Social status and group norms: Indirect reciprocity in a repeated helping experiment

In the economic literature, reciprocity is typically studied in situations of repeated interaction between two individuals. It refers to one individual rewarding kind acts of the other or punishing hostile acts. In contrast, this paper studies indirect reciprocity, where a cooperative action is rewarded by a third actor, not involved in the original exchange. We provide experimental evidence on indirect reciprocity. The experiment is based on the ‘repeated helping game’ developed by Nowak and Sigmund (J. Theoret. Biol. 194 (1998) 561; Nature 393 (1998) 573), involving random pairing in large groups. Pairs consist of a donor and a recipient. Donors decide whether or not to provide costly ‘help’ to the recipients they are matched with, based on information about the recipient's behavior in encounters with third parties. We observe clear evidence of indirect reciprocity. Many decision-makers respond to the information about previous decisions (whether or not to help others) of the recipients. In our experiments, this indirect reciprocity is largely based on norms about how often the recipient should have helped others in the past. We show that these norms develop similarly within groups of interacting subjects, but distinctly across groups. This leads to the emergence of group norms.     

Testing threats in repeated games

Under most game-theoretic solution concepts, equilibrium beliefs are justified by off-equilibrium events. I propose an equilibrium concept for infinitely repeated games, called “Nash Equilibrium with Tests” (NEWT), according to which players can only justify their equilibrium beliefs with events that take place on the equilibrium path itself. In NEWT, players test every threat that rationalizes a future non-myopic action that they take. The tests are an integral part of equilibrium behavior. Characterization of equilibrium outcomes departs from the classical “folk theorems”. The concept provides new insights into the impact of self-enforcement norms, such as reciprocity, on long-run cooperation.     

Which norms are strong reciprocators supposed to enforce? Not all norms are psychologically the same

Gintis’ (2000) analysis of strong reciprocity in terms of group survival leads to the conclusion that any norm, be it cooperative or prudential, that potentially enhances group survival will be enforced by a significant subset of individuals (strong reciprocators) who enforce norms even at their own individual expense. Gintis’ assumption that the human mind is an initially structureless receptacle for cultural norms further reinforces this view. In contrast, I argue that humans possess a natural domain-specific competence for social cooperation that is distinct from our prudential competence in dealing with potential hazards. I review a range of psychological evidence including multidimensional scaling studies, studies of emotional reactions, reasoning, functional MRI and judgments about punishment suggesting that not all norms are psychologically equivalent, with only a subset of norm violations eliciting punitive sentiments.     

Development of the extended linear expenditure system from simple saving assumptions

The extended linear expenditure system (ELES) can be developed as an atemporal maximization of a Stone-Geary utility function wherein saving is treated as a good in itself. The key to this development is the a priori specification of the ‘subsistence quantity’ of saving, γ_{n + 1}, to be zero. Thus, the intertemporal maximization approach to the ELES is equivalent to specifying a Klein-Rubin saving function with γ_{n + 1} = 0 for a linear expenditure system (LES) based on permanent income rather than total expenditure. Any income concept - current, normal, or permanent, for example - is acceptable for the ELES developed from the atemporal maximization.     

Social norms and trust among strangers

We study the development of a social norm of trust and reciprocity among a group of strangers via the “contagious strategy” as defined in Kandori (1992). Over an infinite horizon, the players anonymously and randomly meet each other and play a binary trust game. In order to provide the investors with proper incentives to follow the contagious strategy, there is a sufficient condition that requires that there exists an outside option for the investors. Moreover, the investorsʼ payoff from the outside option must converge to the payoff from trust and reciprocity as the group size goes to infinity. We show that this sufficient condition is also a necessary condition to sustain any sequential equilibrium in which the trustees adopt the contagious strategy. Our results imply that a contagious equilibrium only supports trust if trust contributes almost nothing to the investorsʼ payoffs.     

Formation of cartels in large markets

The von Neumann-Morgenstern concept of solution is applied to nonatomic pure exchange markets consisting of a finite number of different types of trader, initially owning disjoint sets of goods. It is proved that if all traders of each type form a cartel and behave like a single (atomic) trader (their “representative”), then one gets solutions of the original market from those of the finite market of the representatives, and all solutions are obtained in this manner—i.e., the market must organize itself in cartels, and this will indeed be stable.     

