Many bargaining solutions anchor on disagreement, allocating gains with respect to the worstcase scenario. We propose here a solution anchoring on utopia (the ideal, maximal aspirations for all agents), but yielding feasible allocations for any number of agents. The negotiated aspirations solution proposes the best allocation in the direction of utopia starting at an endogenous reference point which depends on both the utopia point and bargaining power. The Kalai-Smorodinsky solution becomes a particular case if (and only if) the reference point lies on the line from utopia to disagreement. We provide a characterization for the two-agent case relying only on standard axioms or natural restrictions thereof: strong Pareto optimality, scale invariance, restricted monotonicity, and restricted concavity. A characterization for the general (n-agent) case is obtained by relaxing Pareto optimality and adding the (standard) axiom of restricted contraction independence, plus the minimal condition that utopia should be selected if available.

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BackgroundWhenever vaccines for a new pandemic or widespread epidemic are developed, demand greatly exceeds the available supply of vaccine doses in the crucial, initial phases of vaccination. Rationing protocols must then fulfill a number of ethical principles balancing equal treatment of individuals and prioritization of at-risk and instrumental subpopulations. For COVID-19, actual rationing methods used a territory-based first allocation stage based on proportionality to population size, followed by locally-implemented prioritization rules. The results of this procedure have been argued to be ethically problematic.MethodsWe use a formal-analytical approach arising from the mathematical social sciences which allows to investigate whether any allocation methods (known or unknown) fulfill a combination of (ethical) desiderata and, if so, how they are formulated algorithmically.ResultsStrikingly, we find that there exists one and only one method that allows to treat people equally while giving priority to those who are worse off. We identify this method down to the algorithmic level and show that it is easily implementable and it exhibits additional, desirable properties. In contrast, we show that the procedures used during the COVID-19 pandemic violate both principles.ConclusionsOur research delivers an actual algorithm that is readily applicable and improves upon previous ones. Since our axiomatic approach shows that any other algorithm would either fail to treat people equally or fail to prioritize those who are worse off, we conclude that ethical principles dictate the adoption of this algorithm as a standard for the COVID-19 or any other comparable vaccination campaigns.

In a “claims problem” (O’Neill 1982), a group of individuals have claims on a resource but its endowment is not sufficient to honour all of the claims. We examine the following question: If a claims problem can be decomposed into smaller claims problems, can the solutions of these smaller problems be added to obtain the solution of the original problem? A natural condition for this decomposition is that the solution to each of the smaller problems is non-degenerate, assigning positive awards to each claimant. We identify the only consistent and endowment monotonic adjudication rules satisfying this property; they are generalizations of the canonical “constrained equal losses rule” sorting claimants into priority classes and distributing the amount available to each class using a weighted constrained equal losses rule. The constrained equal losses rule is the only symmetric rule in this family of rules.

The achievement of Sustainable Development Goals (SDG) related to the environment requires identifying new sources of environmental degradation. This paper analyzes how market size asymmetry affects government decisions on environmental policy in the context of bilateral international trade and imperfect competition. We model an international duopoly with market size asymmetry and product heterogeneity. Each firm produces two different products, one for the domestic and one for the foreign markets, where the firms' production generates local emissions. When planning policies, the government in each country must choose between two options: an emission tax or a production subsidy. The findings of our paper underline the crucial role of market size asymmetry in determining the non-cooperative equilibrium policy in a setting where both firms and governments act strategically. We find that an increase in market size asymmetry between countries encourages governments to shift from emission taxes to production subsidies. Therefore, the environmental policy must consider these aspects to achieve greater effectiveness of regulation in favor of the environment. Actions to mitigate increased pollution should regulate production subsidies and improve the practices of governments and companies.