Entropic selection of Nash equilibrium

This study argues that Nash equilibria with less variations in players' best responses are more appealing. To that regard, a notion measuring such variations, the entropic selection of Nash equilibrium, is presented: For any given Nash equilibrium, we consider the cardinality of the support of a player's best response against others' strategies that are sufficiently close to the behavior specified. These cardinalities across players are then aggregated with a real-valued function on whose form we impose no restrictions apart from the natural limitation to nondecreasingness in order to obtain equilibria with less variations. We prove that the entropic selection of Nash equilibrium is non-empty and admit desirable properties. Some well-known games, each of which display important insights about virtues / problems of various equilibrium notions, are considered; and, in all of these games our notion displays none of the criticisms associated with these examples. These examples also show that our notion does not have any containment relations with other associated and well-known refinements, perfection, properness and persistence

Aggregate efficiency in random assignment problems

We introduce aggregate efficiency (AE) for random assignments (RA) by requiring higher expected numbers of agents be assigned to their more preferred choices. It is shown that the realizations of any aggregate efficient random assignment (AERA) must be an AE permutation matrix. While AE implies ordinally efficiency, the reverse does not hold. And there is no mechanism treating equals equally while satisfying weak strategyproofness and AE. But, a new mechanism, the reservation-1 (R1), is identified and shown to provide an improvement on grounds of AE over the probabilistic serial mechanism of Bogomolnaia and Moulin (2001). We prove that R1 is weakly strategyproof, ordinally efficient, and weak envy--free. Moreover, the characterization of R1 displays that it is the probabilistic serial mechanism updated by a principle decreed by the Turkish parliament concerning the random assignment of new doctors: Modifying the axioms of Hasimoto, et. al. (2012) characterizing the probabilistic serial mechanism to satisfy this principle, fully characterizes R1

Essays in microeconomics theory

This thesis consists of three independent chapters. Each of them represents an area of my research interests. The first chapter of thesis contributes to the Game Theory. We propose a complexity measure and an associated re nement based on the observation that best responses with more variations call for more precise anticipation. The variations around strategy pro les are measured by considering the cardinalities of players' pure strategy best responses when others' behavior is perturbed. After showing that the resulting selection method displays desirable properties, it is employed to deliver a re nement: the tenacious selection of Nash equilibrium. We prove that it exists; does not have containment relations with perfection, properness, persistence and other re nements; and possesses some desirable features. The second chapter of this thesis contributes to the random assignment problem literature. We introduce aggregate e ciency (AE) for random assignments (RA) by requiring higher expected numbers of agents be assigned to their more preferred choices. It is shown that the realizations of any aggregate e cient random assignment (AERA) must be an AE permutation matrix. While AE implies ordinally efficiency, the reverse does not hold. And there is no mechanism treating equals equally while satisfying weak strategyproofness and AE. But, a new mechanism, the reservation-1 (R1), is identi ed and shown to provide an improvement on grounds of AE over the probabilistic serial mechanism of Bogomolnia et al. (2001). We prove that R1 is weakly strategyproof, ordinally e cient, and weak envy{free. Moreover, the characterization of R1 displays that it is the probabilistic serial mechanism updated by a principle decreed by the Turkish parliament concerning the random assignment of new doctors. In the third chapter, we consider a NIRMP matching marketplace consisting of ordered set of doctors and hospitals, and two-stage Interviewing and Preference Reporting Game where hospitals acquire information through interviews and submit contingent rankings to a center enforcing university-optimal matching. In this setting, we provide a `simple' example in which there exist no pure strategy Nash equilibrium. Then, we characterize a domain (of doctors' preferences) where each hospital's interview set forms a `ladder'

Entropic selection of Nash equilibrium

This study argues that Nash equilibria with less variations in players' best responses are more appealing. To that regard, a notion measuring such variations, the entropic selection of Nash equilibrium, is presented: For any given Nash equilibrium, we consider the cardinality of the support of a player's best response against others' strategies that are sufficiently close to the behavior specified. These cardinalities across players are then aggregated with a real-valued function on whose form we impose no restrictions apart from the natural limitation to nondecreasingness in order to obtain equilibria with less variations. We prove that the entropic selection of Nash equilibrium is non-empty and admit desirable properties. Some well-known games, each of which display important insights about virtues / problems of various equilibrium notions, are considered; and, in all of these games our notion displays none of the criticisms associated with these examples. These examples also show that our notion does not have any containment relations with other associated and well-known refinements, perfection, properness and persistence

Tenacious selection of Nash equilibrium

We propose a complexity measure and an associated refinement based on the observation that best responses with more variations call for more precise anticipation. The variations around strategy profiles are measured by considering the cardinalities of players' pure strategy best responses when others' behavior is perturbed. After showing that the resulting selection method displays desirable properties, it is employed to deliver a refinement: the tenacious selection of Nash equilibrium. We prove that it exists; does not have containment relations with perfection, properness, persistence and other refinements; and possesses some desirable features