Mathematical Social Sciences最新文献

In this paper we study clean energy transition in a modified version of the Ramsey growth model by including nonrenewable and renewable resources as well as pollution externalities. The main difference from previous works is that we consider imperfect substitution between nonrenewable and renewable resources. We characterize the social optimum and show that the economy converges to a clean state in the long run. We then study the decentralized equilibrium and show that the economy converges to the same state even without regulation, but with higher environmental damage. Further, we investigate the properties of the taxation trajectory that drives the laissez-faire economy to follow the optimal path and show that it can be either increasing or decreasing over time. We identify different channels that influence the path of optimal taxation and show that it depends, among other things, on the level of capital, the cost of renewable energy and the degree of substitution between renewable and nonrenewable resources.

An abstract decision problem is an ordered pair where the first component is a nonempty and finite set of alternatives from which a society has to make a choice and the second component is an irreflexive relation on that set representing a dominance relation. A crucial problem is to find a reasonable solution that allows to select, for any given abstract decision problem, some of the alternatives. A variety of solutions have been proposed over the years. In this paper we propose a new solution, called maximum flow value set, that naturally stems from the work by Bubboloni and Gori (The flow network method, Social Choice and Welfare 51, pp. 621–656, 2018) and that is based on the concept of maximum flow value in a digraph. We analyze its properties and its relation with other solutions such as the core, the admissible set, the uncovered set, the Copeland set and the generalized stable set. We also show that the maximum flow value set allows to define a new Condorcet social choice correspondence strictly related to the Copeland social choice correspondence and fulfilling lots of desirable properties.

Output uncertainty is a major concern for industries prone to exogenous, persistent and large fluctuations in output, such as agriculture, wind and solar power generation, while technology adoption aimed at mitigating output uncertainty can improve social welfare. This paper constructs a competitive market model with random output fluctuations to examine the scale of technology adoption at the long-term equilibrium and its comparison with the social optimum. We show that the First Welfare Theorem no longer holds in general, and depending on the characteristics of the demand function, the scale of technology adoption in the competitive market may be greater or less than the socially optimal scale.

By endowing the class of tops-only and efficient social choice rules with a dual order structure that exploits the trade-off between different degrees of manipulability and dictatorial power rules allow agents to have, we provide a proof of the Gibbard–Satterthwaite Theorem.

We consider the problem of dividing the cost of a facility when agents can be ordered in terms of the needs they have for it, and accommodating an agent with a certain need allows accommodating all agents with lower needs at no extra cost. This problem is known as the “airport problem”, the facility being the runway. We review the literature devoted to its study, and formulate a number of open questions.

Bolletta (2021) studies a model in which a network is strategically formed and then agents play a linear best-response investment game in it. The model is motivated by an application in which people choose both their study partners and their levels of educational effort. Agents have different one-dimensional types – private returns to effort. A main result claims that (pairwise Nash) stable networks have a locally complete structure consisting of possibly overlapping cliques: if two agents are linked, they are part of a clique composed of all agents with types between theirs. A counterexample shows that the claimed characterization is incorrect. We specify where the analysis errs and discuss implications for network formation models.

We apply the Rawlsian principle to a canonical discrete object allocation problem. A matching is Rawlsian if it is impossible to improve the ranking of assignment for the worst-off agent or reduce the cardinality of the set of the worst-off agent-body. None of the well-known mechanisms are Rawlsian. We introduce an efficient and Rawlsian class of mechanisms. Strategy-proofness is incompatible with Rawlsianism; therefore, no Rawlsian mechanism is strategy-proof.

Today, several social movements in western democracies argue that traditional representative democracy has failed to adequately represent the will of the “people”, and instead support direct democracy as the only political system to restore the will of the majority. We analyze under what conditions the policy – a vector of decisions on every issue – implemented by the winner of a bipartisan electoral competition coincides with the policy that citizens would choose by means of direct democracy. We find necessary and sufficient conditions for this equivalence to hold, implying that, as long as at least one of them is not fulfilled, a divergence of outcomes between direct and representative democracy arises. The first condition requires that the outcome of majority voting issue-by-issue is the Condorcet winner relative to the voters’ preference profile over the set of policies. The second requires that either that outcome is the preferred policy for at least one of the candidates, or that candidates’ preferred policies differ on every single issue. We reinterpret some findings in the literature in the light of our model and present them as potential reasons why the equivalence between direct and representative democracy may fail.

This paper characterizes the Top Trading Cycles (TTC) mechanism for the school choice problem where schools may have multiple available seats to be assigned to students. We first define weaker forms of fairness, consistency, and resource monotonicity. We show that the TTC mechanism is the unique Pareto efficient and strategy-proof mechanism that satisfies these weaker forms of fairness, consistency and resource monotonicity. We also show that in a well-defined sense TTC is the “most stable” Pareto efficient mechanism.

Recently a framework was developed for aggregative variational inequalities by means of the Selten–Szidarovszky technique. By referring to this framework, a powerful Nash equilibrium uniqueness theorem for sum-aggregative games is derived. Payoff functions are strictly quasi-concave in own strategies but may be discontinuous at the origin. Its power is illustrated by reproducing and generalising in a few lines an equilibrium uniqueness result in Corchón and Torregrosa (2020) for Cournot oligopolies with the Bulow–Pfleiderer price function. Another illustration addresses an asymmetric contest with endogenous valuations in Hirai and Szidarovszky (2013).