Mathematical Social Sciences最新文献

This paper investigates the coherence of a new class of ratio-based inequality indices introduced in Chan (2022) with respect to certain partial orderings of the underlying income distributions. While coherence with respect to stochastic dominance has been extensively studied, the appropriate partial ordering for this new class of indices is quantile ratio dominance. This paper also establishes coherence with respect to quantile ratio dominance for some other classes of inequality indices which have been introduced by other authors. Finally, some connections between the notion of coherence and transfer principles are explored.

This study examines the impact of network externalities on the market performance of vertically differentiated luxury products. Luxury consumption triggers vanity-driven utility, which decreases due to the snob effect as market share expands. By employing a duopoly model under price competition, we demonstrate that a higher degree of network externalities enhances high-quality product market share, price, and profit while reducing those for low-quality products. The crowding-out of high-quality products on low-quality products becomes more pronounced as network externalities increase. We analyze the effects of quality improvement on equilibrium outcomes, revealing that a moderate reduction in the quality gap benefits social welfare. In contrast, a marginal gap leads to a lose-lose situation for firms. Our study underscores the importance of retaining low-quality products and adopting quality promotion strategies for high-quality products.

We consider a New Keynesian model with nominal rigidities and fractional cash in-advance constraint on consumption expenditures. We study the stability properties of the model when Taylor rules react either to current inflation or to expected one. We account for different public sector budget identities and different fiscal policies ensuring Government solvency. Under an independent Central Bank, forward-looking Taylor rules promote sunspot fluctuations more easily than contemporaneous ones because they set in motion a mechanism of self-fulfilling prophecies. Conversely, the introduction of capital as an asset alongside public securities facilitates smoothing behavior and reduces the region of indeterminacy but brings out multiple steady states. When public sector budget identities are consolidated, the stabilization of total public liabilities reduces the likelihood of sunspot fluctuations and even rules them out in the presence of capital accumulation. Finally, we perform a complete welfare analysis allowing to rank equilibria and to identify the best policy mix to implement Pareto-superior outcomes.

We study the optimal targeting problem of a firm that is seeking to maximize the diffusion of a product in a society where agents learn from their neighbors. The firm can seed the product to a subset of the population and our goal is to find which the optimal subset to target is. We provide a condition that characterizes the optimal targeting strategy for any network structure. The key parameter in this condition is the agents’ decay centrality, which takes into account how close an agent is to others, in a way that distant agents are weighted less than closer ones.

The Riemann hypothesis (RH) is one of the major unsolved problems in pure mathematics. In the present paper, a parameterized family of non-cooperative games is constructed with the property that, if RH is true, then any game in the family admits a unique Nash equilibrium. We argue that this result is not degenerate. Indeed, neither is the conclusion a tautology, nor is RH used to define the family of games.

This article addresses the polarization of the population around an idea and proposes a simple model that describes its dynamics in a society characterized by asymmetries in freedom of expression. The model considers a population divided into followers of an idea, consisting of moderate sympathizers and staunch defenders, and a group of opponents who try to spread their position but are also susceptible to opinion change. An analysis of stability of the proposed system of differential equations is conducted to examine policies that prevent homogenization around the idea. The results reveal conditionally stable equilibrium points that represent the coexistence of opinions and the extinction of polarization. Two threshold values are proposed to determine the persistence of polarization over time. Furthermore, the results of the model are validated through the analysis of two real cases of polarization in Colombian society, demonstrating its ability to reproduce the general behavior of opinion divergence and its utility in polarization control.

We discuss horizontal mergers in a homogeneous good industry where firms compete à la Bertrand with increasing marginal production costs. We show that profitable mergers can occur even for lower post-merger prices with respect to the pre-merger scenario, thus implying an increase in consumer surplus. The driving force of the result is the ability of the merged entity cutting production costs by sharing the output among its plants. This output rationalization effect can compensate for the revenue loss due to the merged entity producing less than the cumulated pre-merger production of the merging parties.

The note presents a counter example to Li (2023).

This paper examines how the public’s expectations for the chair of the monetary policy committee influence policy outcomes. We show that the expectation that the chair will propose their ideal policy at the meeting can lead a majority of the committee to reject the policy change. The result suggests that the expectation of the chair’s agenda setting is a determinant of interest rate persistence.

In most economic applications of cooperative games, externalities prevail: the worth of a coalition depends on how the other players are organized. We show that there is a unique natural way of extending the prenucleolus to games with coalitional externalities. This is in contrast to the Shapley value and the core for which many different extensions have been proposed.