Whose Opinion Counts? Political Processes and the Implementation Problem

The mechanism used in Nash implementation is a form of direct democracy, taking everyone''s opinion into account. We augment this mechanism with a political process that selects the opinions of a subset of the individuals. We study three such processes -- oligarchy, oligarchic democracy and random sampling -- and compare the social choice rules (SCRs) that can be implemented using each of these processes with those that can be Nash implemented. In oligarchy, only the opinions of a fixed subset of the individuals -- the oligarchs -- determine the implemented alternative. We obtain a negative result for oligarchies: there exist Nash implementable SCRs that cannot be implemented by any oligarchy. Oligarchic democracy is a perturbation of oligarchy, in which the opinions of the oligarchs “almost always” determine the implemented alternative but sometimes, everyone''s opinions are considered. In a sharp contrast to the negative result for oligarchies, we show that in economic environments, every Nash implementable SCR can be implemented by an oligarchic democracy in which any three individuals act as oligarchs. In random sampling, opinions of a fixed number of individuals are selected randomly, which then determine the implemented alternative. We show that in economic environments, every Nash implementable SCR can be implemented by randomly sampling opinions of four individuals.microeconomics ;

Quantity Precommitment and Price Matching

We revisit the question of whether price matching is anti-competitive in a capacity constrained duopoly setting. We show that the effect of price matching depends on capacity. Specifically, price matching has no effect when capacity is relatively low, but it benefits the firms when capacity is relatively high. Interestingly, when capacity is in an intermediate range, price matching benefits only the small firm but does not affect the large firm in any way. Therefore, one has to consider capacity seriously when evaluating if price matching is anti-competitive. If the firms choose their capacities simultaneously before pricing decisions, then the effect of price matching is either pro-competitive or ambiguous. We show that if the cost of capacity is high, then price matching can only (weakly) decrease the market price. On the other hand, if the cost of capacity is low, then the effect of price matching on the market price is ambiguous due to the multiplicity of equilibria. Therefore, this paper challenges the widely accepted belief that price matching is an anti-competititive practice if the firms choose their capacities simultaneously before pricing decisions.Price matching, capacity constraint, quantity precommitment

Whose Opinion Counts? Political Processes and the Implementation Problem ∗

We augment the mechanism used in Nash implementation with a political process that collects the opinions of a subset of individuals with a fixed probability distribution. The outcome is a function of only the collected opinions. We show that the necessary – and sometimes sufficient – condition for implementation by a specific political process can be either weaker or stronger than Maskin monotonicity. We study three such processes: oligarchy, oligarchic democracy, and random sampling. Oligarchy collects only the opinions of the oligarchs (a strict subset of the individuals). We present a Nash implementable social choice rule (SCR) that cannot be implemented by any oligarchy. Oligarchic democracy “almost always ” collects the opinions of the oligarchs but sometimes there is a referendum (i.e., everyone’s opinions are collected). We show that in economic environments, every Nash implementable SCR can be implemented by oligarchic democracy in which any three individuals act as oligarchs. In random sampling, a sample of opinions are collected randomly. We show that in economic environments, every Nash implementable SCR can be implemented by randomly sampling opinions of 4 individuals. We also provide necessary and sufficient conditions for implementation when the planner has the flexibility to choose any political process

The Daycare Assignment Problem

In this paper we take the mechanism design approach to the problem of assigning children of different ages to daycares, motivated by the mechanism currently in place in Denmark. This problem is similar to the school choice problem, but has two distinguishing features. First, it is characterized by an overlapping generations structure. For example, children of different ages may be allocated to the same daycare, and the same child may be allocated to different daycares across time. Second, the daycares' priorities are history-dependent: a daycare gives priority to children currently enrolled in it, as is the case with the Danish system. We first study the concept of stability, and, to account for the dynamic nature of the problem, we propose a novel solution concept, which we call strong stability. With a suitable restriction on the priority orderings of schools, we show that strong stability and the weaker concept of static stability will coincide. We then extend the well known Gale-Shapley deferred acceptance algorithm for dynamic problems and show that it yields a matching that satisfies strong stability. It is not Pareto dominated by any other matching, and, if there is an efficient stable matching, it must be the Gale-Shapley one. However, contrary to static problems, it does not necessarily Pareto dominate all other strongly stable mechanisms. Most importantly, we show that the Gale-Shapley algorithm is not strategy-proof. In fact, one of our main results is a much stronger impossibility result: For the class of dynamic matching problems that we study, there are no algorithms that satisfy strategy-proofness and strong stability. Second, we show that the also well known Top Trading Cycles algorithm is neither Pareto efficient nor strategy-proof. We conclude by proposing a variation of the serial dictatorship, which is strategyproof and efficient.daycare assignment, market design, matching, overlapping generations, weak and strong stability, efficiency