Norms of Cooperation in a Game of Partnership

We study a model of partnership with costly commitment in an evolutionary game-theoretic framework. We introduce various types of cooperative players with different degrees of strategic sophistication. We find that a necessary condition for cooperation at the social equilibrium is that the probability of a high opportunity value falls below a certain critical threshold. Such condition, however, is not sufficient. If players are too naively cooperative, the permanence of cooperation at the equilibrium is put at risk because naive cooperation entails playing inefficient responses to other equilibrium strategies. As a consequence, naive cooperation will be present at the equilibrium selected by the social dynamics only under somewhat special conditions. If cooperators are more flexible, in that they remain in the partnership only if mated to a first stage cooperator and only in lack of favorable outside opportunities, cooperation is almost granted provided that it is Pareto efficient (perverse lock in cases under unfavorable initial conditions are possible). Finally, the selection of Pareto superior cooperation with certainty may be granted by a certain norm-oriented type of strategically sophisticated behavior, that we call Rawlsian altruism.     

Erratum: Betweenness Centralization for Bipartite Graphs

We address two related issues. First, we analyze the effects of risk preferences on cooperation in social dilemmas. Second, we compare social dilemmas in which outcomes represent gains with dilemmas where outcomes represent losses. We show that predictions on gain‐loss asymmetries with respect to conditions for cooperation crucially depend on assumptions concerning risk preferences. Under the assumption of risk aversion for gains as well as losses together with an assumption of decreasing absolute risk aversion, conditions for cooperation are less restrictive if outcomes represent losses than if outcomes represent gains. Conversely ‐ and counterintuitively ‐ under the assumption of S‐shaped utility, conditions for cooperation are more restrictive if outcomes represent losses than if outcomes represent gains. We provide an experimental test of such predictions. Only a minority of subjects behaves consistent with the assumption of S‐shaped utility. Furthermore, we find no empirical evidence for a general difference between cooperation in social dilemmas in which outcomes represent gains and dilemmas where outcomes represent losses. We do find evidence that risk preferences affect cooperation rates.     

Social Motives and Expectations in One-Shot Asymmetric Prisoner's Dilemmas

We propose a formal-behavioral framework with 3 components: nonselfish motives, expectations about others' nonselfish motives, and a game-theoretic component. For nonselfish motives, 3 nonstandard utility models representing altruism, inequality aversion, and norms are considered. Expectations are modeled as certain versus uncertain expectations. The game-theoretic component predicts behavior of actors and actors' expectations about behaviors of others. This framework is applied to asymmetric one-shot prisoner's dilemmas; predictions are tested experimentally. Formal analyses show that asymmetry provides new predictions through which nonstandard utility-expectation models can be distinguished. Empirical tests show that the inequality aversion model does considerably worse than altruistic and normative variants. Statistical tests for own motives, expected motives, and the association between the two are provided, while accounting for decision noise.     

Explaining cooperation in the finitely repeated simultaneous and sequential prisoner’s dilemma game under incomplete and complete information

Explaining cooperation in social dilemmas is a central issue in behavioral science, and the prisoner’s dilemma (PD) is the most frequently employed model. Theories assuming rationality and selfishness predict no cooperation in PDs of finite duration, but cooperation is frequently observed. We therefore build a model of how individuals in a finitely repeated PD with incomplete information about their partner’s preference for mutual cooperation decide about cooperation. We study cooperation in simultaneous and sequential PDs. Our model explains three behavioral regularities found in the literature: (i) the frequent cooperation in one-shot and finitely repeated N-shot games, (ii) cooperation rates declining over the course of the game, and (iii) cooperation being more frequent in the sequential PD than in the simultaneous PD.     

Constraints on social dilemmas: An institutional approach

Many contemporary political and economic problems have attributes of social dilemmas. These dilemmas are simply characterized as settings in which individuals have a dominant strategy to not cooperate in collective action. However, this choice results in a Pareto-inferior outcome. Likewise, a dominated strategy exists that results in a Pareto-superior outcome. Where cooperation is absent, this problem has been described as ann-person prisoner's dilemma. This paper discusses the environmental problem of acid rain as such a social dilemma. Relying on a series of laboratory experimental settings, the argument is that many social dilemmas can be resolved through the construction of institutional mechanisms allowing for the coordination of the participant's joint strategies. Policy analysts in particular can profit from focusing on institutional solutions to social dilemmas.Support for the research reported in this paper was obtained from a summer research grant provided by the Dean of the Division of the Social Sciences, Rice University. This paper also benefited from contributions by Robert M. Thrall, Randy Calvert, Alphons van de Kragt and Mark Ishimatsu. All of the above are absolved of errors stemming from good advice that was ignored.     

