Browsing by Subject "Game theory."

Now showing 1 - 18 of 18

Open Access
Cloning-proof social choice correspondences
(2011) Öztürk, Zeliha Emel
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. Cloningproofness is the requirement that the social choice rule be insensitive to the replication of alternatives, whereas hereditariness requires insensitivity to withdrawal of alternatives.
Open Access
The coauthors' problem revisited : from networks to covers
(2010) Mermer, Ayşe Gül
In this thesis, we reexamine the Coauthors’ Problem, introduced by Jackson and Wolinsky, 1996. We propose the Extended Coauthor Model using the cover notion, allowing for multilateral links among authors. We study the model under two utility functions, which are the extreme members of the class of utility functions induced by different synergy terms. We find the structure of the efficient and the link-wise stable covers formed under different utility functions, which depend on the synergy term under consideration. Moreover we introduce the core and core stability concepts for covers and investigate the properties possessed by core-stable covers. We find the relationship between the allocation induced by core-stable covers and the allocations in core, under player based flexible allocation rule. Finally we investigate the endogenous cover formation via a strategic form game, called the hyper-link formation game. We define Nash stability and Strong Nash stability for covers and study the characteristics of such covers.
Open Access
Do players learn how to learn? : evidence from conctant sum games with varying number of actions
(2009) Saraçgil, İhsan Erman
This thesis investigates the learning behaviour of individuals in strategic environments that have different complexity levels. A new experiment is conducted in which ascending or descending series of constant sum games are played by subjects and the experimental data including both stated beliefs and actual plays are used to estimate which learning model explains the subjects’ behaviour best within and across these games. Taking learning rules that model the opponent as a learning agent and heterogeneity of the population into consideration, the estimation results support that people switch learning rules across games and use different models in different games. This game-dependency is confirmed by both action, beliefs and the joint estimations. Although their likelihoods vary from game to game, best response to uniform beliefs and reinforcement learning are the most commonly used learning rules in the four games considered in the experiment, while fictitious play and iterations on that are rare instances observed only in estimation by stated beliefs. Despite the change across games, there is no significant link between complexity of the game and the cognitive hierarchy of learning models. Belief statements and best response behaviour also differ across games as we observepeople making smoother guesses in large action games and more dispersed beliefs statements in small action games. Inconsistency between actions and stated beliefs is stronger in large action games. The evidence strongly supports that learning and belief formation are both game-dependent.
Open Access
Essays on endogenous time preference and strategic interaction
(2013) Turan, Agah Reha
This thesis includes three self contained essays on the existence and qualitative properties of equilibrium dynamics under endogenous time preference. In the Örst essay, we reconsider the optimal growth model proposed by Stern (2006). We prove the almost everywhere di§erentiability of the value function and uniqueness of the optimal path, which were left as open questions and show how a small perturbation to the price of future oriented capital qualitatively changes the equilibrium dynamics. Almost none of the studies on endogenous time preference consider the strategic interaction among the agents. In the second essay, by considering a strategic growth model with endogenous time preference, we provide the su¢ cient conditions of supermodularity for dynamic games with open-loop strategies and show that the stationary state Nash equilibria tend to be symmetric. We numerically show that the initially rich can pull the poor out of poverty trap even when sustaining a higher level of steady state capital stock for itself. Lastly, in the third essay, we consider the socially determined time preference which depends on the level of Ösh stock and characterize the basic Öshery model under this setup. We provide existence of collusive and open-loop Nash equilibria and compare the e¢ ciency and qualitative properties of them.
