A theory of reciprocity

People are reciprocal if they reward kind actions and punish unkind ones. In this paper we present a formal theory of reciprocity. It takes into account that people evaluate the kindness of an action not only by its consequences but also by its underlying intention. The theory is in line with the relevant stylized facts of a wide range of experimental games, such as the ultimatum game, the gift-exchange game, a reduced best-shot game, the dictator game, the prisoner's dilemma, and public goods games. Furthermore, it predicts that identical consequences trigger different reciprocal responses in different environments. Finally, the theory explains why outcomes tend to be fair in bilateral interactions whereas extremely unfair distributions may arise in competitive markets.     

Intrinsic and instrumental reciprocity: An experimental study

In the context of an indefinitely repeated veto game, we devise an experiment to distinguish between alternative explanations of generous behavior (accepting negative payoffs): altruism, intrinsic backward-looking reciprocity, and instrumental forward-looking reciprocity. Our results are broadly consistent with the hypothesis that observed sacrifices are motivated by equilibrium selfish, forward-looking reciprocal behavior although we find a more subtle way in which past kindness affects behavior.     

A note on the one-deviation property in extensive form games

In an extensive form game, an assessment is said to satisfy the one-deviation property if for all possible payoffs at the terminal nodes the following holds: if a player at each of his information sets cannot improve upon his expected payoff by deviating unilaterally at this information set only, he cannot do so by deviating at any arbitrary collection of information sets. Hendon et al. (1996. Games Econom. Behav. 12, 274–282) have shown that pre-consistency of assessments implies the one-deviation property. In this note, it is shown that an appropriate weakening of pre-consistency, termed updating consistency, is both a sufficient and necessary condition for the one-deviation property. The result is extended to the context of rationalizability.     

An ascending double auction

We show why the failure of the affiliation assumption prevents the double auction from achieving efficient outcomes when values are interdependent. This motivates the study of an ascending price version of the double auction. It is shown that when there is a sufficiently large, but still finite, number of sellers, this mechanism has an approximate perfect Bayesian equilibrium in which traders continue bidding if and only if their true estimates of the ‘value’ of the object being traded exceed the current price. This equilibrium is ex post efficient and has a rational expectations property in the sense that along the equilibrium path traders appear to have made the best possible trades conditional on information revealed by the trading process. We thank two anonymous referees and Dan Kovenock, the Editor, whose detailed comments and suggestions have allowed us to substantially improve the paper. We also thank seminar participants at University of Toronto, University of Wisconsin-Madison, Summer 2003 North American Meetings of the Econometric Society, 2004 NSF Decentralization Conference for their comments.     

Trees and decisions

Summary. The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts define a tree as a connected directed graph without loops and a distinguished node, called the root. But an abstract graph is not a domain for decision theory. Decision theory perceives of acts as functions from states to consequences. Sequential decisions, accordingly, get conceptualized by mappings from sets of states to sets of consequences. Thus, the question arises whether a natural definition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be defined as specific collections of sets. Without loss of generality the elements of these sets can be interpreted as representing plays. Therefore, the elements can serve as states and consequences at the same time.Received: 23 January 2003, Revised: 2 November 2003, JEL Classification Numbers: C72, D70. Correspondence to: Klaus RitzbergerWe are grateful to Larry Blume, Ariel Rubinstein, Jörgen Weibull, an anonymous referee, and seminar participants at the universities of Vienna, Salamanca, and Heidelberg for helpful comments. Financial support from the Austrian Science Fund (FWF) under project P15281 is also gratefully acknowledged.     

Optimal contracting with altruism and reciprocity

Motivated by the recent experimental evidence on altruistic behavior, we study a simple principal–agent model where each player cares about other players' utility, and may reciprocate their attitude towards him. We show that, relative to the selfish benchmark, efficiency improves when players are altruistic. Nevertheless, in contrast to what may be expected, an increase in the degree of the agent's altruism as well as a more reciprocal behavior by players has ambiguous effects on efficiency. We also consider the effects of the presence of spiteful players and discuss how monetary transfers between players depend on their degrees of altruism and spitefulness.     

Evolutionary economics goes mainstream: A review of the theory of learning in games

The Theory of Learning in Games by Fudenberg and Levine surveys a key branch of evolutionary economics from a mainstream perspective. Its publication provides an opportunity to reassess the prospects and goals for evolutionary economics.     