Like family: Network coevolution and the emergence of altruism

Altruism is difficult to explain in an evolutionary context—the mechanisms of selection appear to favor selfishness. Existing scholarly work addressing this puzzle relies on structural and behavioral assumptions that severely limit generalizability. The model presented in this article circumvents the need for such assumptions by incorporating an evolving network component to natural selection. Through a process of coevolution of individual and relational traits, many of the exogenous assumptions of previous models of the evolution of cooperation are realized endogenously within a simulated population. Such endogeneity allows a more precise examination of conditions under which cooperation arises, but also a clearer understanding of how those conditions themselves arise. The model is specified analytically, and interpretation is carried out on simulated outcomes.     

Inequality averse multi-utilitarian bargaining solutions

This paper introduces and analyzes the class of inequality averse multi-utilitarian solutions for cooperative bargaining problems. We show that generalized Gini solutions and inequality averse Choquet solutions are particular cases of this new multi-valued solution concept and provide a complete characterization in which an invariance property, consisting of a weakening of both the linear invariance axiom in Blackorby et al. (Econometrica 62:1161–1178, 1994) and the restricted invariance axiom in Ok and Zhou (Games Econ Behav 33:249–264, 2000), plays an important role. Moreover, by relaxing the assumptions involved in the characterization, the class is extended to include inequality loving multi-utilitarian solutions which are also studied in the paper.     

Meritocratic and monopoly inequality: A computer simulation of income distribution

This paper explores the properties of a model of the distribution of income in which individual income is proportional to a multiplicative function of previous income, ability, chance, a ceiling factor determined by competition among members of an income class for resources held by members of other classes, and an additive factor summarizing effects of altruism and minimal subsistence. The behavior of the model is investigated by computer simulation for combinations of values of three model parameters representing the tendency of income to grow exponentially (the Monopoly effect), the weight of the ability factor (the meritocracy effect), and the weight of the ceiling factor resulting from competitive interactions. Steady state income distributions generated by the model are characterized by measures of income inequality, exchange mobility, elite stability, and meritocracy. Results suggest that for constant Monopoly effect, the effect of the meritocracy parameter on various aggregate outcomes is nonlinear, with a range over which greater returns to ability produce lower inequality, lower exchange mobility, greater elite stability and meritocracy, for constant returns to ability, a greater Monopoly effect generally produces greater inequality, more exchange mobility, less stability of the elite, and lower meritocracy. Results also reveal a nonlinear relationship between exchange mobility and inequality, with mobility decreasing to a minimum and then increasing again as inequality increases; a nonlinear but monotonic negative relationship between elite stability and inequality, with greater inequality, associated with less stability, and a nonlinear relationship between meritocracy and inequality, with meritocracy increasing at first with inequality at low inequality levels, reaching a maximum and then decreasing as inequality increases further. These findings are interpreted in relation to major stratification trends in the course of sociocultural evolution.     

Coordination in Dynamic Social Networks Under Heterogeneity

People often make choices or form opinions depending on the social relations they have, but they also choose their relations depending on their preferred behavior and their opinions. Most of the existing models of coevolution of networks and individual behavior assume that actors are homogeneous. In this article, we relax this assumption in a context in which actors try to coordinate their behavior with their partners. We investigate with a game-theoretic model whether social cohesion and coordination change when interests of actors are not perfectly aligned as compared to the homogeneous case. Using analytical and simulation methods we characterize the set of stable networks and examine the consequences of heterogeneity for social optimality and segregation in emerging networks.     