Open Access
Essays on non-cooperative inventory games
(2012) Körpeoğlu, Evren
In this thesis we study different non–cooperative inventory games. In particular, we focus on joint replenishment games and newsvendor duopoly under asymmetric information. Chapter 1 contains introduction and motivation behind the research. Chapter 2 is a preliminary chapter which introduce basic concepts used in the thesis such as Nash equilibrium, Bayesian Nash equilibrium and mechanism design. In Chapter 3, we study a non-cooperative game for joint replenishment of multiple firms that operate under an EOQ–like setting. Each firm decides whether to replenish independently or to participate in joint replenishment, and how much to contribute to joint ordering costs in case of participation. Joint replenishment cycle time is set by an intermediary as the lowest cycle time that can be financed with the private contributions of participating firms. We consider two variants of the participation-contribution game: in the single–stage variant, participation and contribution decisions are made simultaneously, and, in the two-stage variant, participating firms become common knowledge at the contribution stage. We characterize the behavior and outcomes under undominated Nash equilibria for the one-stage game and subgame-perfect equilibrium for the two-stage game. In Chapter 4, we extend the private contributions game to an asymmetric information counterpart. We assume each firm only knows the probability distribution of the other firms’ adjusted demand rates (demand rate multiplied by inventory holding cost rate). We show the existence of a pure strategy Bayesian Nash equilibrium for the asymmetric information game and provide its characterization. Finally, we conduct some numerical study to examine the impact of information asymmetry on expected and interim values of total contributions, cycle times and total costs. quantities for all firm types except the type that has the highest possible unit cost, who orders the same quantity as he would as a monopolist newsboy. Consequently, competition leads to higher total inventory in the industry. A firm’s equilibrium order quantity increases with a stochastic increase in the total industry demand or with an increase in his initial allocation of the total industry demand. Finally, we provide full characterization of the equilibrium, corresponding payoffs and comparative statics for a parametric special case with uniform demand and linear market shares.
Open Access
Extension of some results from networks to covers
(2008) Per, Emre
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.
Open Access
Extension of symmetric connections model
(2010) Taşcıer, Mehpare Şule
In this thesis, we study an extension of symmetric connections model, which is presented by Matthew O. Jackson and Asher Wolinsky in their paper entitled, “A Strategic Model of Social and Economic Networks”. We examined the network formation process through a dynamic framework where self-interested individuals can form links, then we analyze to which network structures this process converges.
Open Access
First price auctions under prospect theory with linear probability weighting
(2011) Keskin, Kerim
Overbidding in first-price sealed-bid auctions is a well-known result in the auction theory literature. For the possible reasons behind this phenomenon, economists provided many explanations; such as risk aversion, regret theory, and subjective probability weighting. However, for subjective probability weighting to explain overbidding, the probability weighting function (PWF) is needed to be underweighting all probabilities. Such a function is not in accord with PWFs in the prospect theory literature as it suggests a specific function which satisfies certain properties. In this paper we investigate, to what extent prospect theory is able to explain overbidding by using a linear PWF satisfying all of the axiomatic properties (Currim and Sarin, 1989). Moreover, we introduce a non-zero reference point, fully utilizing prospect theory. Our results show that, subjective probability weighting alone is unable to explain overbidding. However, with the non-zero reference point assumption, we obtain partial overbidding.
Open Access
A game theoretic analysis of the Second Punic war
(2013) Altınbay, Egehan Hayrettin
This thesis, through a game theoretic methodology, aims to build an accurate game theoretic model of the Second Punic War, and tries to analyze the military strategies and actions taken by the Carthaginian and Roman Republics. After observing that the modeling literature concerning the game theoretic studies of war has generally analyzed the wars beginning from the 19th century, this thesis also aims to provide a contribution to the game theoretic literature by constructing a model that displays the strategic interaction between Rome and Carthage. By starting from the question of how one could game theoretically model the Second Punic War and what argumentations would such a model would give, the work presented here compiles the available historical information regarding the military choices of the two Republics, and by using those literary findings, tries to explain the reasons behind Carthage’s offense and Rome’s defense choices. By arguing that the findings through game theoretic analysis is compatible with the historical literary evidence, iv the model also reveals novel argumentations concerning under what conditions both states would or would not prefer a particular military action.
Open Access
Games of sharing airport costs
(2009) Yüksel, Ayşe Müge
In this study, noncooperative games defined for various cooperative solution concepts in airport problems have been addressed. The existence of a relationship between the design of the games and the equilibrium outcomes has been investigated. This study explores the conditions where, in a noncooperative game designed with downstream-subtraction consistent or uniform-subtraction consistent solution concept, the cost allocation proposed by this cooperative solution concept appears as the Nash outcome. Then, the uniqueness of this equilibrium has been examined.
Open Access
Implementation in dominant strategy equilibrium
(1995) Kıbrıs, Özgür
A social choice rule is any proposed solution to the problem of collective decision making and it embeds the normative features that can be attached to the mentioned problem. Implementation of social choice rules in dominant strategy equilibrium is the decentralization of the decision power among the agents such that the outcome that is a priori recommended by the social choice rule can be obtained as a dominant strategy equilibrium outcome of the game form which is endowed with the preferences of the individuals. This work has two features. First, it is a survey on the literature on implementation in dominant strategy and its link with the economic theory. Second, it constructs some new relationships among the key terms of the literature. In this framework, it states and proves a slightly generalized version of the Gibbard-Satterthwaite impossibility theorem. Moreover, it states and proves that the cardinality of a singlepeaked domain converges to zero as the number of alternatives increase to infinity.
