Mathematical Social Sciences最新文献

This paper examines the conditions under which separating outcomes occur in informed persuasion, that is, in Bayesian persuasion settings in which the sender is privately informed about the payoff-relevant state prior to committing to an experiment. We consider a setting with finite payoff-relevant states and sender payoffs that are continuous and monotonic in the receiver’s posterior beliefs. The paper finds that if full disclosure of the payoff-relevant state reduces the sender’s expected payoff under any common prior (i.e., if the sender’s payoff function is outer concave), then single-crossing properties arise such that the high sender type can separate from the low type by choosing more informative experiments. This single-crossing condition leads to the selection of “least costly” separating equilibria by the D1 criterion, i.e., the sender’s choice of experiment signals his type. Further, separating equilibria are characterized by simple constrained maximization problems.

We develop an overlapping generations model to explore the role of grandparents in grandchildren’s education and its impact on human capital growth. We examine the quantity–quality (Q–Q) trade-off faced by parents in choosing the number and education of children, incorporating an active role for grandparents. Findings underscore the significance of the elderly in human capital accumulation, fertility, and economic growth. When grandparents invest more time, resources are freed, fostering greater human capital growth and mitigating the effects of the Q–Q trade-off.

We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to a strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required while communicating with a strategic sender. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, non-cooperative regime of communication involving a strategic sender.

Two acts are comonotonic if they co-vary in the same direction. The main purpose of this paper is to derive a new characterization of Cumulative Prospect Theory (CPT) through simple properties involving comonotonicity. The main novelty is a concept dubbed gain–loss hedging: mixing positive and negative acts creates hedging possibilities even when acts are comonotonic. This allows us to clarify in which sense CPT differs from Choquet expected utility. Our analysis is performed under the assumption that acts are real-valued functions. This entails a simple (piece-wise) constant marginal utility representation of CPT, which allows us to clearly separate the perception of uncertainty from the evaluation of outcomes.

For the cooperative equilibria in $\alpha$-core form, the balancedness and coalitionally $C-$security of games with usual utilities are extended to the games with discontinuous set payoffs. The existence of $\alpha -$core for these games is established, which can deduce some typical results for normal form games. For continuous games, a quasi-concave-like set payoff is introduced. Based on the introduced set payoffs, the existence of $\alpha -$core is also obtained. Examples are given to verify these results. Comparison with existing results in references shows that the introduced conditions are new to guarantee the existence of $\alpha -$core for games with set payoffs.

The concept of compromise has been present in the theory of social choice from the very beginning. The result of social choice functions as such is often called a social compromise. In the last two decades, several functions of social choice dedicated to the concept of compromise, such as Fallback bargaining, Majoritarian compromise, Median voting rule or $p$-measure of compromise rules, have been considered in the literature. Furthermore, compromise axioms were formed in several attempts. However, we believe that the previous formalizations of compromise did not axiomatically describe this feature of the social choice functions. In this paper we will follow the line of thought presented by Chatterji, Sen and Zeng (2016) and form a weak and strong version of a Compromise axiom, one that should capture understanding of compromise based on an ability to elect a winner which is not top-ranked in any preference on a profile. After that we will analyze an interaction of those axioms and established social choice functions. We will show that the division of SCFs in three classes with respect to these axioms fairly reflect relationship between those SCFs and colloquial expectations from notion of compromise. We then compare the defined axioms with the compromise axioms of Börgers and Cailloux. Finally, for SCFs that satisfy the strong compromise axiom, we define a compromise intensity function that numerically expresses the degree of tolerance of the SCF for choosing a compromise candidate.

We consider a school choice matching model where priorities for schools are represented by binary relations that may not be linear orders. Even in that case, it is necessary to construct linear orders from the original priority relations to execute several mechanisms. We focus on the (linear order) extensions of the priority relations, because a matching that is stable for an extension profile is also stable for the profile of priority relations. We show that if the priority relations are partial orders, then for each stable matching for the original profile of priority relations, an extension profile for which it is also stable exists. Furthermore, if there are multiple stable matchings that are ranked by Pareto dominance, then there is an extension for which all these matchings are stable. We apply the result to a version of efficiency adjusted deferred acceptance mechanisms.

In matching markets, objects are allocated to agents without monetary transfers, based on agents’ preferences. However, agents may not have enough information to determine their preferences over the objects precisely. How should a benevolent planner optimally reveal information to maximize social welfare in this context? I show that when agents are symmetric and there are just two options, letting each agent know his rank in the realized distribution of preferences – but not his actual preferences – always improves social welfare over providing no information. When there are more objects, this rank-based information policy generalizes to the Object Recommendation (OR) Signal, which consists of simply recommending each agent to pick his socially-optimal choice. Under a mild regularity condition, I show that, when agents’ a priori relative preferences over the objects are “not too strong”, the OR Signal, used together with any standard ordinal mechanism, not only maximizes welfare, but achieves the unconstrained social optimum — formalizing the intuition that when people do not have strong opinions over several options, it is easy to sway them.

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.