I consider the problem of allocating N indivisible objects among N agents according to their preferences when transfers are absent and an outside option may exist. I study the tradeoff between fairness and efficiency in the class of strategy-proof mechanisms. The main finding is that for strategy-proof mechanisms the following efficiency and fairness criteria are mutually incompatible: (1) ex-post efficiency and envy-freeness, (2) ordinal efficiency and weak envy-freeness, and (3) ordinal efficiency and equal division lower bound. Result 1 is the first impossibility result for this setting that uses ex-post efficiency ; results 2 and 3 are more practical than similar results in the literature. In addition, for N=3, I give two characterizations of the celebrated random serial dictatorship mechanism: it is the unique strategy-proof, ex-post efficient mechanism that (4) provides agents that have the same ordinal preferences with assignments not dominated by each other (weak envy-freeness among equals), or (5) provides agents that have the same cardinal preferences with assignments of equal expected utility (symmetry). These results strengthen the characterization by Bogomolnaia and Moulin (2001); result 5 implies the impossibility result by Zhou (1990).
Reservation price equilibria (RPE) do not accurately assess market power in consumer search markets. In most search markets, consumers do not know important elements of the environment in which they search (such as, for example, firms' cost). We argue that when consumers learn when searching, RPE suffer from theoretical issues, such as non-existence and critical dependence on specific out-of-equilibrium beliefs. We characterize equilibria where consumers rationally choose search strategies that are not characterized by a reservation price. Non-RPE always exist and do not depend on specific out-of-equilibrium beliefs. Non-RPE have active consumer search and are consistent with recent empirical findings.
Enlightening of the individual product demand functions. The equilibrium product line constitutes the highest upper envelope. In the generalized vertical differentiation framework, the first line and the best socially optimal line. Synthetic Cournot oligopoly.
We provide a new, welfarist, interpretation of the well-known Serial rule in the random assignment problem, strikingly different from previous attempts to define or axiomatically characterize this rule. For each agent i we define ti(k) to be the total share of objects from her first k indifference classes this agent i gets. Serial assignment is shown to be the unique one which leximin maximizes the vector of all such shares (ti(k)). This result is very general; it applies to non-strict preferences, and/or non-integer quantities of objects, as well. In addition, we characterize Serial rule as the unique one sd-efficient, sd-envy-free, and strategy-proof on the lexicographic preferences extension to lotteries. © 2015 Elsevier Inc. All rights reserved.
Although the linear-in-means model is the workhorse model in empirical work on peer effects, its theoretical properties are understudied. In this study, we develop a social-norm model that provides a microfoundation of the linear-in-means model and investigate its properties. We show that individual outcomes may increase, decrease, or vary non-monotonically with the taste for conformity. Equilibria are usually ineffcient and, to restore the rst best, the planner needs to subsidize (tax) agents whose neighbors make efforts above (below) the social norms. Thus, giving more subsidies to more central agents is not necessarily effcient. We also discuss the policy implications of our model in terms of education and crime.
It is proved that, among all restricted preference domains that guarantee consistency (i.e. transitivity) of pairwise majority voting, the single-peaked domain is the only minimally rich and connected domain that contains two completely reversed strict preference orders. It is argued that this result explains the predominant role of single-peakedness as a domain restriction in models of political economy and elsewhere. The main result has a number of corollaries, among them a dual characterization of the single-dipped domain; it also implies that a single-crossing (‘order-restricted’) domain can be minimally rich only if it is a subdomain of a single-peaked domain. The conclusions are robust as the results apply both to domains of strict and of weak preference orders, respectively.
We propose a general model of monopolistic competition, which encompasses existing models while being flexible enough to take into account new demand and competition features. Even though preferences need not be additive and/or homothetic, the market outcome is still driven by the sole variable elasticity of substitution. We impose elementary conditions on this function to guarantee empirically relevant properties of a free-entry equilibrium. Comparative statics with respect to market size and productivity shocks are characterized through necessary and sufficient conditions. Furthermore, we show that the attention to the CES based on its normative implications was misguided: we propose a new class of preferences, which express consumers' uncertainty about their love for variety, that yield variable markups and may sustain the optimum. Last, we show how our approach can cope with heterogeneous firms once it is recognized that the elasticity of substitution is firm-specific.
We study stochastic voting models where the candidates are allowed to have any smooth, strictly increasing utility functions that translate vote shares into payoffs. We find that if a strict Nash equilibrium exists in a model with an infinite number of voters, then nearby equilibria should exist for similar large, but finite, electorates. If the votes are independent random events, then equilibria will not depend on the utility functions of the candidates. Our results have implications for existing models of redistributive politics and spatial competition, as the properties of pure-strategy equilibria in such games carry over to equilibria in games with arbitrary candidate preferences. On the other hand, candidate utility functions will matter if the individual voting decisions are correlated. In the presence of aggregate uncertainty, such as changing economic conditions or political scandals, the preferences of parties and candidates with respect to shares of votes will have an effect on political competition.