Sustainability standards, multicriteria maximin, and viability

Abstract

This paper deals with sustainability criteria and standards. The maximin criterion, as the highest performance that can be sustained over time, promotes intergenerational equity, a pivotal issue for sustainability. The viable control approach, by investigating trajectories and actions complying over time with various standards and constraints, provides major insights into strong sustainability. The present paper addresses the links between maximin and viability approaches in a multicriteria context. It first shows how “Pareto maximin” can be characterized through viability kernels. Such a result makes it possible to determine the trade‐offs and/or synergies between nonsubstitutable economic and ecological standards underlying strong sustainability. The second main result of the paper is to propose algorithms derived from the viability version of dynamic programming to approximate numerically Pareto maximin values, controls, and sustainability standards. Two examples relying on renewable resource management illustrate these analytic and numerical findings. In particular, synergies between sustainability standards of resource conservation, production or profitability are identified for overexploited stocks.

On the set of robust sustainable thresholds

“…, and ( ) satisfy (I ) for any . Doyen and Gajardo (2020) and Gajardo and Hermosilla (2021) for the deterministic case, there is a duality between the robust viability kernel and the set of robust sustainable thresholds. This relation is expressed by the following equivalence: for any…”

“…In this section, we illustrate the computation of the set of robust sustainable thresholds ξ ( ) for one example based on renewable resource management, inspired by Clark (1990) and Doyen and Gajardo (2020). In the example, the stock of a renewable resource in period k is represented by x 0 k ≥ , and its dynamics with harvesting (or catch) u k are described by…”

“…Remark 4.2. Note that, in a general setting, if ω Ω ∈ and we consider the constant scenario ω w = ( ) ) defined in Doyen and Gajardo (2020) and Gajardo and Hermosilla (2021). From the definition of the set of robust sustainable thresholds ξ ( ) in (1), it is straightforward to verify that…”

“…Taking into account some of the challenges mentioned above, such as developing tools to manage and visualize multiple objectives and their tradeoffs related to sustainability, a different strategy has been proposed from that focused on the viability kernel: to characterize the set of sustainable thresholds or standards that can mathematically be regarded as the inverse mapping of the viability kernel. In the context of deterministic systems, this set has been studied recently in Barrios et al (2018), Gajardo et al (2018), Martinet (2011), Martinet et al (2011) and characterized in Doyen and Gajardo (2020) and Gajardo and Hermosilla (2021).…”

Characterizing sustainability in discrete time

“…In the viability approach(Aubin 1991), the set S(c) is referred to as the viability kernel, a concept which is applied in the continuous-time DHS model byMartinet and Doyen (2007) andDoyen and Martinet (2012) and in discrete time byDoyen and Gajardo (2019). Furthermore, the price pair (P t , Q t ) established in Proposition 1 corresponds to an element in the normal cone to the viability kernel S(c) at (k t , m t ).…”