Mathematical Social Sciences最新文献

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).

Distributional economies are defined by a probability distribution in the space of characteristics where the commodity space is an ordered separable Banach space. We characterize the continuity of the equilibrium correspondence and an associated stability concept which allows us to give a positive answer to an open question about the continuity of the Walras correspondence in infinite-dimensional spaces. As a byproduct, we study a stability concept where differentiability assumptions are not required, as is usual in the literature on regularity. Moreover, since distributional economies do not specify a space of agents, our setting encompasses several results in the literature on large economies.

The potential emergence of artificial general intelligence (AGI) systems has sparked intense debate among researchers, policymakers, and the public due to their potential to surpass human intelligence in all domains. This note argues that for an AI to be considered “general”, it should achieve superhuman performance not only in zero-sum games but also in general-sum games, where winning or losing is not clearly defined. In this note, I propose a game-theoretic framework that captures the strategic interactions between a representative human agent and a potential superhuman machine agent. Four assumptions underpin this framework: Superhuman Machine, Machine Strategy, Rationality, and Strategic Unpredictability. The main result is an impossibility theorem, establishing that these assumptions are inconsistent when taken together, but relaxing any one of them results in a consistent set of assumptions. This note contributes to a better understanding of the theoretical context that can shape the development of superhuman AI.

This paper studies a simple model inspired by the seminal connections model of Jackson and Wolinsky (1996). Node-players can invest in links to connect with other nodes forming networks, but only direct links transmit value. Nodes may have different values and different decreasing returns abilities/technologies to form/strengthen links. The strength of a link depends on the amounts invested in it by the two nodes that it connects and is determined by a separable function of the investments of the players which form the link. Nash-stable and efficient networks are characterized, and a variety of their architectures identified for different configurations of values and technologies.

We reexamine core-stability, incorporating inequality-averse preferences and challenging the conventional core’s stability under such preferences. We integrate existing social preferences tied to inequality aversion into a cooperative game model with transferable utility (TU games), introducing a novel core. We characterize the new core through inequalities akin to the “coalitional rationality” in TU games and conduct a comparative statics analysis on two parameters–envy and sympathy–representing inequality aversion. Our findings reveal that an increase in the envy parameter reduces elements in the new core, while heightened sympathy does not consistently decrease core elements.

We consider the aggregation of classifications of objects that are graded in a single dimension into categories that are ranked. Grading is a sufficient domain restriction to avoid dictatorship. In contrast to other results, it is possible to use a majority-based aggregator when objects can be located in any number of categories. The aggregator locates an object below a boundary between specified categories just if a majority do so. In contrast, preponderance aggregators that are directly based on locations of objects can locate a higher graded object in a lower ranked category. Any aggregator that satisfies other independence conditions relating to the locations of objects or positions of boundaries must be dictatorial.

This paper extends Scarf’s (1971) $\alpha$-core result to a dynamic Cournot oligopoly. It shows that the $\alpha$, $\beta$, $\gamma$-cores are all non-empty in an $n$-firm dynamic Cournot oligopoly with linear demand and symmetric quadratic costs.

This paper examines the impact of delegating decision-making authority to a biased and uninformed agent in a Bayesian persuasion model. We find that delegation can incentivize the sender to produce more information about the merits of the sender’s proposed project. This is because an agent with a small negative bias requires more compelling evidence than the principal to implement the project. The improvement in evidence quality does not occur if the agent’s bias is positive. When the informational benefits exist, delegation lead to higher organizational welfare than centralization. The informational benefits of delegation extend to cases where the principal delegates authority through a general delegation mechanism and when the agent’s bias is privately known.