arXiv subjects

Ata Atay

Publications and source records attributed to Ata Atay.

9 recordsLinked to original sources

arXiv2024

A many-to-one job market: more about the core and the competitive salaries

This paper studies many-to-one assignment markets, or matching markets with wages. Although it is well-known that the core of this model is non-empty, the structure of the core has not been fully investigated. To the known dissimilarities with the one-to-one assignment game, we add that the bargaining set does not coincide with the core and the kernel may not be included in the core. Besides, not all extreme core allocations can be obtained by means of a lexicographic maximization or a lexicographic minimization procedure, as it is the case in the one-to-one assignment game. The maximum and minimum competitive salaries are characterized in two ways: axiomatically and by means of easily verifiable properties of an associated directed graph. Regarding the remaining extreme core allocations of the many-to-one assignment game, we propose a lexicographic procedure that, for each order on the set of workers, sequentially maximizes or minimizes each worker's competitive salary. This procedure provides all extreme vectors of competitive salaries, that is all extreme core allocations.

econ.TH↗

arXiv2024

Optimistic and pessimistic approaches for cooperative games

Cooperative game theory studies how to allocate the joint value generated by a set of players. These games are typically analyzed using the characteristic function form with transferable utility, which represents the value attainable by each coalition. In the presence of externalities, coalition values can be defined through various approaches, notably by trying to determine the best and worst-case scenarios. Typically, the optimistic and pessimistic perspectives offer valuable insights into strategic interactions. In many applications, these approaches correspond to the coalition either choosing first or choosing after the complement coalition. In a general framework in which the actions of a group affects the set of feasible actions for others, we explore this relationship and show that it always holds in the presence of negative externalities, but only partly with positive externalities. We then show that if choosing first/last corresponds to these extreme values, we also obtain a useful inclusion result: allocations that do not allocate more than the optimistic upper bounds also do not allocate less than the pessimistic lower bounds. Moreover, we show that when externalities are negative, it is always possible to guarantee the non-emptiness of these sets of allocations. Finally, we explore applications to illustrate how our findings provide new results and offer a means to derive results from the existing literature.

econ.TH↗

arXiv2023

Complementarities in childcare allocation under priorities

We investigate the allocation of children to childcare facilities and propose solutions to overcome limitations in the current allocation mechanism. We introduce a natural preference domain and a priority structure that address these setbacks, aiming to enhance the allocation process. To achieve this, we present an adaptation of the Deferred Acceptance mechanism to our problem, which ensures strategy-proofness within our preference domain and yields the student-optimal stable matching. Finally, we provide a maximal domain for the existence of stable matchings using the properties that define our natural preference domain. Our results have practical implications for allocating indivisible bundles with complementarities.

econ.TH↗

arXiv2023

Matching markets with farsighted couples

We adopt the notion of the farsighted stable set to determine which matchings are stable when agents are farsighted in matching markets with couples. We show that a singleton matching is a farsighted stable set if and only if the matching is stable. Thus, matchings that are stable with myopic agents remain stable when agents become farsighted. Examples of farsighted stable sets containing multiple non-stable matchings are provided for markets with and without stable matchings. For couples markets where the farsighted stable set does not exist, we propose the DEM farsighted stable set to predict the matchings that are stable when agents are farsighted.

econ.TH↗

arXiv2022

School Choice with Farsighted Students

We consider priority-based school choice problems with farsighted students. We show that a singleton set consisting of the matching obtained from the Top Trading Cycles (TTC) mechanism is a farsighted stable set. However, the matching obtained from the Deferred Acceptance (DA) mechanism may not belong to any farsighted stable set. Hence, the TTC mechanism provides an assignment that is not only Pareto efficient but also farsightedly stable. Moreover, looking forward three steps ahead is already sufficient for stabilizing the matching obtained from the TTC.

econ.TH↗

arXiv2022

Limited Farsightedness in Priority-Based Matching

We consider priority-based matching problems with limited farsightedness. We show that, once agents are sufficiently farsighted, the matching obtained from the Top Trading Cycles (TTC) algorithm becomes stable: a singleton set consisting of the TTC matching is a horizon-$k$ vNM stable set if the degree of farsightedness is greater than three times the number of agents in the largest cycle of the TTC. On the contrary, the matching obtained from the Deferred Acceptance (DA) algorithm may not belong to any horizon-$k$ vNM stable set for $k$ large enough.

econ.TH↗

arXiv2022

Queueing games with an endogenous number of machines

This paper studies queueing problems with an endogenous number of machines with and without an initial queue, the novelty being that coalitions not only choose how to queue, but also on how many machines. For a given problem, agents can (de)activate as many machines as they want, at a cost. After minimizing the total cost (processing costs and machine costs), we use a game theoretical approach to share to proceeds of this cooperation, and study the existence of stable allocations. First, we study queueing problems with an endogenous number of machines, and examine how to share the total cost. We provide an upper bound and a lower bound on the cost of a machine to guarantee the non-emptiness of the core (the set of stable allocations). Next, we study requeueing problems with an endogenous number of machines, where there is an existing queue. We examine how to share the cost savings compared to the initial situation, when optimally requeueing/changing the number of machines. Although, in general, stable allocation may not exist, we guarantee the existence of stable allocations when all machines are considered public goods, and we start with an initial schedule that might not have the optimal number of machines, but in which agents with large waiting costs are processed first.

econ.TH↗

arXiv2021

Matching markets with middlemen under transferable utility

This paper studies matching markets in the presence of middlemen. In our framework, a buyer-seller pair may either trade directly or use the services of a middleman; and a middleman may serve multiple buyer-seller pairs. Direct trade between a buyer and a seller is costlier than a trade mediated by a middleman. For each such market, we examine an associated cooperative game with transferable utility. First, we show that an optimal matching for a matching market with middlemen can be obtained by considering the two-sided assignment market where each buyer-seller pair is allowed to use the mediation service of the middlemen free of charge and attain the maximum surplus. Second, we prove that the core of a matching market with middlemen is always non-empty. Third, we show the existence of a buyer-optimal core allocation and a seller-optimal core allocation. In general, the core does not exhibit a middleman-optimal matching. Finally, we establish the coincidence between the core and the set of competitive equilibrium payoff vectors.

econ.TH↗

arXiv2019

Open shop scheduling games

This paper takes a game theoretical approach to open shop scheduling problems with unit execution times to minimize the sum of completion times. By supposing an initial schedule and associating each job (consisting in a number of operations) to a different player, we can construct a cooperative TU-game associated with any open shop scheduling problem. We assign to each coalition the maximal cost savings it can obtain through admissible rearrangements of jobs' operations. By providing a core allocation, we show that the associated games are balanced. Finally, we relax the definition of admissible rearrangements for a coalition to study to what extend balancedness still holds.

cs.GT↗