Theses supervised by Prof. Dr. Semih Koray
21 theses · İhsan Doğramacı Bilkent University
Faydanın yarı aktarılabilir olduğu durumlarda işbirlikli davranışın incelenmesi
The primary purpose of this study is to analyze both cooperative and noncooperative games under semitransferable utility. In game theory literature, utility seems so far to have been assumed not to be transferable at all in noncooperative games, while both fully transferable and nontransferable utility are considered in the context of cooperative games. There are, however, an abundance of real life situations, where utility is partially transferable. Here we introduce the notion of semitransferable utility, which encompasses full-transferability and nontransferability as its two extreme special subcases. We explore and exemplify what changes some well-known equilibrium notions undergo when one allows utility to be only partially transferable. In particular, we relate core allocations in a convex cooperative transferable utility (TU) game to their counterparts in a corresponding strategic context, to show that, for each core allocation of a given TU game, there is a strategic form game, where that allocation survives, while almost all other allocations are eliminated.
Nash-uygulanabilir sosyal seçim kurallarının nötrallik aracığıyla yeni bir karakterizasyonu
In this thesis, we study Nash implementability of social choice rules in relation with the neutrality notion. Several works in the literature provide a characterization of Nash-implementable social choice rules. However, they do not explicitly show the degree of neutrality property in the Nash equilibrium concept which is also existing in Nash-implementable rules. In this study, we define a weak version of the neutrality condition critical neutrality which is associated with the critical domain of a social choice rule. The critical neutrality notion when conjoined with Maskin monotonicity turns out to be equivalent to Nash implementability. Moreover, we propose an algorithm to obtain a maximal domain of preference profiles on which a specified social choice rule is Nash-implementable, by utilizing critical neutrality as a tool. The main result of the thesis is in support of the view that implementability on the full domain of preference profiles is highly related with implementability on the critical domain in Nash equilibrium and possibly, in other solution concepts.
Yoldan bağımsız seçme kurallarının Aizerman ve Malishevski temsilini inceltmeye yönelik araştırmalar
This dissertation consists of four main parts in which we explore Aizerman Malishevski's representation result for path independent choice rules. Each path independent choice rule is known to have a maximizer-collecting (MC) representation: There exists a set of priority orderings such that the choice from each choice set is the union of the priority orderings' maximizers (Aizerman and Malishevski, 1981). In the first part, we introduce the maximal and prime sets to characterize all possible MC representations and show that the size of the largest anti-chain of primes determines its smallest size MC representation. In the second part, we focus on q-acceptant and path independent choice rules. We introduce prime atoms and prove that the number of prime atoms determines the smallest size MC representation. We show that q-responsive choice rules require the maximal number of priority orderings in their smallest size MC representations among all q-acceptant and path independent choice rules. In the third part, we aim to generalize q-responsive choice rules and introduce responsiveness as a choice axiom. In order to provide a new representation for responsive and path independent choice rules, we introduce weighted responsive choice rules. Then, we show that all responsive and path independent choice rules are weighted responsive choice rules with an additional regularity condition. In the final part, we focus on the assignment problem. In this problem, Probabilistic Serial assignment is always sd-efficient and sd--envy-free. We provide a sufficient and almost necessary condition for uniqueness of sd-efficient and sd--envy-free assignment via a connectedness condition over preference profile.
Kota ve bütçe kısıtları altında doktora kabul problemi
In this thesis, we have studied the graduate admission problem with quota and budget constraints as a two sided matching market. We constructed algorithms which are extensions of the Gale - Shapley algorithm and showed that if the algorithms stop then the resulting matchings are core stable (and thus Pareto optimal). However the algorithms may not stop for some problems. Also it is possible that the algorithms do not stop and there is a core stable matching. Also there is no department optimal matching and no student optimal matching under budget constraints. Hence straightforward extensions of the Gale - Shapley algorithm do not work for the graduate admission problem with quota and budget constraints. The presence of budget constraints play an important role in these results. Keywords: pairwise stable matching, core stable matching, Pareto optimal match ing, the Gale - Shapley algorithm, quota and budget constraints.
Sistemik risk ve iflas sigortası ile ağ oluşumu
In this paper, we study the networks that arise in the equilibrium when risk averse investors play a network formation game for making joint investments with each other. The outcomes of these projects are stochastic and hence, depending on the shock realizations, investors may choose to default. However, counterparty defaults are damaging and investors have the option to buy default insurances against this damage. We show that in this model, equilibrium networks consist of complete components of a certain size, which maximize the expected utility of investors in that component. For a wide variety of parameters, it turns out that investors choose not to buy any insurance at the equilibrium. Keywords: Default Insurance, Network Formation, Risk Aversion, Strong-Stability, Systemic Risk.