How to identify trust and reciprocity

This paper uses a three-games (or triadic) design to identify trusting and reciprocating behavior. A large literature on single-game trust and reciprocity experiments is based on the implicit assumption that subjects do not have altruistic or inequality-averse other-regarding preferences. Such experimental designs test compound hypotheses that include the hypothesis that other-regarding preferences do not affect behavior. In contrast, experiments with the triadic design do discriminate between transfers resulting from trust or reciprocity and transfers resulting from other-regarding preferences that are not conditional on the behavior of others. Decomposing trust from altruism and reciprocity from altruism or inequality aversion is critical to obtaining empirical information that can guide the process of constructing models that can increase the empirical validity of game theory.     

Second chance offers versus sequential auctions: theory and behavior

Second chance offers in online marketplaces involve a seller conducting an auction for a single object and then using information from the auction to offer a losing bidder a take-it-or-leave-it price for another unit. We theoretically and experimentally investigate this practice and compare it to two sequential auctions. We show that the equilibrium bidding strategy in the second chance offer mechanism only exists in mixed strategies, and we observe that this mechanism generates more profit for the auctioneer than two sequential auctions. We also observe virtually no rejections of profitable offers in the ultimatum bargaining stage.      

Extremism, campaigning and ambiguity

This paper studies a model of how political parties use resources for campaigning to inform voters. Each party has a predetermined ideology drawn from some distribution. Parties choose a platform and campaign to inform voters about the platform. We find that, the farther away parties are from each other (on average), the less resources are spent on campaigning (on average). Thus, if parties are extreme, less information is supplied than if parties are moderate. We also show that if a public subsidy is introduced, we have policy convergence, given some mild technical restrictions on the public subsidy.     

Inequity aversion and trustees' reciprocity in the trust game

The introduction of inequity concerns into the Trust Game gives rise to complementary concepts of conditional trustworthiness and unconditional untrustworthiness. When the inequity concern is not accounted for, unconditional untrustworthiness is overestimated. The high proportion of trustees adopting the equal division behavioural norm suggests that an unequal distribution of show-up fees may deter trustors from placing trust, and may eventually reduce the incentive to cooperate for both players. It also follows that increases in income inequality can explain declines in self-reported trust in high-income countries.     

Strategic alliances and internationalisation in the aircraft manufacturing industry

Based on an indicator measuring the technological level of aircraft, this paper shows that in the aircraft industry, firms are obliged to deal not only with high technological barriers, but growing financial and market barriers, too. In order to reduce these, a complex network of relationships has developed over time. This network involves both main firms belonging to the world oligopoly and firms capable of offering specialised technology and/or a potential broadening of the market. The result is a worldwide production organisation. This paper highlights the fact that the aircraft industry is undergoing a global reorganisation featuring an integration process where six groups (two in Europe and four in the United States) have come to the fore. In the future, it will be possible to imagine new forms of co-operation between the emerging European and American groups.     

On weighted Kalai–Samet solutions for non-transferable utility coalitional form games

We investigate the implications of the axiom of coalitional concavity for non-transferable utility coalitional form games. This axiom says that if the feasible set of some coalition is uncertain whereas the feasible sets of other coalitions are known, then all players in the coalition with the uncertain feasible set should (weakly) benefit from reaching a compromise before the uncertainty is resolved. By imposing this axiom, in addition to other minor axioms, we characterize the weighted Kalai–Samet [Econometrica 53 (1985) 307] solutions: these solutions coincide with the weighted egalitarian solutions on the domain of bargaining problems, and with the weighted Shapley values on the domain of transferable utility coalitional form games.     