Open Access
Limit sets of best-reply processes
(2007) Aköz, Kemal Kıvanç
I analyze limiting behavior of best-reply processes. I find that without inertia Nash Equilibria are not limit sets. Moreover, even for processes with inertia, Nash Equilibria are not stable. I argue that minimal CURB sets are reasonable candidates for limit sets if best-reply processes are indeterminate or Nash Equilibria satisfy evolutionary stability (Oechssler 1997). In such cases, limit sets necessarily contain a Nash Equilibrium. Otherwise limit sets may not be close to any Nash Equilibria unless they satisfy some support consistency condition.
Open Access
A model of boundedly rational learning in dynamic games
(1997) Aksoy, Hakan
There are various computer-based algorithms about boundedly rational players’ learning how to behave in dynamic games, including classifier systems, genetic algorithms and neural networks. Some examples of studies using boundedly rational players are Axelrod (1987), Miller (1989), Andreoni and Miller (1990) who use genetic algorithm and Marimon etal. (1990) and Arthur (1990) who use classifier systems. In this dissertation, a Two Armed Bandit Problem and the KiyotakiWright (1989) Economic Environment are constructed and the learning behaviour ol the boundedly rational players is observed by using classifier systems in computer programs. From the simulation results, we observe that experimentation and imitation enables faster convergence to the correct decision rules of players in both repeated static decision problems and dynamic games.
Open Access
Nash bargaining solution under predonation
(2008) Akyol, Ethem
We consider two person bargaining problems under predonation. Before the bargaining solution is applied we allow the alteration of the bargaining set by means 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 next stage.We firstly concentrate on the simple bargaining problems with bargaining sets that have linear pareto frontier and show that the stronger bargainer (with greater ideal payoff) giving a pre-donation, her best pre-donation transforming the bargaining set into one on which the Nash bargaining solution distributes payoffs so that while other bargainer gets exactly the same payoff (as applied to the original simple bargaining problem), stronger bargainer makes strictly better off. Then, we look for Stackelberg and Nash equilibria of the so called ”predonation game”. Furthermore, we list our results for two by two normal form games.
Open Access
Nash equilibria in claim based estate division problems
(2014) İnel, Abdulkadir
Estate division game is an allocation of an estate between players based on a rule. In this thesis, we consider estate division games and study the necessary and sufficient conditions for division rules under which Nash equilibria induce equal division. Ashlagi, Karag¨ozoˇglu, Klaus (2012) introduce classes of properties for division rules and show that they are sufficient for all Nash equilibria to induce equal division. In this study, we propose a different property, namely conditional full compensation, and prove that it is also a sufficient condition for division rules in order for all Nash equilibria outcomes under these rules to be equal division. We, then, show that under any rule satisfying claims boundedness and conditional equal division lower bound, equal division is a Nash equilibrium outcome. Finally, we prove that letting at least one player get more than the difference between the whole estate and the sum of other players’ claims is a necessary condition for all Nash equilibria to induce equal division.
Open Access
A new approach to age and risk taking behavior of agents
(2012) Kozan, Zeynep
In this thesis, we use evolutionary game theory techniques to analyze the relation between risk taking behavior of agents and their ages. We suppose that risk aversion is the stable pattern for the old agents and risk seeking is the stable pattern for the young agents as it is commonly assumed so in economics literature. First, we solve a benchmark model without heterogeneity in terms of age di§erentiations. In such a case, we observe that mutation either increases or decreases with respect to the payo§ levels, depending on the initial Ötness levels of the population groups. In the second step, we introduce heterogeneous population frontier. The anticipated level of the initial mutant proportion provides incentives to triger the evolution. Then, we analyze numerically the e§ects of the initial level of Ötness, initial risk averse and risk seeking proportions on the pattern of the evolution process. Finally, we studied the intertemporal e§ects of di§erent risk averse and risk seeking population proportions on mutation.
Open Access
On stability and efficiency in different economic environments
(2011) Karakaya, Mehmet
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 (ET EA), is introduced, and it is shown that if a social choice rule is implementable via some Rechtsstaat satisfying ET EA 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.
Open Access
Preservation of implementability under algebraic operations
(2011) Doğan, Serhat
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 first 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 exemplifies the potential use of our findings for further research.