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on Economic Design |
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Issue of 2022‒06‒27
eleven papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Chao Huang |
| Abstract: | This paper studies two-sided many-to-one matching in which firms have complementary preferences. We show that stable matchings exist under a balancedness condition that rules out a specific type of odd-length cycles formed by firms' acceptable sets. We also provide a class of preference profiles that satisfy this condition. Our results indicate that stable matching is compatible with a wide range of firms' complementary preferences. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.05599&r= |
| By: | Mustafa Oguz Afacan; Umut Dur; A. Arda Gitmez; \"Ozg\"ur Y{\i}lmaz |
| Abstract: | In school choice problems, the motivation for students' welfare (efficiency) is restrained by concerns to respect schools' priorities (fairness). Even the best matching in terms of welfare among all fair matchings (SOSM) is in general inefficient. Moreover, any mechanism that improves welfare over the SOSM is manipulable by the students. First, we characterize the "least manipulable" mechanisms in this class: upper-manipulation-proofness ensures that no student is better off through strategic manipulation over the objects that are better than their assigned school. Second, we use the notion that a matching is less unfair if it yields a smaller set of students whose priorities are violated, and define minimal unfairness accordingly. We then show that the Efficiency Adjusted Deferred Acceptance (EADA) mechanism is minimally unfair in the class of efficient and upper-manipulation-proof mechanisms. When the objective is to improve students' welfare over the SOSM, this characterization implies an important insight on the frontier of the main axioms in school choice. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.00032&r= |
| By: | Hidemasa Ishii; Nariaki Nishino |
| Abstract: | The literature on centralized matching markets often assumes that a true preference of each player is known to herself and fixed, but empirical evidence casts doubt on its plausibility. To circumvent the problem, we consider evolutionary dynamics of preference revelation games in marriage problems. We formulate the asymptotic stability of a matching, indicating the dynamical robustness against sufficiently small changes in players' preference reporting strategies, and show that asymptotically stable matchings are stable when they exist. The simulation results of replicator dynamics are presented to demonstrate the asymptotic stability. We contribute a practical insight for market designers that a stable matching may be realized by introducing a learning period in which participants find appropriate reporting strategies through trial and error. We also open doors to a novel area of research by demonstrating ways to employ evolutionary game theory in studies on centralized markets. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.08079&r= |
| By: | Wanchang Zhang |
| Abstract: | A single unit of a good is sold to one of two bidders. Each bidder has either a high prior valuation or a low prior valuation for the good. Their prior valuations are independently and identically distributed. Each bidder may observe an independently and identically distributed signal about her prior valuation. The seller knows the distribution of the prior valuation profile and knows that signals are independently and identically distributed, but does not know the signal distribution. In addition, the seller knows that bidders play undominated strategies. I find that a second-price auction with a random reserve maximizes the worst-case expected revenue over all possible signal distributions and all equilibria in undominated strategies. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.04137&r= |
| By: | Fupeng Sun; Yanwei Sun; Chiwei Yan; Li Jin |
| Abstract: | By modeling contests as all-pay auctions, we study two-stage sequential elimination contests (SEC) under incomplete information, where only the players with top efforts in the first stage can proceed to the second and final stage to compete for prizes. Players have privately held type/ability information that impacts their costs of exerting efforts. We characterize players' Perfect Bayesian Equilibrium strategies and discover a somewhat surprising result: all players exert weakly lower efforts in the final stage of the SEC compared to those under a one-round contest, regardless of the number of players admitted to the final stage. This result holds under any multi-prize reward structure, any type distribution and cost function. As a consequence, in terms of the expected highest effort or total efforts of the final stage, the optimal SEC is equivalent to a one-round contest by letting all players proceed to the final stage. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.08104&r= |
| By: | Soo Hong Chew; Wenqian Wang |
| Abstract: | Two dynamic game forms are said to be behaviorally equivalent if they share the "same" profiles of structurally reduced strategies (Battigalli et al., 2020). In the context of dynamic implementation, behaviorally equivalent game forms are interchangeable under a wide range of solution concepts for the purpose of implementing a social choice function. A gradual mechanism (Chew and Wang, 2022), which designs a procedure of information transmission mediated by a central administrator, enables a formal definition of information flow. We provide a characterization of behavioral equivalence between gradual mechanisms in terms of their informational equivalence -- each agent is designed the "same" information flow. Information flow also helps in defining an intuitive notion of immediacy for gradual mechanisms which is equivalent to their game structures being minimal. Given that the class of gradual mechanisms serves as a revelation principle for dynamic implementation (Li, 2017; Akbarpour and Li, 2020; Mackenzie, 2020; Chew and Wang, 2022), the class of immediate gradual mechanisms provides a refined revelation principle. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.10844&r= |
| By: | Moshe Babaioff; Uriel Feige |
