A principal and an agent enter into a sequence of agreements. The principal faces an interim participation constraint at each date, but can commit to the current agreement; in contrast, the agent has the opportunity to renege on the current agreement. We study the time structure of agreement sequences that satisfy participation and no-deviation constraints and are (constrained) efficient. We show that every such sequence must, after a finite number of dates, exhibit a continuation that maximizes the agent's payoff over all such efficient, self-enforcing sequences. Additional results are provided for situations with transferable payoffs.

We study informal insurance within communities, explicitly recognizing the possibility that subgroups of individuals may destabilize insurance arrangements among the larger group. We therefore consider self-enforcing risk-sharing agreements that are robust not only to single-person deviations but also to potential deviations by subgroups. However, such deviations must be credible, in the sense that the subgroup must pass exactly the same test that we apply to the entire group; it must itself employ some self-enforcing risk-sharing agreement. We observe that the stability of subgroups is inimical to the stability of the group as a whole. Two surprising consequences of this analysis are that stable groups have (uniformly) bounded size, a result in sharp contrast to the individual-deviation problem, and that the degree of risk-sharing in a community is generally non-monotonic in the level of uncertainty or need for insurance in the community.

We study cooperative behaviour in communities where the flow of information regarding past conduct is limited or missing. Players are initially randomly matched with no knowledge of each other's past actions; they endogenously decide whether or not to continue the repeated relationship. There is incomplete information regarding player types: a subset of the population is myopic, while the remainder have discount factors that permit cooperation, in principle. We define social equilibrium in such communities. Such equilibria are characterized by an initial testing phase, followed by cooperation if the test is successful. It is precisely the presence of myopic types that permit cooperation, by raising barriers to entry into new relationships. We examine the implications of increased patience, which takes two forms: an increase in the number of non-myopic types, and an increase in the discount factor of non-myopic types. These two notions turn out to have strikingly different implications for the degree of cooperation that can be sustained.

Harsanyi (1974) and Ray and Vohra (2015) extended the stable set of von Neumann and Morgenstern to impose farsighted credibility on coalitional deviations. But the resulting farsighted stable set suffers from a conceptual drawback: while coalitional moves improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable and easily verifiable properties is unaffected by the imposition of these stringent maximality constraints. The properties we describe are satisfied by many, but not all, farsighted stable sets.

This paper develops a theory in which society-wide economic outcomes shape individual aspira-tions, which affect the investment incentives of individuals. Through its impact on investments, aspirations in turn affect ambient social outcomes. We explore this two-way link. A central feature is that aspirations that are moderately above an individual’s current standard of living tend to encourage investment, while still higher aspirations may lead to frustration and lower investment. When integrated with the feedback effect from investment, we are led to a the-ory in which aspirations and income evolve jointly, and the social determinants of preferences play an important role. We examine conditions under which growth is compatible with long-run equality in the distribution of income. More generally, we describe steady state income distri-butions, which are typically clustered around local poles. Finally, the theory has predictions for the growth rates along the cross-section of income. We use these predictions to calibrate the model so that it fits growth data by income percentile for 43 countries, and back out the implicit aspirations-formation process that underlies these observations.

Harsanyi (1974) criticized the von Neumann–Morgenstern (vNM) stable set for its presumption that coalitions are myopic about their prospects. He proposed a new dominance relation incorporating farsightedness, but retained another feature of the stable set: that a coalition S can impose any imputation as long as its restriction to S is feasible for it. This implicitly gives an objecting coalition complete power to arrange the payoffs of players elsewhere, which is clearly unsatisfactory. While this assumption is largely innocuous for myopic dominance, it is of crucial significance for its farsighted counterpart. Our modification of the Harsanyi set respects “coalitional sovereignty.” The resulting farsighted stable set is very different from both the Harsanyi and the vNM sets. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single-payoff allocation. This condition roughly establishes an equivalence between core allocations and the union of allocations over all single-payoff farsighted stable sets. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games. This last exercise throws light on both single-payoff and multi-payoff stable sets, and suggests that they do not coexist.

We study collaborative work in pairs when potential collaborators are motivated by the reputational implications of (joint or solo) projects. In equilibrium, individual collaboration strategies both influence and are influenced by the public assignment of credit for joint work across the two partners. We investigate the fragility of collaboration to small biases in the public’s credit assignment. When collaborators are symmetric, symmetric equilibria are often fragile, and in nonfragile equilibria individuals receive asymmetric collaborative credit based on payoff-irrelevant “identities.” We study payoff distributions across identities within asymmetric equilibria, and compare aggregate welfare across symmetric and asymmetric equilibria. (JEL A11, D82, I23)

We conceptualize and measure upward mobility over income or wealth. At the core of our exercise is the Growth Progressivity Axiom: transfers of instantaneous growth rates from relatively rich to poor individuals increases upward mobility. This axiom, along with mild auxiliary restrictions, identifies an “upward mobility kernel” with a single free parameter, in which mobility is linear in individual growth rates, with geometrically declining weights on baseline incomes. We extend this kernel to trajectories over intervals. The analysis delivers an upward mobility index that does not rely on panel data. That significantly expands our analytical scope to data-poor settings. (JEL D31, D63, I32, O15, O40)

Alphabetical name order is the norm for joint publications in economics. However, alphabetical order confers greater benefits on the first author. In a two-author model, we introduce and study certified random order: the uniform randomization of names made universally known by a commonly understood symbol. Certified random order (i) distributes the gain from first authorship evenly over the alphabet; (ii) allows either author to signal when contributions are extremely unequal; (iii) will invade an environment where alphabetical order is dominant; (iv) is robust to deviations; (v) may be ex ante more efficient than alphabetical order; and (vi) is no more complex than the existing alphabetical system modified by occasional reversal of name order. (JEL A14, Z13)

A strategic situation with payoff-based externalities is one in which a player’s payoff depends on her own action and others’ payoffs. We place restrictions on the resulting interdependent utility system that generate a standard normal form, referred to as a “game of love and hate.” Our central theorem states that every equilibrium of a game of love and hate is Pareto optimal. While externalities are restricted to flow only through payoffs, there are no other constraints: they could be positive or negative or of varying sign. We examine the philosophical implications of the restrictions that underlie this theorem.