Incorporating the information from direct and indirect neighbors into fitness evaluation enhances the cooperation in the social dilemmas

We propose an improved fitness evaluation method to investigate the evolution of cooperation in the spatial social dilemmas. In our model, a focal player’s fitness is calculated as the linear combination of his own payoff, the average payoffs of direct and indirect neighbors in which two independent selection parameters (α and β) are used to control the proportion of various payoff contribution to the current fitness. Then, the fitness-based strategy update rule is still Fermi-like, and asynchronous update is adopted here. A large plethora of numerical simulations are performed to validate the behaviors of the current model, and the results unambiguously demonstrate that the cooperation level is greatly enhanced by introducing the payoffs from the surrounding players. In particular, the influence of direct neighbors become more evident when compared with indirect neighbors since the correlation between focal players and their direct neighbors is much closer. Current outcomes are significant for us to further illustrate the origin and emergence of cooperation within a wide variety of natural and man-made systems.     

The Promotion and Evolution of Cooperation Through Projection: Implications for Social Dilemmas and Trust

It is rational for individuals to defect in social dilemmas. However, sometimes individuals display cooperative behaviors. This article focuses on one psychological mechanism proposed by some researchers as a promoter of cooperation—projection. Projection is a psychological mechanism that leads an individual to expect others to behave as he or she behaves. I model the emergence of cooperation in society through agent-based simulations. Results of the simulations suggest that projection evolves and promotes cooperation in a society where both structural embeddedness and opportunity costs are high, or where structural embeddedness is moderate and opportunity costs are low. I discuss the implication of the simulation results for studies of social dilemmas and trust.     

Discrimination decisions for 100,000-dimensional spaces

Discrimination decisions arise in many natural language processing tasks. Three classical tasks are discriminating texts by their authors (author identification), discriminating documents by their relevance to some query (information retrieval), and discriminating multi-meaning words by their meanings (sense discrimination). Many other discrimination tasks arise regularly, such as determining whether a particular proper noun represents a person or a place, or whether a given work from some teletype text would be capitalized if both cases had been used.We [9] introduced a method designed for the sense discrimination problems mentioned.We also discuss areas for research based on observed shortcomings of the method. In particular, an example in the author identification task shows the need for a robust version of the method. Also, the method makes an assumption of independence which is demonstrably false, yet there has been no careful study of the results of this assumption.     

Dynamics of knowledge-intensive production: An agency-structure framework

In the vast majority of modern technological and knowledge-intensive production systems, human agency and the structure of social interactions among the human individuals are implicated in each other. While the force of agency drives an individual’s urge to introduce innovation and novelty into production, the force of the structuring interactions demands shared expectations and mutual adaptation for co-creation. In an organizational context, when the objective is to manage production work that is governed by the concurrent interplay of both these forces, one might ask whether the cumulative output of each could be reconciled through the emergence of a stable balance between them over time. In this article, I introduce a framework to study the conditions under which this balance can be attained. Based on a real-life application, I show, in particular, that, while a direct realization of the condition is unlikely in practice, it is possible, nevertheless, to establish indirectly the condition through adjustments of certain parameters relevant to the dynamics of a networked system. The work contributes to the growing body of literature that explores the role of coordination between self-driven activities of individuals and their structure-mediated interactions in an underlying social context.     

Dissonance Minimization as a Microfoundation of Social Influence in Models of Opinion Formation

Models of opinion formation are used to investigate many collective phenomena. While social influence often constitutes a basic mechanism, its implementation differs between the models. In this article, we provide a general framework of social influence based on dissonance minimization. We only premise that individuals strive to minimize dissonance resulting from different opinions compared to individuals in a given social network. Within a game theoretic context, we show that our concept of dissonance minimization resembles a coordination process when interactions are homogeneous. We further show that different models of opinion formation can be represented as best response dynamics within our framework. Thus, we offer a unifying perspective on these heterogeneous models and link them to rational choice theory.     

Statistical mechanics of classical particles with logarithmic interactions

The inhomogeneous mean-field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions. The results apply to various physical models of translation invariant plasmas, gravitating systems, as well as to planar fluid vortex motion. For attractive interactions a critical behavior occurs which can be classified as an extreme case of a second-order phase transition. To include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic-geometric mean inequality. The method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions. In addition, it also provides us with a new proof of the Trudinger-Moser inequality known from differential geometry – in its sharp form.     

