مشارکت، روابط متقابل و طراحی تیم

This paper studies the effect of intention-based reciprocity preferences on the free-riding problem arising in partnerships. Our results suggest a tendency of efficient partnerships to consist of members whose sensitivity to reciprocity is – individually or jointly – sufficiently high. Sufficient conditions for the implementation of the efficient strategy profile require a reciprocity-based sharing rule so that each partner gets a fraction of the output, which is a percentage of his own sensitivity to reciprocity with respect to the overall sensitivity in the team. Finally, we introduce the concept of psychological strong Nash equilibrium and show that it allows for the unique and collusion-proof implementation of the efficient strategy profile.

It is widely believed, and has been suggested by experimental evidence, that agents' preferences often exhibit an important intention-based component.1 In this paper, we examine the role played by intention-based reciprocity preferences in the partnership framework, which appears to be one of the most natural environments for reciprocity to play a central role. In particular, we study a classical model of partnership where partners jointly produce according to a non-stochastic technology, and share the resulting output among themselves. It is generally accepted that partnerships are inefficient if the partners' actions are not verifiable, i.e. neither the identity of a free-rider nor the one of a non-free-rider is revealed after a deviation. In fact, in this case a partner could shirk because he must share the marginal benefit of his effort, but he alone bears its cost. Holmstrom (1982) formalizes this argument showing that in certain differentiable, monotonic partnerships, no sharing rule can elicit an efficient set of actions; that is, the efficient action profile cannot be implemented as a Nash equilibrium of the corresponding partnership game. If a player is sufficiently sensitive to reciprocity, he will have incentives to work harder if he believes that his partners' intentions are good, in the sense that they plan to exert a level of effort which is higher than the one they expect from him. Conversely, he will have incentives to free ride if he believes that the other players' intentions are bad. In other words, the player will have incentives to match the other agents' intentions to avoid experiencing a disutility from his anti-reciprocal behavior. Building on this simple intuition, we construct a class of intention-based preferences and design teams of reciprocity-driven partners. It turns out that symmetric efficient strategy profiles can be sustained (in equilibrium) by reciprocity-driven partners even when, in case of self-interested partners, they are not.2 Conversely, we show that reciprocity motives incentivize partners to deviate, destroying asymmetric equilibria; therefore, asymmetric efficient profiles can no longer be implemented as an equilibrium if agents are sufficiently sensitive to reciprocity. In particular, our first result gives useful insights for the optimal design of the team by describing the psychological attitudes of the team members required to sustain the symmetric efficient strategy profile as a psychological Nash equilibrium—for any given sharing rule. The second result, on the other hand, takes a psychological characteristic of the partners (namely the minimal level of individual sensitivity to reciprocity) as given, and finds a condition on the overall level of reciprocity and a sharing rule which implement the symmetric strategy profile as a psychological equilibrium. This reciprocity based sharing rule is such that each partner gets a fraction of the output, which is a percentage of his own sensitivity to reciprocity with respect to the overall sensitivity in the team. However, even if the efficient strategy profile is sustained, there could be other (inefficient) strategy profiles which are sustained as a Nash equilibrium or as a psychological Nash equilibrium for the same set of sharing rules. Moreover, the conditions used to prove the previous results are not sufficient to sustain efficiency if some partners can collude. We introduce the concept of psychological strong Nash equilibrium and show that it solves both problems allowing for the unique and collusion-proof implementation of the efficient strategy profile. This paper demonstrates that, despite their apparent complexity, intention-based reciprocity models can be useful to study economically relevant settings like team-production in a novel and simple way. Our contribution builds on and extends three different literatures. First, after the seminal contribution by Holmstrom (1982) successive papers on partnership have shown that the efficiency or near efficiency can be obtained in partnerships with a random technology (Matsushima, 1989, Legros and Matsushima, 1991 and Williams and Radner, 1995), with risk-averse partners and random-sharing rules (Rasmusen, 1987), with repeated play (Radner, 1986), or finally through the use of mixed strategies, provided the partners have unlimited liability (Legros and Matthews, 1993). More recently, Rahman and Obara (2010) employ a mediator who, by allocating private information differently across agents, provides the right incentives if after any unilateral deviation innocence is statistically attributable to someone. In this paper, without requiring any form of monitoring, we get equilibrium-implementation results for efficient action profiles in one-shot, non-stochastic partnerships with symmetric production functions.3 Second, the experimental evidence in Fehr et al. (1997) suggests that reciprocal motives contribute to the enforcement of contracts. In this vein, Dufwenberg and Kirchsteiger (2000), Englmaier and Leider (2008) and Netzer and Schmutzler (2010) all show that efficiency is generally increased when a materialistic principal interacts with a reciprocal agent.4 We show that the efficiency-enhancing role of reciprocity, extends also to partnerships.5 Third, we contribute to the theoretical literature on psychological games (Geanakoplos et al., 1989, Rabin, 1993, Dufwenberg and Kirchsteiger, 2004, Falk and Fischbacher, 2006 and Battigalli and Dufwenberg, 2009) by extending the definition of strong Nash equilibrium that has been introduced by Aumann (1959) to environments with reciprocal players. The present paper is also related to a growing literature that studies the impact of inequity aversion on partnership (Li, 2009 and Bartling and von Siemens, 2010) and on principal multiple agent models (Itoh, 2004, Demougin and Fluet, 2006 and Rey Biel, 2008). These articles find that inequity aversion can improve incentives since agents work harder to avoid suffering from unfavourable inequality. However, as also recognized by Itoh (2004) “reciprocity and inequity aversion are distinct motives, and often intention matters more, in particular in the domain of punishing behaviour, as suggested by recent evidence.” Moreover, the effects of inequity aversion on utilities depend substantially on differences in material payoffs between the partners in the team rather than differences in efforts. Therefore, the implementation results are strongly related to the choice of particular sharing rules. In particular, the equal sharing rule seems to be crucial to obtain the implementation results. More precisely, in Bartling and von Siemens (2010), the authors argue that equal sharing arises endogenously as an outcome of inequity aversion, since it is the unique sharing rule that maximizes the partners' incentives to exert effort. Instead, Li (2009) shows that if the sharing rule distributes the team output equally when the output is high and punishes some random

Even the best people do not always work together as well as they could. Simply assigning a group of people to a task does not magically turn them into a well-functioning team. Basic skills for managing a team may include: how to set agendas, leading priority setting, leading without dominating, project management skills, encouraging and facilitating a discussion, monitoring team progress, and so on. However, our results indicate that how well a partnership can overcome free riding depends between other things on the set of partners. In a world in which this choice is endogenous, there should be a tendency for the most efficient partnerships to form. Our efficiency results suggest a tendency of partnerships to consist of members whose sensitivity to reciprocity is – individually or jointly – sufficiently high. Our theory is a first step in understanding the impact of intention-based reciprocity preferences on the design of a team and on the design of sharing rules that lead to efficiency in the simple and relevant partnership framework where the efficient strategy profile is symmetric. The peculiarity of the partnership model is that it allows us to consider measures of kindness which depend only on effort and not on the particular material preferences representation. This captures the idea that a partner may react badly to other partners free-riding regardless of rewards. To conclude we discuss two possible extensions. Contingent reciprocity: To focus on the fact that kindness depends only on effort and not on the particular material preferences representation, in the previous analysis we considered constant reciprocity parameters and find conditions on such parameters which allow for the (unique) implementation of the efficient strategy profile. A more general analysis could take into account reciprocity parameters which depend on the sharing rule. However, this approach would require to use the concept of dynamic psychological equilibrium (Battigalli and Dufwenberg, 2009) and its refinements.