查看更多>>摘要：In this paper, we consider a sequence of multi-prize all-pay auctions, where low-performing players are eliminated along the way. We provide sufficient conditions such that equilibrium behavior is unaffected by the prospects of winning prizes in later rounds. When these conditions are not met, we identify a novel externality effect and derive equilibria in a model with two rounds. We compare our results to knockout tournaments in which players are partitioned into subcontests in each round. (C) 2021 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：We consider school choice problems (Abdulkadiroglu and Sonmez, 2003) where students are assigned to public schools through a centralized assignment mechanism. We study the family of so-called rank-priority mechanisms, each of which is induced by an order of rank-priority pairs. Following the corresponding order of pairs, at each step a rank-priority mechanism considers a rank-priority pair and matches an available student to an unfilled school if the student and the school rank and prioritize each other in accordance with the rank-priority pair. The Boston or immediate acceptance mechanism is a particular rank-priority mechanism. Our first main result is a characterization of the subfamily of rank-priority mechanisms that Nash implement the set of stable matchings (Theorem 1). Our second main result is a strong impossibility result: under incomplete information, no rank-priority mechanism implements the set of stable matchings (Theorem 2).(c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We show that on the domain of convex games, Dutta-Ray's egalitarian solution is characterized by core selection, aggregate monotonicity, and bounded richness, a new property requiring that the poorest players cannot be made richer within the core. Replacing "poorest "by "poorer "allows to eliminate aggregate monotonicity. Moreover, we show that the egalitarian solution is characterized by constrained welfare egalitarianism and either bilateral consistency a la Davis and Maschler or, together with individual rationality, by bilateral consistency a la Hart and Mas-Colell.(c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The "invisible hand "of the free market is remarkably effective at producing near-equilibrium prices. This is difficult to quantify, however, in the absence of an agreed model for out-of-equilibrium trade. Short of a fully reductionist model, a useful substitute would be a scaling law relating equilibration time and other market parameters. Even this, however, is missing in the literature. We make progress in this direction. We examine a class of Arrow-Debreu markets with price signaling driven by continuous-time proportional-tatonnement. We show that the connectivity among the participants in the market determines quite accurately a scaling law for convergence time of the market to equilibrium, and thus determines the effectiveness of the price signaling. To our knowledge this is the first characterization of price stability in terms of market connectivity. At a technical level, we show how convergence in our class of markets is determined by a market-dependent Laplacian matrix. If a market is not isolated but, rather, subject to external noise, equilibrium theory has predictive value only to the extent to which that noise is counterbalanced by the price equilibration process. Our model quantifies this predictive value by providing a scaling law that relates the connectivity of the market with the variance of its prices. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：I analyze the optimal favoritism in a complete-information all-pay contest with two players, whose costs of effort are weakly convex. The contest designer could favor or harm some contestants using one of two instruments: head starts and handicaps. I find that any given player's effort distribution is ranked in the sense of first-order stochastic dominance according to how (ex post) symmetric the players are in terms of competitiveness. Consequently, as long as the designer values effort from both contestants, "leveling the playing field"is optimal regardless of which instrument is used. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper compares the first-price auction and the second-price auction with several asymmetric bidders who are either weak or strong. The ranking of these auctions in terms of profit may flip as the exogenous reserve price or the number of weak or strong bidders change. Similarly, with endogenous reserve prices the ranking may depend on the seller's own-use valuation. In other words, the ranking may be fragile to changes along these dimensions. Existing models rule out such ranking reversals by imposing substantial structure on type distributions. The current paper relies on simple mechanism design arguments that require less structure.(c) 2021 Elsevier B.V. All rights reserved.
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