Cooperation in harsh environments and the emergence of spatial patterns

This paper concerns the confluence of two important areas of research in mathematical biology: spatial pattern formation and cooperative dilemmas. Mechanisms through which social organisms form spatial patterns are not fully understood. Prior work connecting cooperation and pattern formation has often included unrealistic assumptions that shed doubt on the applicability of those models toward understanding real biological patterns. I investigated a more biologically realistic model of cooperation among social actors. The environment is harsh, so that interactions with cooperators are strictly needed to survive. Harshness is implemented via a constant energy deduction. I show that this model can generate spatial patterns similar to those seen in many naturally-occuring systems. Moreover, for each payoff matrix there is an associated critical value of the energy deduction that separates two distinct dynamical processes. In low-harshness environments, the growth of cooperator clusters is impeded by defectors, but these clusters gradually expand to form dense dendritic patterns. In very harsh environments, cooperators expand rapidly but defectors can subsequently make inroads to form reticulated patterns. The resulting web-like patterns are reminiscent of transportation networks observed in slime mold colonies and other biological systems.     

Some consequences of correlation aversion in decision science

Very often in decision problems with uni- or multivariate objective, many results depend upon the signs of successive direct or cross derivatives of the utility function at least up to the 4th order. The purpose of the present paper is to provide a new and unified interpretation of these signs. It is based on the observation that decision-makers like to combine assets the return of which are negatively correlated (i.e., they have a preference for hedging). More specifically, this attitude is modelled through the concept of an “elementary correlation increasing transformation” defined by Epstein and Tanny (Can. J. Econ. 13:16–34, 1980). Decision-makers are said to be correlation averse if they dislike such a transformation. It will be shown that correlation aversion underlies many aspects of a decision-maker’s behavior under risk, including risk aversion, prudence, and temperance. Hence, correlation aversion provides a unifying, elegant and powerful framework to analyze risky decisions in the bivariate case. In this framework, also the concave version of the bivariate stochastic orderings introduced in Denuit, Lefèvre and Mesfioui (Insur. Math. Econ. 24:31–50, 1999a) turns out to be appropriate for comparing correlated outcomes and for comparing bivariate distributions with ordered marginals. The main result of this paper states that a decision-maker who is averse to correlation would rank bivariate outcomes as if using such higher order concave stochastic orderings. In particular, some features of decision-making under bidimensional risk, such as cross-prudence and cross-temperance, can also be linked to correlation aversion.     

Evolution of shame as an adaptation to social punishment and its contribution to social cohesiveness

Feelings of shame are common among humans although shameless individuals do not seem to be handicapped in achieving social success in life. What then is the adaptive value of shame? How can shame have evolved? Here I simulate shame as the emotion that induces an increase in pro‐social behavior after receiving social punishment. Simulations with the agent‐based model, Sociodynamica, show that shame is evolutionary stable in a context of individual selection, without the need for including group selection as an evolutionary force. The adaptive advantage of shame is based on the fact that it increases flexibility to the shameful individual, allowing it to act selfish if the probabilities of being punished are low and achieving a reduction in the costs of social punishment when frequent punishment is likely. The results show that shame, together with pro‐social punishment and social cooperation, produce a fluctuating dynamics of social cooperation, achieving long periods where the populations stabilizes pro‐social behavior interspersed with periods where selfish behavior predominates. This temporal stabilization of pro‐social behavior might provide societies with sufficient time to build institutions that might stabilize sustainable pro‐social behavior. © 2008 Wiley Periodicals, Inc. Complexity, 2008     

Evolutionary Selection of Socially Sensitive Preferences in Random Matching Environments

In this paper we study the evolutionary selection of socially sensitive preferences in the context of reference interaction settings such as coordination failure and cooperation. We refer to a specific class of socially sensitive preferences in which players weigh additively their own material payoff against the opponent with either a positive or negative coefficient (λ-players). Preference evolution is guided by replicator dynamics in a context of perfect observability of preferences types and stochastic pairwise matching. We take an indirect evolutionary approach, that is, the selection mechanism operates on the actual material payoffs earned by players, so that any instance of socially sensitive preference can be thought of as instrumentally maintained. We find that the evolutionary viability of socially sensitive preferences basically depends on whether or not they cause a substantial improvement in the achievement of socially efficient outcomes with respect to the case where only self-serving or unconditionally focused preference orientations are observed. Our results suggest that moderate pro-social preference orientations are likely to emerge from social selection even in the absence of an intrinsic motivational drive, whereas extremely pro-social orientations as well as competitive and anti-social ones may need a stronger motivational base.