A new epistemic model

Meier (2012) gave a "mathematical logic foundation" of the purely measurable universal type space (Heifetz and Samet, 1998). The mathematical logic foundation, however, discloses an inconsistency in the type space literature: a finitary language is used for the belief hierarchies and an infinitary language is used for the beliefs. In this paper we propose an epistemic model to fix the inconsistency above. We show that in this new model the universal knowledgebelief space exists, is complete and encompasses all belief hierarchies. Moreover, by examples we demonstrate that in this model the players can agree to disagree Aumann (1976)'s result does not hold, and Aumann and Brandenburger (1995)'s conditions are not sufficient for Nash equilibrium. However, we show that if we substitute selfevidence (Osborne and Rubinstein, 1994) for common knowledge, then we get at that both Aumann (1976)'s and Aumann and Brandenburger (1995)'s results hold.

Three essays on trade and investment

From H. G. Johnson's work (Review of Economic Studies, 1953–54) on tariff retaliation, the questions of whether a country can win a “tariff war” and how or even the broader question of what will affect a country's strategic position in setting bilateral tariff have been tackled in various situations. Although it is widely accepted that a country will have strategic advantages in winning the tariff war if its relative monopoly power is sufficiently large, it is unclear what are the forces behind such power formation. The goal of this research is to provide a unified framework and discuss various forces such as relative country size, absolute advantages and relative advantages simultaneously. In a two-country continuum-of-commodity neoclassical trade model, it is shown that sufficiently large relative country size is a sufficient condition for a country to choose a non-cooperative tariff Nash equilibrium over free trade. It is also shown that technology disparities such as absolute advantage, rate of technology disparity and the distribution of the technology disparity all contribute to a country's strategic position and interact with country size. ^ Leverage effect is usually used to explain the phenomenon of asymmetric volatility in equity returns. However, leverage itself can only account for parts of the asymmetry. In this research, it is shown that stock return volatility is related to firms’ financial status. Financially constrained firms tend to be more sensitive to the return changes. Financial constraint factor explains why some firms tend to be more volatile than others. I found that the financial constraint factor explains the stock return volatility independent of other factors such as firm size, industry affiliation and leverage. Firms’ industry affiliations are shown to be very weak in differentiating volatility. Firm size is proven to be a good factor in distinguishing the different levels of volatility and volatility-return sensitivity. Leverage hypothesis is also partly corroborated and the situation where leverage effect is not applicable is discussed. Finally, I examined the macroeconomic policy's effects on overall market volatility. ^

Strategic interactions of urban land developers in the housing market

This thesis studies the supply side of the housing market taking into account the strategic interactions that occur between urban land developers. The thesis starts by reviewing the literature on new housing supply, concluding that there are very few studies where strategic interactions are taken into account. Next, we develop a model with two urban land developers, who rst decide the quality of housing and then compete in prices, considering that the marginal production costs depend on the housing quality. First, we analyze the price competition game and characterize the Nash equilibrium of the price game. Finally, we examine the rst stage of the game and determine numerically the subgame perfect Nash equilibrium (SPNE) of the quality-price game. In the price competition game, our results show that the equilibrium price of an urban land developer is an increasing function of its own quality, while it is a non-monotonic function of the rival s quality. The behavior of the equilibrium pro ts reveals that, in general, urban land developers gain by di¤erentiating their quality. However, the urban land developer located at the Central Business District (CBD), may prefer to have the same quality than the rival when transportation costs are high by exploiting its locational advantage. The analysis of the rst stage of the game also reveals that, in general, the rms best response is to di¤erentiate their quality and that, in most cases, there are two subgame perfect Nash equilibria that involve quality di¤erentiation. However, the results depend on transportation costs and the quality valuation parameter. For small quality valuations, in equilibrium, the market is not fully covered and, if the unit transportation costs are high, only the urban land developers located at the CBD operates. For higher quality valuations, all the consumers are served. Furthermore, the equilibrium qualities and pro ts are increasing with quality valuation parameter. RESUMO: Esta tese estuda a oferta no mercado da habitação, tendo em conta as interações es- tratégicas que ocorrem entre os produtores de habitação. A tese revê a literatura sobre a oferta de habitação, concluindo que existem poucos estudos que tenham tido em conta as interações estratégicas. De seguida, desenvolvemos um modelo com dois produtores de habitação, que primeiro decidem a qualidade da habitação e depois competem em preços, considerando que os custos marginais de produção dependem da qualidade. Primeiro analisamos o jogo em preços e caracterizamos o equilíbrio de Nash. Posteriormente, ex- aminamos o primeiro estágio do jogo e determinamos numericamente o equilíbrio perfeito em todos os subjogos (SPNE) do jogo. No jogo de competição em preços, os resultados mostram que, o preço de equilíbrio, é uma função crescente da qualidade da habitação, sendo uma função não monótona da qualidade do rival. O lucro de equilíbrio revela que, geralmente, os produtores de habitação têm ganhos em diferenciar a qualidade. No entanto, o produtor localizado no Centro (CBD), pode preferir oferecer a mesma qualidade que o rival, caso os custos unitários de transporte sejam elevados, através da sua vantagem de localização. A análise do primeiro estágio do jogo, revela que, geralmente, a melhor resposta de um produtor é a de diferenciar a qualidade. Na maior parte dos casos existem dois SPNE que envolvem essa diferenciação. No entanto, os resultados dependem dos custos unitários de transporte e da valorização da qualidade por parte do consumidor. Para uma reduzida valorização da qualidade, em equilíbrio, o mercado não é totalmente coberto e, se o custo unitário de transporte é elevado, apenas o produtor localizado no CBD opera no mercado. Para uma valorização elevada da qualidade, todos os consumidores são servidos. Além disso, as qualidades e os lucros de equilíbrio são crescentes com a valorização da qualidade.