Erkek-optimal eşleşmelerin alt-oyun-yetkin uygulanması
In this study, we explore monotonicities and implementability of different matching rules. We find a self-monotonicity of the stable rule and an \textit{h}-monotonicity for the men-optimal rule, which does not satisfy Maskin-monotonicity. We then offer a sequential matching mechanism that implements the men-optimal rule in subgame perfect equilibrium, when there is no other matching that weakly Pareto-dominates the men-optimal matching for men. In our mechanism, women propose to men in an arbitrary hierarchy order, and each man either accepts or rejects the proposals he receives, where accepting means permanent matching with the proposing woman.
X-kendini seçerlik üzerine incelemeler
X-self selectivity of a social choice function is de ned as being self selective relative to the set of test functions X and all of its subsets. We explore the self-selectivity of social choice functions which satisfy independence of irrelevant alternatives, against different kinds of sets of test functions. We observe that testing against a smaller set can be sufficient to deduce that a given social choice function is also self-selective relative to a larger set, under certain conditions. Moreover, we show that X-self selectivity is closed under set intersection and union. This leads to the notion of degree of self-selectivity, which allows us to compare the self-selectivities of two social choice functions under certain conditions.
Ağ çekirdekleri ve dışbükeylik üzerine bazı gözlemler
In this study, we analyze the relationships between the value function - allocation rule setting and the TU game setting induced by value functions. As several different value functions may induce the same TU game, there is some information lost when passing to the TU game setting. We inquire in this study the impact of this lost information upon the preservation of the nonemptiness of the core when we pass from the network to the TU game setting. We pass from a value function to a TU game by associating with each coalition the maximal value of the graphs this coalition can form under the given value function. Conversely, we may associate with each TU game one of the value functions that induce the given TU game. Keeping this fixed, we define the network core as the collection of graphs where no coalition has an incentive to change the cooperation structure in itself, assuming that the rest of the society consists of isolated agents. Besides, we define convexity in the value function setting in an manalogous fashion to convexity for the TU games. As convexity implies the nonemptiness of the core in both settings (a well-known result in the TU setting, and a trivial one in the value function setting), we inquire if convexity is preserved in passing from one setting to the other. We find that convexity of the value function is equivalent to a stronger type of convexity of the induced game. Keywords: value function, convexity, network core IV
Şeçmen Sayısı büyük seçimlerde bilgi üzerinden manipülasyon
This thesis studies manipulations of equilibria by candidates in two-alternativeelections along with their effects on voter turnout, winner of the election and socialwelfare where voters have common values, and both voting and manipulating are costly.We show that manipulation is not desirable for the society, and the candidates? incentivesfor manipulating can be mitigated by appropriately sequencing the order ofmanipulations. We present some results of a manipulation game which may ratherunexpected under the assumption that the candidates have prior beliefs about each others?manipulations. Finally we determine the set of manipulations which can be prevented byinformed voters for a given composition of society.
Tarihsel olarak standart olan tanım bölgelerinde imkansızlık sonuçları geçerli olmayı sürdürür mü?
One of the major assumptions common to all impossibility results in socialchoice theory is that of ?full? or rich enough domain. Thus, a major streamof attempts has focused on how to restrict the domains of social choice functionsin order to escape impossibilities, without paying much attention to thequestion of whether there exist actual societies with such restricted domainsof preference profiles, however. The notion of an unrestricted domain is basedon the assumption that the individuals form their preferences independentof each other. If one replaces this assumption by one under which individualpreferences are clustered around a ?social norm? in a unipolar standard society,the question of how this kind of restricted domain restriction influencesthe existence of a Maskin monotonic, surjective and nondictatorial socialchoice function becomes important.We employ the so-called Manhattan metric to measure the degree of howclustered a society around a social norm is. We then try to characterize forwhat degrees of clustering around a social norm allows us to escape impossibilityresults, in an attempt to shed some light on the question of whetherimpossibilities in social choice theory arise assuming the existence of historicallyimpossible societies.
