Cagatay Kayi - Academia.edu (original) (raw)
Papers by Cagatay Kayi
* We would like to thank Bettina Klaus and William Thomson for their helpful and detailed suggest... more * We would like to thank Bettina Klaus and William Thomson for their helpful and detailed suggestions and discussions.
SSRN Electronic Journal
This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a ... more This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents' rankings. Finally, we show that most of our bounds are tight.
A set of agents with possibly different waiting costs have to receive the same service one after ... more A set of agents with possibly different waiting costs have to receive the same service one after the other. Efficiency requires to maximize total welfare. Equity requires to at least treat equal agents equally. One must form a queue, set up monetary transfers to compensate agents having to wait, and not a priori arbitrarily exclude agents from positions. As one may not know agents' waiting costs, they may have no incentive to reveal them. We identify the only rule satisfying Paretoefficiency, a weak equity axiom as equal treatment of equals in welfare or symmetry, and strategyproofness. It satisfies stronger axioms, as no-envy and anonymity. Further, its desirability extends to related problems. To obtain these results, we prove that even non-single-valued rules satisfy Pareto-efficiency of queues and strategy-proofness if and only if they select Pareto-efficient queues and set transfers in the spirit of Groves (1973). This holds in other problems, provided the domain of quasi-linear preferences is rich enough.
Brit J Ind Relat, 2007
We consider the model of two-sided matching with contracts introduced in Hatfield and Milgrom (20... more We consider the model of two-sided matching with contracts introduced in Hatfield and Milgrom (2005) and analyze solutions under variable preferences and populations. Therefore, we study Maskin-monotonicity as introduced by Haake and Klaus (2005). Also, we define population-monotonicity and consistency axioms. In particular, we introduce own-side population-monotonicity, which requires that no agent should benefit (loose) from an increase (a decrease) in its own side of the market population, and other-side population-monotonicity, which requires that no agent should loose (benefit) from an increase (a decrease) of the other side of the market population. We prove that the stable correspondence is the only rule that satisfies unanimity, a weak notion of own-side population-monotonicity, and Maskin-monotonicity. Moreover, if a rule satisfies unanimity, a weak notion of own-side population-monotonicity, and a weak notion of consistency, then it is a subsolution of the stable correspondence. Finally, on the smaller domain of separable preferences, we prove that the stable correspondence is single-valued and that many of our results still hold.
British Journal of Industrial Relations, 2007
Games and Economic Behavior, 2015
A set of agents with different waiting costs have to receive a service of different length of tim... more A set of agents with different waiting costs have to receive a service of different length of time from a single provider which can serve only one agent at a time. One needs to form a queue and set up monetary transfers to compensate the agents who have to wait. We prove that no rule satisfies efficiency of queues and coalitional strategy-proofness.
We consider the problem of sharing the cost of a public facility among agents who have different ... more We consider the problem of sharing the cost of a public facility among agents who have different needs for it. We base two characterizations of the sequential equal contributions rule on smallest-cost consistency. Namely, (i) the rule is the only rule satisfying equal treatment of equals, independence of all but the smallest-cost, and smallest-cost consistency, and (ii) it is the only rule satisfying equal share lower bound, cost monotonicity, and smallest-cost consistency.
ABSTRACT This paper studies many-to-one matching markets where each student is assigned to a hosp... more ABSTRACT This paper studies many-to-one matching markets where each student is assigned to a hospital. Each hospital has possibly multiple positions and responsive preferences. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.Roth and Sotomayor (1990) showed that there can be unstable equilibrium outcomes. We prove that any stable matching can be obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the so-called 'rural hospital theorem' cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the particular equilibrium that is reached and (b) welfare levels are not bounded by the student and hospital-optimal stable matchings (with respect to the true preferences).
Social Choice and Welfare, 2014
When allocating a resource, geographical and infrastructural constraints have to be taken into ac... more When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and an agent depicts the possibility of a transfer from the source to the agent. Given the supplies at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on consistent and resource monotonic rules in claims problems that satisfy equal treatment of equals. We call these rules fairness principles and we extend fairness principles to allocation rules on networks. We require that * We would like to thank Paula Jaramillo, Herve Moulin, and William Thomson for detailed comments on an earlier draft of the paper. We also thank the seminar participants
* We would like to thank Bettina Klaus and William Thomson for their helpful and detailed suggest... more * We would like to thank Bettina Klaus and William Thomson for their helpful and detailed suggestions and discussions.
