Philippe Bich

Imagine a cohort of economic experts appraising long-term projects through the quasi-hyperbolic discounting criterion. The parameters (long-run and short-run discount rates) used by each expert may differ, which implies different policy recommendations. Subsequently, a decision maker is faced with the task of selecting an efficient aggregation from these varied opinions. This paper proposes a solution to reconcile these conflicting recommendations, taking into account the decision maker’s adoption of a “prudent” behavior.

We introduce a new order on income distributions that we call “social tension” order, based on the concepts of absolute satisfaction and absolute deprivation, as introduced by Chakravarty (1997) (see also Chateauneuf and Moyes, 2006). Our order postulates that antagonist groups of individuals behave differently when comparing welfare: each “poor” individual compares herself with richer individuals, while each “rich” individual compares herself with poorer ones. We prove that reducing social tension corresponds to fair taxation and provide an explicit algorithm that allows for transitioning from a dominated distribution to a dominating one through a sequence of elementary transfers that respect our order. Additionally, we construct a new index from the “social tension” order, which may better capture the various sources of inequality compared to the Gini index. Lastly, we characterize those expected utility functions that respect our order.

We extend standard tools from equilibrium refinement theory in non-cooperative games to a cooperative framework of network formation. First, we introduce the new concept of perfect pairwise stability. It transposes the idea of “trembling hand” perfection to network formation theory and strictly refines the pairwise stability concept of Jackson and Wolinsky (1996). Second, we study basic properties of perfect pairwise stability: existence, admissibility and perturbation. We further show that our concept is distinct from the concept of strongly stable networks introduced by Jackson and Van den Nouweland (2005), and perfect Nash equilibria of the Myerson network formation game studied by Calvó-Armengol and İlkılıç (2009). Finally, we apply perfect pairwise stability to sequential network formation and prove that it enables a refinement of sequential pairwise stability, a natural analogue of subgame perfection in a setting with cooperative, pairwise link formation.

In this paper, we give axiomatic foundations for a social planner objective function that takes the form of the maxmin of quasi-hyperbolic criteria. The minimum is taken over a set Q of possible pairs of discount rates δ and present bias parameters p0. When there is no present bias, we recover Chambers and Echenique’s axiomatization of maxmin exponential preferences, and when Q reduces to a singleton, we get Montiel Olea and Strzalecki’s axiomatization of quasi-hyperbolic preferences. To prove our main result, we provide some intertemporal variational representation results of interest for its own sake.