Ağlardaki bazı sonuçların örtülere genişletilmesi
In this thesis, we use covers as an extension of networks. The cover notion is almost the same as the conference structure that is proposed by Myerson. However, we extend several notions pertaining to networks to covers in different ways, reflecting the differences in our points of departure. In this framework, we extend the result of Jackson and Wollinsky(1996) to covers which provides a characterization of the Shapley-Myerson allocation rule in terms of component balancedness and equal bargaining power in networks.
Önden bağış altında Nash pazarlık çözümü
We consider two person bargaining problems under predonation. Before thebargaining solution is applied we allow the alteration of the bargaining set bymeans of pre-donations of a share in one?s would-be payoffs to one?s opponent.Thus, a pre-bargain stage is instituted in which the bargainers may manipulate,via pre-donations, the (Nash) bargaining solution as applied in the nextstage.We firstly concentrate on the simple bargaining problems with bargainingsets that have linear pareto frontier and show that the stronger bargainer(with greater ideal payoff) giving a pre-donation, her best pre-donation transformingthe bargaining set into one on which the Nash bargaining solutiondistributes payoffs so that while other bargainer gets exactly the same payoff(as applied to the original simple bargaining problem), stronger bargainermakes strictly better off. Then, we look for Stackelberg and Nash equilibriaof the so called ?predonation game?. Furthermore, we list our results for twoby two normal form games.
Haklar yapısı aracılığıyla uygulanabilirlik
Implementation of a social choice rule can be thought of as a design of power(re)distribution in the society whose ?equilibrium outcomes? coincide withthe alternatives chosen by the social choice rule at any preference profile ofthe society. In this paper, we introduce a new societal framework for implementationwhich takes the power distribution in the society, representedby a code of rights, as its point of departure. We examine and identify howimplementation via code of rights (referred to as gamma implementation) isrelated to classical Nash implementation via mechanism. We characterizegamma implementability when the state space on which the rights structureis to be specified consists of the alternatives from which a social choice is to bemade. We show that any social choice rule is gamma implementable if it satisfiespivotal oligarchic monotonicity condition that we introduce. Moreover,pivotal oligarchic monotonicity condition combined with Pareto optimalityis sufficient for a non-empty valued social choice rule to be gamma implementable.Finally we revisit liberal?s paradox of A.K. Sen, which turns outto fit very well into the gamma implementation framework.
Evrensel seçmede-kapalı sosyal seçim fonksiyonu aileleri
In this thesis, we introduce a new notion of consistency for families of social choice functions, called selection-closedness. This concept requires that every member of a family of social choice functions that are to be employed by a society to make its choice from an alternative set it faces, should choose a member of the given family, when it is also employed to choose the socialchoice function itself in the presence of other rival such functions along with the members of the initial family. We show that a proper subset of neutral social choice functions is universally selection-closed if and only if it is a subset of the set of dictatorial and anti-dictatorial social choice functions. Finally, we introduce a weaker version of selection-closedness and conclude that a "rightextendable scoring correspondence" is strict if and only if the set consisting of its singleton valued renements is universally weakly selection-closed.Keywords: Social Choice, Self-selectivity, Selection-Closed, Weakly Selection-Closed, Scoring Correspondence.
Tedüzelik üzerine bazı sonuçlar
In this thesis, we investigate several issues concerning social choice rules whichsatisfy different degrees of Maskin type monotonicities. Firstly, we introduceg-monotonicity and monotonicity region notions which enable one to comparemonotonicity properties of non-Maskin-monotonic social choice rules. Wecompare self-monotonicities of standard scoring rules and study monotonicityof Majoritarian compromise. Secondly we determine domains of impossibilityand possibility when the individual preferences are clustered around twoopposing norms and the degree of clustering is measured via the Manhattanmetric. In the last chapter we investigate the relation between monotonicityand dictatoriality when agents are allowed to have thick indifference classes.
Genelleştirilmiş Condorcet kuralları ile kendini-seçerliğin ölçülmesi
In this thesis, we introduce a method to measure self-selectivity of social choice functions. Due to Koray [2000], a neutral and unanimous social choice function is known to be universally self-selective if and only if it is dictatorial. Therefore, in this study, we confine our set of test social choice functions to particular singleton-valued refinements of generalized Condorcet rules. We show that there are some non-dictatorial self-selective social choice functions. Moreover, we define the notion of self-selectivity degree which enables us to compare social choice functions according to the strength of their self-selectivities. We conclude that the family of generalized Condorcet functions is an appropriate set of test social choice functions when we localize the notion of self-selectivity.