SSRN Electronic Journal
This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a ... more This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents' rankings. Finally, we show that most of our bounds are tight.
A set of agents with possibly different waiting costs have to receive the same service one after ... more A set of agents with possibly different waiting costs have to receive the same service one after the other. Efficiency requires to maximize total welfare. Equity requires to at least treat equal agents equally. One must form a queue, set up monetary transfers to compensate agents having to wait, and not a priori arbitrarily exclude agents from positions. As one may not know agents' waiting costs, they may have no incentive to reveal them. We identify the only rule satisfying Paretoefficiency, a weak equity axiom as equal treatment of equals in welfare or symmetry, and strategyproofness. It satisfies stronger axioms, as no-envy and anonymity. Further, its desirability extends to related problems. To obtain these results, we prove that even non-single-valued rules satisfy Pareto-efficiency of queues and strategy-proofness if and only if they select Pareto-efficient queues and set transfers in the spirit of Groves (1973). This holds in other problems, provided the domain of quasi-linear preferences is rich enough.
Brit J Ind Relat, 2007
We consider the model of two-sided matching with contracts introduced in Hatfield and Milgrom (20... more We consider the model of two-sided matching with contracts introduced in Hatfield and Milgrom (2005) and analyze solutions under variable preferences and populations. Therefore, we study Maskin-monotonicity as introduced by Haake and Klaus (2005). Also, we define population-monotonicity and consistency axioms. In particular, we introduce own-side population-monotonicity, which requires that no agent should benefit (loose) from an increase (a decrease) in its own side of the market population, and other-side population-monotonicity, which requires that no agent should loose (benefit) from an increase (a decrease) of the other side of the market population. We prove that the stable correspondence is the only rule that satisfies unanimity, a weak notion of own-side population-monotonicity, and Maskin-monotonicity. Moreover, if a rule satisfies unanimity, a weak notion of own-side population-monotonicity, and a weak notion of consistency, then it is a subsolution of the stable correspondence. Finally, on the smaller domain of separable preferences, we prove that the stable correspondence is single-valued and that many of our results still hold.
British Journal of Industrial Relations, 2007
Games and Economic Behavior, 2015
A set of agents with different waiting costs have to receive a service of different length of tim... more A set of agents with different waiting costs have to receive a service of different length of time from a single provider which can serve only one agent at a time. One needs to form a queue and set up monetary transfers to compensate the agents who have to wait. We prove that no rule satisfies efficiency of queues and coalitional strategy-proofness.
We consider the problem of sharing the cost of a public facility among agents who have different ... more We consider the problem of sharing the cost of a public facility among agents who have different needs for it. We base two characterizations of the sequential equal contributions rule on smallest-cost consistency. Namely, (i) the rule is the only rule satisfying equal treatment of equals, independence of all but the smallest-cost, and smallest-cost consistency, and (ii) it is the only rule satisfying equal share lower bound, cost monotonicity, and smallest-cost consistency.
ABSTRACT This paper studies many-to-one matching markets where each student is assigned to a hosp... more ABSTRACT This paper studies many-to-one matching markets where each student is assigned to a hospital. Each hospital has possibly multiple positions and responsive preferences. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.Roth and Sotomayor (1990) showed that there can be unstable equilibrium outcomes. We prove that any stable matching can be obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the so-called 'rural hospital theorem' cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the particular equilibrium that is reached and (b) welfare levels are not bounded by the student and hospital-optimal stable matchings (with respect to the true preferences).
Social Choice and Welfare, 2014
When allocating a resource, geographical and infrastructural constraints have to be taken into ac... more When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and an agent depicts the possibility of a transfer from the source to the agent. Given the supplies at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on consistent and resource monotonic rules in claims problems that satisfy equal treatment of equals. We call these rules fairness principles and we extend fairness principles to allocation rules on networks. We require that * We would like to thank Paula Jaramillo, Herve Moulin, and William Thomson for detailed comments on an earlier draft of the paper. We also thank the seminar participants