsteiligen Wirtschaftsweise geradezu ein innerer Zwang zur Kooperation besteht. Gewinnbringende Kooperationen (...) sind für Unternehmen nützlicher als blinder Wettbewerb. (shrink)

Sacred values differ from material or instrumental values in that they incorporate moral beliefs that drive action in ways dissociated from prospects for success. Across the world, people believe that devotion to essential or core values – such as the welfare of their family and country, or their commitment to religion, honor, and justice – are, or ought to be, absolute and inviolable. Counterintuitively, understanding an opponent's sacred values, we believe, offers surprising opportunities for breakthroughs to peace. Because of the (...) emotional unwillingness of those in conflict situations to negotiate sacred values, conventional wisdom suggests that negotiators should either leave sacred values for last in political negotiations or try to bypass them with sufficient material incentives. Our empirical findings and historical analysis suggest that conventional wisdom is wrong. In fact, offering to provide material benefits in exchange for giving up a sacred value actually makes settlement more difficult because people see the offering as an insult rather than a compromise. But we also found that making symbolic concessions of no apparent material benefit might open the way to resolving seemingly irresolvable conflicts. We offer suggestions for how negotiators can reframe their position by demonstrating respect, and/or by apologizing for what they sincerely regret. We also offer suggestions for how to overcome sacred barriers by refining sacred values to exclude outmoded claims, exploiting the inevitable ambiguity of sacred values, shifting the context, provisionally prioritizing values, and reframing responsibility. (shrink)

In _Work and the Evolving Self_, Steven Axelrod begins to remedy this serious oversight by setting forth a comprehensive psychoanalytic perspective on work life. Consonant with his analytic perspective, Axelrod sets out to illuminate the workplace by examining the psychodynamic meaning of work throughout the life cycle. He begins by exploring the various dimensions of work satisfaction from a psychoanalytic perspective and then expands on the relationship between work life and the adult developmental process. This developmental perspective frames (...) Axelrod's central task: an examination of the typical work-related problems encountered in clinical practice, beginning with a psychodynamic definition of a "work disturbance." Moving on to treatment issues, Axelrod elaborates on the manner in which assessment, supportive, and exploratory interventions all enter into the treatment of work disturbances. Axelrod concludes by considering issues of career development that emerge in individual psychotherapy and exploring the psychological implications of dramatic changes now taking place in the workplace. As such, _Work and the Evolving Self_ is an impressive contribution to the task with which psychoanalytic therapists are increasingly engaged: that of broadening their identities and treatment approaches in a world that increasingly demands flexibility and innovation. (shrink)

A Scientific Approach The facts detailed in this briefing are the results of scientific exploration of terror networks and sacred values and their association to political violence. The research is sponsored by the Air Force Office of Scientific Research and the National Science Foundation.

Resolution of quarrels arising from conflicting sacred values, as in the Middle East, may require concessions that acknowledge the opposition's core concerns.

In a recent target article, Buchbinder et al. (2024) advance moral stress as a complement to the more familiar, albeit contested, concept of moral distress. They are concerned that moral distress m...