Çeşitli iktisadi ortamlarda kararlılık ve verimlilik üzerine
This thesis consists of four main chapters. In the first main part, hedonic coalition formation games where each player's preferences rely only upon the members of her coalition are studied. A new stability notion under free exit-free entry membership rights, referred to as strong Nash stability, is introduced which is stronger than both core and Nash stabilities studied earlier in the literature. The weak top-choice property is introduced and shown to be sufficient for the existence of a strongly Nash stable partition. It is also shown that descending separable preferences guarantee the existence of a strongly Nash stable partition. Strong Nash stability under different membership rights is also studied. In the first main part, hedonic coalition formation games are also extended to cover formation games, where a player can be a member of several different coalitions, and these games are studied. In the second main part, Nash implementability of a social choice rule (via a mechanism) which is implementable via a Rechtsstaat is studied. A new condition on a Rechtsstaat, referred to as equal treatment of equivalent alternatives (ETEA), is introduced, and it is shown that if a social choice rule is implementable via some Rechtsstaat satisfying ETEA then it is Nash implementable via a mechanism provided that there are at least three agents in the society. In the third main part, a characterization of the Borda rule on the domain of weak preferences is studied. A new property, which is referred to as the degree equality, is introduced, and it is shown that the Borda rule is characterized by weak neutrality, reinforcement, faithfulness and degree equality. In the fourth main part, the graduate admissions problem with quota and budget constraints is studied as a two sided many to one matching market. The students proposing algorithm, which is an extension of the Gale-Shapley algorithm, is constructed, and it is shown that the students proposing algorithm ends up with a core stable matching if the algorithm stops. However, there exist graduate admissions problems for which there exist core stable matchings, while neither the departments proposing nor the students proposing algorithm stops. It is proved that the students proposing algorithm stops if and only if no cycle occurs in the algorithm. It is also shown that no random path to core stability for the graduate admissions problem exists.
Klonlamaya karşı dirençli sosyal seçim kuralları
In this thesis study, we provide axiomatic characterizations of the well-known Condorcet and Plurality rules via consistency axioms when the alternative set is endogeneous, namely hereditariness and cloning-proofness. Cloning-proofness is the requirement that the social choice rule be insensitive to the replication of alternatives, whereas hereditariness requires insensitivity to withdrawal of alternatives.
Uygulanabilirliğin cebirsel işlemler altında korunması
In this thesis, we investigate whether union and intersection preserve Nash and subgame perfect implementability. Nash implementability is known to be preserved under union. Here we rst show that, under some reasonably mild assumptions, Nash implementability is also preserved under intersection. The conjunction of these two results yields an almost lattice-like structure for Nash implementable social choice rules. Next, we carry over these results to subgame perfect implementability by employing similar arguments. Finally, based on the fact that Nash implementable social choice rules are closed under union, we provide a new characterization of Nash implementability, which also exemplies the potential use of our ndings for further research.
Farklı haklar yapıları altında örtülerin kararlılığı
A country?s social welfare depends on firms? profits and consumers? surplus. Given unions of countries, a country?s aim is to maximize its own social welfare when it decides to enter or exit a union. For examining unions, we use the notion of a cover as elaborated in Koray (2007).We utilize the findings of İlkiliç(2010) about the Cournot equilibrium in our setting to examine core stability and efficiency of covers of countries.We adapt different rights? structures based on; free exit, free entry, approved exit and approved entry introduced by Sertel (1992) to the context of covers, along with introducing some stronger structures and study how stability of covers varies when linkage costs are imposed upon countries.
Ortanca kuralı ve çoğunlukçu uzlaşı
In this thesis, we analyze the relationship between Majoritarian Compromise (Sertel & Y lmaz, 1984) and the Median Rule (Basset & Persky, 1999). We show that, for the populations with odd size, these two rules are equivalent and we describe the relationship for the case where population size is even. Then, we explore some axiomatic properties of Median Rule. It turns out that Median Rule satis es all properties that Majoritarian Compromise sat- is es in Sertel and Y lmaz (1999) and it fails all properties that Majoritarian Compromise fails in Sertel and Y lmaz (1999). We, then, introduce two ax- ioms which di erentiate these rules. We conclude that, the Median Rule can be considered as a viable alternative to Majoritarian Compromise, as it satis- es all axioms that Majoritarian Compromise is known to satisfy except one particular axiom. Keywords: Social Choice, Majoritarian Compromise, Median Rule, Subgame Perfect Implementability