|
on Economic Design |
| By: | Muntasir Chaudhury (East West University); Szilvia Papai (Concordia University and CIREQ) |
| Abstract: | We study three basic welfare axioms for school choice mechanisms with a reserve or quota-based affirmative action policy, namely non-wastefulness, respecting the affirmative action policy, and minimal responsiveness, and show that none of the previously proposed mechanisms satisfy all of them. Then we introduce a new mechanism which satisfies these three axioms. This mechanism issues immediate acceptances to minority students for minority reserve seats and otherwise it employs deferred acceptance. We analyze the fairness and incentive properties of this newly proposed affirmative action mechanism and provide possibility and impossibility results which highlight the trade-offs. |
| Keywords: | school choice, affirmative action, minority reserves, non-wastefulness, minimal responsiveness, deferred acceptance, immediate acceptance, priority violations, strategyproofness |
| JEL: | C78 D47 D63 D78 |
| Date: | 2024–05–17 |
| URL: | http://d.repec.org/n?u=RePEc:crd:wpaper:24001&r= |
| By: | Luke Snow; Vikram Krishnamurthy |
| Abstract: | This paper constructs an algorithmic framework for adaptively achieving the mechanism design objective, finding a mechanism inducing socially optimal Nash equilibria, without knowledge of the utility functions of the agents. We consider a probing scheme where the designer can iteratively enact mechanisms and observe Nash equilibria responses. We first derive necessary and sufficient conditions, taking the form of linear program feasibility, for the existence of utility functions under which the empirical Nash equilibria responses are socially optimal. Then, we utilize this to construct a loss function with respect to the mechanism, and show that its global minimization occurs at mechanisms under which Nash equilibria system responses are also socially optimal. We develop a simulated annealing-based gradient algorithm, and prove that it converges in probability to this set of global minima, thus achieving adaptive mechanism design. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.15391&r= |
| By: | Hadi Hosseini; Aghaheybat Mammadov; Tomasz W\k{a}s |
| Abstract: | In fair division of indivisible items, domain restriction has played a key role in escaping from negative results and providing structural insights into the computational and axiomatic boundaries of fairness. One notable subdomain of additive preferences, the lexicographic domain, has yielded several positive results in dealing with goods, chores, and mixtures thereof. However, the majority of work within this domain primarily consider strict linear orders over items, which do not allow the modeling of more expressive preferences that contain indifferences (ties). We investigate the most prominent fairness notions of envy-freeness up to any (EFX) or some (EF1) item under weakly lexicographic preferences. For the goods-only setting, we develop an algorithm that can be customized to guarantee EF1, EFX, maximin share (MMS), or a combination thereof, along the efficiency notion of Pareto optimality (PO). From the conceptual perspective, we propose techniques such as preference graphs and potential envy that are independently of interest when dealing with ties. Finally, we demonstrate challenges in dealing with chores and highlight key algorithmic and axiomatic differences of finding EFX solutions with the goods-only setting. Nevertheless, we show that there is an algorithm that always returns an EF1 and PO allocation for the chores-only instances. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.19740&r= |
| By: | Qianjun Lyu |
| Abstract: | This paper studies the optimal refund mechanism when an uninformed buyer can privately acquire information about his valuation of a product over time. We consider a class of refund mechanisms based on stochastic return policies: if the buyer requests a return, the seller will issue a (partial) refund while allowing the buyer to keep the product with some probability. Such return policies can affect the buyer's learning process and thereby influence the return rate. Nevertheless, we show that the optimal refund mechanism is deterministic and takes a simple form: either the seller offers a sufficiently low price and disallows returns to deter buyer learning, or she offers a sufficiently high price with free returns to implement maximal buyer learning. The form of the optimal refund mechanism is non-monotone in the buyer's prior belief regarding his valuation. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.14927&r= |