A typology of explicative models

This paper identifies and discusses the variety of approaches we use to explain the events and acts which comprise the socio-organizational phenomena we strive to understand. In the past few years a number of thoughtful discussions have been published on the differences and similarities of the various methods of explanation. The discussion has been stimulated in part by the limitations of traditional causal determinism, (as used in the physical sciences) for explaining phenomena encountered in both the biological and social sciences. By and large, however, little attempt has been made to create typologies of the different explanatory approaches. Notable exceptions are Aristotle (4 types of causes), MacIver (6 types of causation) and Bunge (causal, semi-causal and a-causal determinism). From discussions of three different approaches, namely causal, teleological and gestaltic explanations, (together with their derivatives and their hybrids), a typology is presented. The basis of the typology is the temporal relationship between the events to be explained (the explicandum) and the events which are employed as part of the explanation (the explicans events). The purpose of the article is to draw attention to the almost paradoxical contrast between the future-oriented nature of what practicing managers actually do, and the past-oriented nature of most of our scientific theories. It is suggested that past-oriented explanations may be intrinsically incapable of producing viable theories of social/organizational change.     

Optimal collusion-resistant mechanisms with verification

We present the first general positive result on the construction of collusion-resistant mechanisms, that is, mechanisms that guarantee dominant strategies even when agents can form arbitrary coalitions and exchange compensations (sometimes referred to as transferable utilities or side payments). This is a much stronger solution concept as compared to truthful or even group strategyproof mechanisms, and only impossibility results were known for this type of mechanisms in the “classical” model.We describe collusion-resistant mechanisms with verification that return optimal solutions for a wide class of mechanism design problems (which includes utilitarian ones as a special case). Note that every collusion-resistant mechanism without verification must have an unbounded approximation factor and, in general, optimal solutions cannot be obtained even if we content ourselves with truthful (“non-collusion-resistant”) mechanisms. All these results apply to problems that have been extensively studied in the algorithmic mechanism design literature like, for instance, task scheduling and inter-domain routing.     

On equilibrium in Hart's securities exchange model

In this paper, we use a no unbounded arbitrage condition to give a very direct proof of the existence of equilibrium in Hart's unbounded securities exchange model (J. Econ. Theory, 9 (1974), 293–311). We also examine the relationship between the no unbounded arbitrage condition and the sufficiency conditions of Hart, ibid. and Hammond (J, Econ. Theory, 31 (1983), 170–175). We present an example to show that if traders are not sufficiently risk averse, then Hammond's overlapping expectations condition is not, in general, equivalent to the no unbounded arbitrage condition or Hart's sufficiency conditions, and therefore, is not sufficient to guarantee the existence of equilibrium. We also present an example to show that it is possible for the no unbounded arbitrage condition to hold without overlapping expectations, and therefore, it is possible for equilibrium to exist without overlapping expectations.     

Trust and reciprocity: extensions and robustness of triadic design

Our paper reconsiders the triadic design proposed by Cox (Games and Economic Behavior 46:260–281, 2004) to identify trust and reciprocity in investment games. Specifically, we extend the design in two directions. First, we collect information on investors’ choices by using both the direct-response (as does Cox) and strategy methods. Using the latter, we are able to condition reciprocity on initial inequality, which is endogenous when investigating reciprocity. We demonstrate that the triadic design provides evidence for reciprocity once that initial inequality is considered. Second, we elicit expectations and test their coherence with the triadic outcomes. By examining the relationship between trust actions and expected gains, we analyze whether investors’ expectations are consistent with their behavior. Finally, we test for the existence of an emotional bias, i.e., whether expectation mismatches induce trustees to change actual choices from the planned ones.     

Aristotle's analysis of bilateral exchange: an early formal approach to the bargaining problem

Exchange, as analysed by Aristotle in the Nichomachean Ethics, should be viewed as a bilateral relation to be approached not as a market phenomenon but in terms of cooperation between two contractors. This paper accordingly proposes a reconsideration of Aristotle's analysis in the light of modern bargaining theory. This reconsideration reconciles the two principles of distributive and corrective justice as ruling simultaneously exchange relations through the figures of geometric and arithmetic proportions, respectively. It also suggests a new reconstitution of the missing diagram supposedly illustrating Aristotle's analysis, which — contrary to the conventional square endowed with diagonals, used since Albertus Magnus' commentary — fits the function to which such a diagram was probably designed, that of exhibiting Aristotle's solution to the bargaining problem.     

Reciprocity and economics in historical perspective

There is now compelling evidence to suggest that people respond in kind to helpful or hostile behaviour, so much so that some have been led to suggest that the subject of economic behaviour is not so much homo economicus as homo reciprocans. This recent interest in the phenomenon of reciprocity is part of a wider (and very welcome) rethinking of the basic attributes of the economic actor. On the basis of this recent work, economic theorising has moved some distance from the traditional modern-economic approach—an approach that simply assumes a strategically rational, egotistical actor and develops elaborate theorems therefrom—and towards a richer, more complex conceptualisation of the economic actor and her acts. On revisiting a remarkably similar debate that took place some 250 years earlier, however, we wonder whether this re-conceptualisation has yet moved far enough.     

