Mathematical Social Sciences最新文献

We propose an ultimatum bargaining model in which the parties experience an envy-based externality that is private information. Our results indicate that there is a threshold for the proposer’s envy which determines whether there will be either a perfectly equitable, certain agreement or an uncertain, inequitable agreement, and that this threshold rises as the distribution of the responder’s envy level improves in a first-order stochastic-dominance sense. In addition, conditionally on the scenario ruling out a perfectly equitable agreement, we show that the proposer’s envy level plays a dual role: (i) it increases the probability of a negotiation breakdown, and (ii) it constitutes a source of bargaining power. Numerical simulations also allow us to explore some properties of the role played by the responder’s envy and by changes in the envy distributions of the two players. Overall, our theoretical results are consistent with the main evidence from ultimatum experiments conducted in behavioral and neuroscience settings. In addition, we provide testable implications of our model for future experiments.

Electoral volatility measures the degree of vote switching between political parties in two consecutive elections. Political scientists use this as an indicator of party system (in)stability. Pedersen (1979) states that volatility should increase when the number of parties changes and/or relevant parties experience vote transfer between elections. However, his proposed functional form of measuring volatility does not always respond to these changes. To address these limitations, we introduce a class of additively separable electoral volatility measures which are responsive to changes in both the number of parties and their vote shares. We present a set of axioms that are both necessary and sufficient to characterize the proposed class of indices, making the structure of the indices more transparent. The paper also introduces two quasi orders which can rank party systems in terms of all electoral volatility indices satisfying certain intuitively reasonable axioms. Finally, applications of the proposed class of indices and the quasi orders are provided using data from Indian state elections.

A major concern with Bayesian decision making under uncertainty is the use of a single probability measure to quantify all relevant uncertainty. This paper studies prior robustness as a form of continuity of the value of a decision problem. I show that this notion of robustness is characterized by a form of stable choice over a sequence of perturbed decision problems, in which the available acts are perturbed in a precise fashion. I then introduce a choice-based measure of prior robustness and apply it to models of climate mitigation and portfolio choice.

We analyze centralized markets for indivisible objects without money through pairwise exchange when each agent initially owns a single object. We consider rules that for each profile of agents preferences select an assignment of the objects to the agents. We present a family of domains of preferences (minimal reversal domains) that are maximal rich domains for the existence of rules that satisfy individual rationality, efficiency, and strategy-proofness. Each minimal reversal domain is defined by a common ranking of the set of objects, and agents’ preferences over admissible objects coincide with such common ranking but for a specific pair of objects.

Complexity of the problem of choosing among uncertain acts is a salient feature of many of the environments in which departures from expected utility theory are observed. I study a class of Generalized Simple Bounds preferences in which acts that are complex from the perspective of the decision maker are bracketed by “simple” acts to which they are related by statewise dominance. I then study a refinement of the model in which the size of the partition with respect to which an act is measurable arises endogenously as a measure of subjective complexity. Finally, I consider choice behavior characterized by a “cautious completion” of Simple Bounds preferences, and discuss the relationship between this model and models of ambiguity aversion. I develop general comparative statics results, and explore applications to portfolio choice and insurance choice.

Models of optimal retirement should reflect market incompleteness in reality caused by disability risk. In this paper, we develop an analytic approach for optimal retirement models with disability risk. More precisely, we provide an analytically tractable characterization of total wealth that is the sum of financial wealth and the present value of future income. We then provide analytic properties of the retirement wealth threshold. Finally, we derive the analytical optimal consumption and portfolio choice with retirement and disability risk.

We study matching with couples problems where hospitals have one vacant position. We introduce a constraint on couples’ preferences over pairs of hospitals called restricted complementarity, which is a “translation” of bilateral substitutability in matching with contracts. Next, we extend Klaus and Klijn’s (2007) path to stability result by showing that if couples’ preferences satisfy restricted complementarity, then from any arbitrary matching, there exists a finite path of matchings where each matching on the path is obtained by “satisfying” a blocking coalition for the previous one and the final matching is stable.

We consider the intertemporal price discrimination problem of a durable good monopolist facing a population of consumers who are time inconsistent. We show that price trajectories, profits and welfare are sensitive to consumers’ first- and second-order beliefs regarding their time preferences. Surprisingly, we find that sales and profits are largest when consumers are sophisticated, i.e., when consumers hold correct expectations on their own future choices. The monopolist is thus unable to take advantage of consumers’ naiveté, and could instead benefit from informing consumers about their true preferences and commitment problems, or otherwise communicate its beliefs about them.

We study the problem of fairly allocating indivisible goods to agents with weights corresponding to their entitlements. Previous work has shown that, when agents have binary additive valuations, the maximum weighted Nash welfare rule is resource-, population-, and weight-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time. We generalize these results to the class of weighted additive welfarist rules with concave functions and agents with matroid-rank (also known as binary submodular) valuations.

The static analysis shows that a merger among complementary input suppliers or complementary patent holders benefits the consumers and the society by reducing the input prices. We show that the effects of a merger of complements are not so straightforward in a dynamic set up with endogenous product differentiation in the final goods market. The merger of complements reduces the total input prices and increases product differentiation. However, whether it increases or decreases consumer surplus and welfare depends on the market expansion following product differentiation, the number of merged input suppliers and the intensity of competition. Hence, in a dynamic setup with endogenous product differentiation, the antitrust authorities may need to be more careful about mergers of complements. Our analysis has also relevance for vertical mergers.