Essays on Matching Markets and Their Equilibria

Matching theory and matching markets are a core component of modern economic theory and market design. This dissertation presents three original contributions to this area. The first essay constructs a matching mechanism in an incomplete information matching market in which the positive assortative match is the unique efficient and unique stable match. The mechanism asks each agent in the matching market to reveal her privately known type. Through its novel payment rule, truthful revelation forms an ex post Nash equilibrium in this setting. This mechanism works in one-, two- and many-sided matching markets, thus offering the first mechanism to unify these matching markets under a single mechanism design framework. The second essay confronts a problem of matching in an environment in which no efficient and incentive compatible matching mechanism exists due to matching externalities. I develop a two-stage matching game in which a contracting stage facilitates subsequent conditionally efficient and incentive compatible Vickrey auction stage. Infinite repetition of this two-stage matching game enforces the contract in every period. This mechanism produces inequitably distributed social improvement: parties to the contract receive all of the gains and then some. The final essay demonstrates the existence of prices which stably and efficiently partition a single set of agents into firms and workers, and match those two sets to each other. This pricing system extends Kelso and Crawford's general equilibrium results in a labor market matching model and links one- and two-sided matching markets as well.

EXISTENCE OF UNUSED MANAGED CAPACITY ON DEDICATED LANES AND AN ALTERNATIVE ON HOW TO SELL IT VIA AUCTIONS

This dissertation verifies whether the following two hypotheses are true: (1) High-occupancy/toll lanes (and therefore other dedicated lanes) have capacity that could still be used; (2) such unused capacity (or more precisely, “unused managed capacity”) can be sold successfully through a real-time auction. To show that the second statement is true, this dissertation proposes an auction-based metering (ABM) system, that is, a mechanism that regulates traffic that enters the dedicated lanes. Participation in the auction is voluntary and can be skipped by paying the toll or by not registering to the new system. This dissertation comprises the following four components: a measurement of unused managed capacity on an existing HOT facility, a game-theoretic model of an ABM system, an operational description of the ABM system, and a simulation-based evaluation of the system. Some other and more specific contributions of this dissertation include the following: (1) It provides a definition and a methodology for measuring unused managed capacity and another important variable referred as “potential volume increase”. (2) It proves that the game-theoretic model has a unique Bayesian Nash equilibrium. (3) And it provides a specific road design that can be applied or extended to other facilities. The results provide evidence that the hypotheses are true and suggest that the ABM system would benefit a public operator interested in reducing traffic congestion significantly, would benefit drivers when making low-reliability trips (such as work-to-home trips), and would potentially benefit a private operator interested in raising revenue.

Hotelling-downs competition with free entry when voters have an option to contest

Osborne shows that for almost all distributions of voters' preferences, a pure strategy Nash equilibrium does not exist in the classical Hotelling-Downs model of electoral competition with free entry. We show that equilibrium is generically possible if in addition one allows voters an option to announce their candidacy to compete side-by-side with office-seeking players. The model studied in this paper renders Osborne and the celebrated citizen-candidate model à la Osborne and Slivinski as two extreme cases. We characterize the equilibrium set with two central questions: (i) can there be equilibria where only voters contest? and (ii) are equilibria with contesting office-seeking players possible? We also show that in our general setting, extremists are typically voter-candidates so that in every two-party contest, office-seeking politicians stay out of competition.