Existence and fairness of value allocation without convex preferences

Shafer (Econometrica, 48 (1980), 467–476) proved that in a finite exchange economy value allocations exist, provided that each agent has convex, complete, transitive, compact and monotone preferences. However, if preferences are not convex, then value allocations may not exist. To remedy this difficulty we enlarge the set of value allocations by introducing the concept of approximate value allocations, and show that in a finite exchange economy approximate value allocations exist, even if preferences are not convex, or compact, or monotone. This value existence result can be used to provide a very general value existence theorem for a sequence of finite economies. Further, we show that value allocations may discriminate in favor of or against a coalition of agents.     

Reciprocity—an indirect evolutionary analysis

This paper investigates agents who face a stylized pecuniary ‘game of life’ comprising the ultimatum game and the dictator game. Utility may but need not be attached to equity and reciprocity, as formalized by Falk and Fischbacher (Games Econom Behav, 54(2): 293–315, 2006) but, critically, this social component of preferences cannot be conditioned on whether an ultimatum or a dictator game is played. Evolutionary fitness of agents is determined solely by material success. Under these conditions, a strong preference for reciprocity, but little interest in equity as such evolves. Possible exogenous constraints that link reciprocity and equity concerns imply long-run levels of both which depend on the relative frequency of ultimatum vs. dictator interaction in agents’ multi-game environment. Financial support from the German Academic Exchange Service (DAAD) is gratefully acknowledged.     

An admissible set occurring in various bargaining situations

Given a set of alternatives S and a binary relation M on S the admissible set of the pair (S, M) is defined to be the set of maximal elements with respect to the transitive closure of M. It is shown that existing solutions in game theory and mathematical economics are special cases of this concept (they are admissible sets of a natural S and M). These include the core of an n-person cooperative game, Nash equilibria of a noncooperative game, and the max-min solution of a two-person zero sum game. The competitive equilibrium prices of a finite exchange economy are always contained in its admissible set. Special general properties of the admissible set are discussed. These include existence, stability, and a stochastic dynamic process which leads to outcomes in the admissible set with high probability.     

Tracing the Origins of Personalist Economics to Aristotle and Aquinas

Personalist Economics has identified a central problem in Neoclassical Economics that originates in its representation of the economic agent as homo economicus and its grounding in individualism. Both flaws are directly addressed by Personalist Economics that has a different perspective on human nature as set forth in Personalism. Our remarks are presented in three sections. In the first section we address why individualism is an unsatisfactory philosophical foundation for modern economic theory. In the second section we trace the origins of Personalist Economics to Aristotle and Aquinas. While others, such as Heinrich Pesch and Joseph Schumpeter, played important roles in the evolution of Personalist Economics, here our efforts are restricted to the contributions of Aristotle and Aquinas. In the third section we explore how, in terms of 18 tenets, Personalist Economics and a Personalist economy differ from Mainstream Economics and the individualistic market economy.     

Classifying exchange rate regimes: Deeds vs. words

Most of the empirical literature on exchange rate regimes uses the IMF de jure classification based on the regime announced by the governments, despite the recognized inconsistencies between reported and actual policies in many cases. To address this problem, we construct a de facto classification based on data on exchange rates and international reserves from all IMF-reporting countries over the period 1974-2000, which we believe provides a meaningful alternative for future empirical work on the topic. The classification sheds new light on several stylized facts previously reported in the literature. In particular, we find that the de facto pegs have remained stable throughout the last decade, although an increasing number of them shy away from an explicit commitment to a fixed regime (“hidden pegs”). We confirm the hollowing out hypothesis but show that it does not apply to countries with limited access to capital markets. We also find that pure floats are associated with only relatively minor nominal exchange rate volatility and that the recent increase in the number of de jure floats goes hand in hand with an increase in the number of de facto dirty floats (“fear of floating”).     

Learnability and rationality of choice

In this paper we study the learnability of the class of rationalizable choice functions using the basic concept of PAC-learnability from statistical learning theory. We prove that the class of rationalizable choice functions on N alternatives is learnable from O(N) examples and is optimal in terms of PAC-learnability among classes which are invariant under permutations of the elements.     

Monetary policy channels in Brazil through the lens of a semi-structural model

We develop and estimate a medium-sized, semi-structural model for the Brazilian economy during the inflation targeting period. The model describes fairly well key features of the economy and allows us to decompose the transmission mechanism of monetary policy. In the baseline decomposition, the transmission mechanism is broken down into household interest rate, firm interest rate, and exchange rate channels. In addition, we carry out an alternative decomposition that allows us to evaluate the expectations channel as well. In both procedures, the household interest rate channel is the most important for explaining the response of output to a monetary policy shock. In the baseline decomposition of inflation, both the household interest rate and the exchange rate channels are the main transmission channels. However, in the alternative decomposition, the expectations channel accounts for the bulk of the inflation response.