| Abstract: | We consider fair allocation of a set $M$ of indivisible goods to $n$ equally-entitled agents, with no monetary transfers. Every agent $i$ has a valuation $v_i$ from some given class of valuation functions. A share $s$ is a function that maps a pair $(v_i,n)$ to a value, with the interpretation that if an allocation of $M$ to $n$ agents fails to give agent $i$ a bundle of value at least equal to $s(v_i,n)$, this serves as evidence that the allocation is not fair towards $i$. For such an interpretation to make sense, we would like the share to be feasible, meaning that for any valuations in the class, there is an allocation that gives every agent at least her share. The maximin share was a natural candidate for a feasible share for additive valuations. However, Kurokawa, Procaccia and Wang [2018] show that it is not feasible. We initiate a systematic study of the family of feasible shares. We say that a share is \emph{self maximizing} if truth-telling maximizes the implied guarantee. We show that every feasible share is dominated by some self-maximizing and feasible share. We seek to identify those self-maximizing feasible shares that are polynomial time computable, and offer the highest share values. We show that a SM-dominating feasible share -- one that dominates every self-maximizing (SM) feasible share -- does not exist for additive valuations (and beyond). Consequently, we relax the domination property to that of domination up to a multiplicative factor of $\rho$ (called $\rho$-dominating). For additive valuations we present shares that are feasible, self-maximizing and polynomial-time computable. For $n$ agents we present such a share that is $\frac{2n}{3n-1}$-dominating. For two agents we present such a share that is $(1 - \epsilon)$-dominating. Moreover, for these shares we present poly-time algorithms that compute allocations that give every agent at least her share. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.07519&r= |
| By: | Ritesh Jain and (Institute of Economics, Academia Sinica.); Michele Lombardi (University of Liverpool Management School, Università di Napoli Federico II, and CSEF) |
| Abstract: | Interim Rationalizable Monotonicity, due to Oury and Tercieux (2012), fully characterizes the class of social choice functions that are implementable in interim correlated rationalizable (and Bayes-Nash equilibrium) strategies. |
| Keywords: | temporary contracts, young workers, flexibility, institutional reforms, employment protection legislation. |
| JEL: | C79 D82 |
| Date: | 2022–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:645&r= |
| By: | Bugra Caskurlu; Fatih Erdem Kizilkaya |
| Abstract: | Hedonic games are a prominent model of coalition formation, in which each agent's utility only depends on the coalition she resides. The subclass of hedonic games that models the formation of general partnerships, where output is shared equally among affiliates, is referred to as hedonic games with common ranking property (HGCRP). Aside from their economic motivation, HGCRP came into prominence since they are guaranteed to have core stable solutions that can be found efficiently. We improve upon existing results by proving that every instance of HGCRP has a solution that is Pareto optimal, core stable and individually stable. The economic significance of this result is that efficiency is not to be totally sacrificed for the sake of stability in HGCRP. We establish that finding such a solution is {\bf NP-hard} even if the sizes of the coalitions are bounded above by $3$; however, it is polynomial time solvable if the sizes of the coalitions are bounded above by $2$. We show that the gap between the total utility of a core stable solution and that of the socially-optimal solution (OPT) is bounded above by $n$, where $n$ is the number of agents, and that this bound is tight. Our investigations reveal that computing OPT is inapproximable within better than $O(n^{1-\epsilon})$ for any fixed $\epsilon > 0$, and that this inapproximability lower bound is polynomially tight. However, OPT can be computed in polynomial time if the sizes of the coalitions are bounded above by $2$. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.11939&r= |
| By: | Wu, Haoyang |
| Abstract: | In a mechanism, a designer may reveal some information to influence agents' private types in order to obtain more payoffs. In the literature, the information is usually represented as random variables, the value of which are realized by the nature. However, this representation of information may not be proper in some practical cases. In this paper, we propose a type-adjustable mechanism where the information sent by the designer is modeled as a solution of her optimization problem. From the designer's perspective, the probability distributions of agents' private types may be optimally controlled. By constructing a type-adjustable first-price sealed-bid auction, we show that the seller may obtain more expected payoffs than what she could obtain at most in the traditional optimal auction model. Interestingly, to the satisfaction of all, each agent's \emph{ex-ante} expected payoffs may be increased too. In the end, we compare the type-adjustable mechanism with other relevant models. |
| Keywords: | Mechanism design; Optimal auction; Bayesian implementation. |
| JEL: | D71 |
| Date: | 2022–05–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:113150&r= |
| By: | B. Ravikumar; Raymond G. Riezman; Yuzhe Zhang |
| Abstract: | We study infant industry protection using a dynamic model in which the industry’s cost is initially higher than that of foreign competitors. The industry can stochastically lower its cost via learning by doing. Whether the industry has transitioned to low cost is private information. We use a mechanism-design approach to induce the industry to reveal its true cost. We show that (i) the optimal protection, measured by infant industry output, declines over time and is less than that under public information, (ii) the optimal protection policy is time consistent under public information but not under private information, (iii) the optimal protection policy can be implemented with minimal information requirements, and (iv) a government with a limited budget can use a simple approach to choose which industries to protect. |
| Keywords: | protection, infant industry, private information, mechanism design, time consistency |
| JEL: | F10 F13 O25 D82 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9772&r= |