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This dissertation contains three essays in game theory, focusing particularly on the issues of information, knowledge, and stability in complex interactions. It begins with an introductory overview. / Chapter 2 offers a general framework for analyzing complex economic and social environments. Specifically, I introduce new notions of a general system and a ϕ-stable set. By making use of Tarski's fixed point theorem, I then establish the existence of a ϕ-stable set. I further apply the proposed notions to game theory, e.g., rationalizability is derived from the largest ϕ-stable set. / Chapter 3 establishes epistemic foundations for the criterion of "stability." Specifically, in strategic games, achieving common knowledge of rationality (CKR) implies an internally ϕ-stable set that is contained in an externally ϕ-stable set and, moreover, whenever mutually known, a ϕ-stable set is implied by rationality alone. In the case of two-person games, achieving CKR implies a ϕ-stable set. In extensive games with perfect information, achieving CKR implies a unique ϕ-stable set. On the other hand, in both strategic and extensive games, any of the commonly known ϕ-stable sets implies CKR. Furthermore, any ϕ-stable set can be achieved in terms of CKR. / Chapter 4 presents a new solution concept of stable equilibrium in beliefs (SEB) by assuming it is common knowledge that players are uncertainty averse. By making use of an appealing criterion of "stability," an SEB is defined as a strategy profile supported by a stable belief system. It is shown that all SEBs constitute a unique stable belief system, and an SEB satisfies subgame perfectness; moreover, it is shown that the notion of SEB "refines" that of subgame perfect equilibrium in terms of path of play. Finally, we establish the epistemic foundation for the notion of SEB.

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(2+1)-dimensional gravity with a negative cosmological constant is a topological theory with no local degrees of freedom. When confined to compact universes which are topologically genus g Riemann surfaces times time, its classical phase space is the cotangent bundle of the moduli space of Riemann surfaces. We consider the quantization of moduli space itself, emerging as the zero-momentum slice of this phase space. When a parity-violating Chern-Simons term is added to the gravitational action, a nontrivial symplectic form is induced on this slice which is a multiple of the Weil-Petersson Kähler form. By demanding that this symplectic form integrate to 2 pi h-bar times an integer on every nontrivial two-cycle in moduli space—which is a necessary condition for the system to be quantizable—we find a new quantization condition on the Chern-Simons coupling k'. Our result strongly suggests that k' must be an integer multiple of 24 in order to define a self-consistent theory of quantum gravity. / La gravitation en 2+1 dimensions avec une constante cosmologique négative est une théorie topologique, sans degrés de liberté locaux. Lorsqu'elle est limitée à des univers compacts qui sont topologiquement un produit direct des surfaces de Riemann au genre g et du temps, son espace de phase classique est le fibré cotangent de l'espace des modules des surfaces de Riemann. Nous considérons la quantification de l'espace des modules lui-même, qui se produit comme la tranche zéro dynamique de cet espace de phase. Quand on ajoute un terme Chern-Simons, qui brise la parité, à l'action gravitationelle, une forme symplectique non triviale est induite sur cette tranche qui est un multiple de la forme Kähler de Weil-Petersson. En exigeant que cette forme symplectique doit intégrer à 2 pi fois h barre multiplié par un entier sur tous les cycles non triviaux de degré 2 dans l'espace des modules—condition nécessaire pour faire la quantification du système—nous trouvons une nouvelle condition de quantification pour k', le couplage Chern-Simons. Notre résultat suggère fortement que k' doit être un multiple entier de 24, afin de définir une théorie cohérente de la gravitation quantique.

The large N thermal Quantum Chromodynamics (QCD) that we study here is a generalization of SU(3) QCD with two gauge groups at high energy scales, i.e. in the ultraviolet (UV). Both gauge groups are related to N as SU(N)×SU(kN) with k < 1. In our construction, we have a model that has a complete UV description, as well as a low energy, i.e. infrared (IR), behaviour that mimicks that of QCD. Our model has three regions. The IR region is the well known cascading model with extensions to include favours. The two gauge groups of this theory reduce to a single SU(kN) group which then confines. The UV region uses congurations from type IIB string theory on the conifold to describe the dynamics. The intermediate region smoothly connects the two, i.e. the UV and the IR, so that we have a complete model for all energy scales. All regions are related to the gauge theory by gauge/gravity duality. In particular, we analyze the renormalization group (RG) flow of the gauge coupling in the effective field theory. We see that it asymptotically approaches a constant at high energies and flows toward permanent confinement as energy scale decreases. In the IR, we obtain the mesonic spectrum by compactifying extra dimensions and analyzing the wave functions in Minkowski space-time. / Cette these etudies la limit N -> ∞ de la theorie chromodynamique quantique avec les deux groupes de jauge SU(N)×SU(kN) avec k < 1. Un modele est popose pour donner un description complete a la fois dans le regime ultraviolet(UV) et infrarouge(IR). Le regime IR concorde avec celui d'un modele de cascade, qui reduit de seule groupe de jaude SU(N) puis confine, tandis que le regime UV correspond a la theorie des cordes de type IIB sur conifold. Le regime UV possede alors une dualite de supergravite/jauge s'inscritvant dans la correspondance AdS/CFT. Dans le regime intermediere, notre molele connecte de maniere reguliere entre IR et UV. Le group de renormalization de la theorie effective est ensuite analyse. Nous comparons les resultats experimentaux en spectre du meson de notre modele das le regime IR.

Relativistic Hydrodynamics has successfully described the bulk of the data on soft hadrons at the Relativistic Heavy Ion Collider (RHIC), including the elliptic flow and the momentum spectra. In this work, we apply the hydrodynamic evolution model to the quark-gluon plasma (QGP) and hadronic phases created in relativistic heavy-ion collision at RHIC and at the Super Proton Synchrotron for different systems and energies. In these conditions, we calculate the spectra of dileptons and their elliptic flow. / Le model d'évolution hydrodynamique relativiste a décrit avec succès les propriétésd'ensemble des données sur les hadron "soft" produit au RHIC, incluant le flot elliptique. Dans ce travail, nous avons appliqué l'hydrodynamique relativiste aux phasesde plasma de quark et de gluons (PQG) et hadronique créées dans les collisions àhautes énergies aux Relativistic Heavy Ion Collider et Super Proton Synchrotron.Nous étudions le spectre et le flot elliptique des dileptons produits dans ces collisionsd'ions lourds.

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