# On Markovian collective choice with heterogeneous quasi-hyperbolic discounting

*Jean-Pierre Drugeon* () and
*Bertrand Wigniolle*

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Jean-Pierre Drugeon: Paris School of Economics and Centre National de la Recherche Scientifique.

*Economic Theory*, 2021, vol. 72, issue 4, No 7, 1257-1296

**Abstract:**
Abstract A general setup is considered where quasi-hyperbolic discounting agents differ in assuming heterogeneous bias for the present as well as heterogeneous discounting parameters, consumptions being, moreover, subject to a standard feasibility constraint. A collective utility function is defined as a linear combination of the inter-temporal utilities of the selves of the different agents, the elementary unit being thus the self of a given period of a given agent. Such a framework generating a tension between Pareto-optimality and time consistency for the optimal allocations, a new approach is introduced in order to tackle this issue. This builds from an a priori time-inconsistent collective utility function where the benevolent planner is to be apprehended in terms of a sequence of successive incarnations, any of these incarnations being endowed with its own objective. The associated optimal policy is the equilibrium of a game between the successive incarnations of the planner when the players follow Markovian strategies. This is compared with a more standard approach where restrictions would be imposed on the collective utility function that ensure the time consistency of the optimal decisions.

**Keywords:** Heterogeneities; Hyperbolic discounting; Markovian strategies; Collective choice (search for similar items in EconPapers)

**JEL-codes:** C62 E32 (search for similar items in EconPapers)

**Date:** 2021

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Working Paper: On Markovian collective choice with heterogeneous quasi-hyperbolic discounting (2021)

Working Paper: On Markovian collective choice with heterogeneous quasi-hyperbolic discounting (2021)

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**DOI:** 10.1007/s00199-020-01291-z

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