A location game on disjoint circles

Two players are endowed with resources for setting up N locations on K identical circles, with N > K < 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. They face a resource mobility constraint such that not all N locations can be placed in the first round. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that for K = 1, the second mover always has a winning strategy in this game. In this paper we show that with K > 1, the second mover advantage disappears as in this case both players have a tying strategy. We also study a natural variant of this game where the resource mobility constraint is more stringent so that in each round each player chooses a single location where we show that the second mover advantage re-appears. We suggest some Nash equilibrium configurations of locations in both versions of the game.

Pareto Dominance of Deferred Acceptance through Early Decision

An early decision market is governed by rules that allow each student to apply to (at most) one college and require the student to attend this college if admitted. This market is ubiquitous in college admissions in the United States. We model this market as an extensive-form game of perfect information and study a refinement of subgame perfect equilibrium (SPE) that induces undominated Nash equilibria in every subgame (SPUE). Our main result shows that this game can be used to define a decentralized matching mechanism that weakly Pareto dominates student-proposing deferred acceptance.

A game-theoretic resource allocation approach for intercell device-to-device communications in cellular networks

Device-to-Device (D2D) communication is a recently emerged disruptive technology for enhancing the performance of current cellular systems. To successfully implement D2D communications underlaying cellular networks, resource allocation to D2D links is a critical issue, which is far from trivial due to the mutual interference between D2D users and cellular users. Most of the existing resource allocation research for D2D communications has primarily focused on the intracell scenario while leaving the intercell settings not considered. In this paper, we investigate the resource allocation issue for intercell scenarios where a D2D link is located in the overlapping area of two neighboring cells. Specifically, We present three intercell D2D scenarios regarding the resource allocation problem. To address the problem, we develop a repeated game model under these scenarios. Distinct from existing works, we characterize the communication infrastructure, namely Base Stations (BSs), as players competing resource allocation quota from D2D demand, and we define the utility of each player as the payoff from both cellular and D2D communications using radio resources. We also propose a resource allocation algorithm and protocol based on the Nash equilibrium derivations. Numerical results indicate that the developed model not only significantly enhances the system performance including sum rate and sum rate gain, but also sheds lights on resource configurations for intercell D2D scenarios.

Pareto Dominance of Deferred Acceptance through Early Decision

An early decision market is governed by rules that allow each student to apply to (at most) one college and require the student to attend this college if admitted. This market is ubiquitous in college admissions in the United States. We model this market as an extensive-form game of perfect information and study a refinement of subgame perfect equilibrium (SPE) that induces undominated Nash equilibria in every subgame (SPUE). Our main result shows that this game can be used to define a decentralized matching mechanism that weakly Pareto dominates student-proposing deferred acceptance.

Nash equilibria of network formation games under consent

We investigate the Nash equilibria of game theoretic models of network formation based on explicit consent in link formation. These so-called “consent models” explicitly take account of link formation costs. We provide characterizations of Nash equilibria of such consent models under both one-sided and two-sided costs of link formation. We relate these equilibrium concepts to link-based stability concepts, in particular strong link deletion proofness.

Nash Demand Game and the Kalai-Smorodinsky Solution

We introduce two new variations on the Nash demand game. One, like all known Nash-like demand games so far, has the Nash solution outcome as its equilibrium outcome. In the other, the range of solutions depends on an exogenous breakdown probability; surprisingly, the Kalai-Smorodinsky outcome proves to be the most robust equilibrium outcome. While the Kalai- Smorodinsky solution always finishes on top, there is no possible general ranking among the remaining solution concepts considered; in fact, the rest of the solution concepts take their turns at the bottom at various bargaining problems, depending on the specifics of the bargaining setup.

NASH game and mixed H2/H∞ control

In this work a Nonzero-Sum NASH game related to the H2 and H∞ control problems is formulated in the context of convex optimization theory. The variables of the game are limiting bounds for the H2 and H∞ norms, and the final controller is obtained as an equilibrium solution, which minimizes the `sensitivity of each norm' with respect to the other. The state feedback problem is considered and illustrated by numerical examples.