Implications of trust, fear, and reciprocity for modeling economic behavior

This paper reports three experiments with triadic or dyadic designs. The experiments include the moonlighting game in which first-mover actions can elicit positively or negatively reciprocal reactions from second movers. First movers can be motivated by trust in positive reciprocity or fear of negative reciprocity, in addition to unconditional other-regarding preferences. Second movers can be motivated by unconditional other-regarding preferences as well as positive or negative reciprocity. The experimental designs include control treatments that discriminate among actions with alternative motivations. Data from our three experiments and a fourth one are used to explore methodological questions, including the effects on behavioral hypothesis tests of within-subjects vs. across-subjects designs, single-blind vs. double-blind payoffs, random vs. dictator first-mover control treatments, and strategy responses vs. sequential play. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C70, C91, D63, D64     

Polycentricity, reciprocity, and farmer adoption of conservation practices under community-based governance

Significant steps have occurred under Australia's ‘regional delivery model’ towards devolving responsibilities for natural resource management (NRM) to community-based regional bodies, particularly in respect of motivating farmers to adopt priority conservation practices. Challenges remain in effectively engaging the large populations covered by these bodies, especially with these bodies expected to assume responsibilities that risk them becoming perceived as extensions of government and favoring particular stakeholders. In this article, I examine whether polycentric systems of collaborative community-based governance can help address these challenges. The examination involves double-censored regression analyses of data from postal surveys of farmers in three regions. The findings suggest that community-based approaches are capable under the regional delivery model of motivating greater voluntary cooperation from farmers than otherwise possible. They highlight the importance of farmers coming to adopt reciprocity strategies in their key institutional relationships under this model. It seems subregional bodies have an advantage over regional bodies in motivating such behavior from farmers because the former are better positioned to engage them sufficiently to turn around norms of free-riding or opposition entrenched by earlier paternalistic approaches to agri-environmental conservation. This indicates the value of a polycentric approach to community-based NRM wherein responsibilities are devolved to the lowest possible governance level consistent with the principle of subsidiarity. The economic dividend from increased voluntary adoption of conservation practices under this approach arises from the reduced transaction, political and other opportunity costs of achieving the same result entirely through coercion or financial inducements.     

Reputation and Reciprocity: Consequences for the Labour Relation

Recent evidence highlights the importance of social norms in many economic relations. However, many of these relationships are long term and provide repeated game incentives for performance. We experimentally investigate interaction effects of reciprocity and repeated game incentives in two treatments (one-shot and repeated) of a gift-exchange game. In both treatments we observe reciprocity, which is strengthened in the repeated game. A detailed analysis shows that, in the repeated game, some subjects imitate reciprocity. Thus, reciprocity and repeated game incentives reinforce each other. Observed behaviour is robust against experience. We conclude that long-term interaction is a "reciprocity-compatible" contract enforcement device.
JEL classification : J 30; C 91     

Altruism, equity, and reciprocity in a gift-exchange experiment: an encompassing approach

Considerable experimental evidence suggests that non-pecuniary motives must be addressed when modeling behavior in economic contexts. Recent theories of non-pecuniary motives can be classified as altruism-, equity-, or reciprocity-based. We outline the qualitative differences in prediction these alternative explanations yield in a gift-exchange game. We estimate and compare leading approaches in these categories, using experimental data. We then offer a flexible approach that nests the above three approaches, thereby allowing for nested hypothesis testing and for determining the relative strength of each of the competing theories. In addition, the encompassing approach provides a functional form for utility in different settings without the restrictive nature of the approaches nested within it. Using this flexible form for nested tests, we find that intentional reciprocity, distributive concerns, and altruistic considerations all play a significant role in players' decisions.     

On economic applications of evolutionary game theory

Evolutionary games have considerable unrealized potential for modeling substantive economic issues. They promise richer predictions than orthodox game models but often require more extensive specifications. This paper exposits the specification of evolutionary game models and classifies the possible asymptotic behavior for one and two dimensional models.     

Trust and reciprocity behavior and behavioral forecasts: Individuals versus group-representatives

Individuals are often given the responsibility of making decisions on behalf of a group or an organization. However, little is known about preferences or behavior in such contexts. In an adapted trust game, I examine whether the perspectives and behavior of group-representatives differ from those of the same individuals in an analogous situation. Group-representatives are given the responsibility of unilaterally and privately making a decision on behalf of a three-person group. Results from both the main and the follow-up studies show that people trust less and reciprocate less as group-representatives, and thus demonstrate that the interindividual-intergroup discontinuity effect not only exists in group behavior but also in individual behavior of group-representatives. Moreover, results show that trusting behavior is driven by reciprocity expectations, while reciprocating behavior is not sensitive to the first mover's behavior, i.e., the level of trust experienced.