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Thesis (Ph.D.)--University of Tulsa, 1971. / Bibliography: leaves 34-36.

The dissertation deals with the interplay of fiscal and monetary policy in face of uncertainty about the estimation of the true output gap. Theoretical framework of the dissertation set this interplay of monetary and fiscal policy into the realm of game theory, in particularly non-cooperative games of the Nash and Stackelberg equilibrium, respectively. The theoretical framework continued with a description of various methods used for estimation of potential output and output gap, with a special emphasis on methods used in both the Czech National Bank and Czech Ministry of Finance. In the applied part of the dissertation, I studied the interplay of monetary and fiscal policy in the case of Czech economy facing an uncertainty about the estimation of the true output gap. I studied the impact of this interplay on major macroeconomic variables and I tried to determine, which of these two policies plays the role of a leader and which plays the role of a follower in the case of Czech economic environment.

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For systems that are in equilibrium, fluctuations can be understood through interactions with external heat reservoirs. For this reason these fluctuations are known as thermal noise, and they usually become vanishingly small in the thermodynamic limit. However, many systems comprising interacting constituents studied by physicists in recent years are both far from equilibrium, and sufficiently small so that they must be considered finite. The finite number of constituents gives rise to an inherent demographic noise in the system, a source of fluctuations that is always present in the stochastic dynamics. This thesis investigates the role of stochastic fluctuations in the macroscopically observable dynamical behaviour of non-equilibrium, finite systems. To facilitate such a study, we construct microscopic models using an individual based modelling approach, allowing the explicit form of the demographic noise to be identified. In many physical systems and theoretical models, absorbing states are a defining feature. Once a system enters one, it cannot leave. We study the dynamics of a system with two symmetric absorbing states, finding that the amplitude of the multiplicative noise can induce a transition between two universal modes of domain coarsening as the system evolves to one of the absorbing states. In biological and ecological systems, cycles are a ubiquitously observed phenomenon, but are di cult to predict analytically from stochastic models. We examine a potential mechanism for cycling behaviour due to the flow of probability currents, induced by the athermal nature of the demographic noise, in a single patch population comprising two competing species. We find that such a current by itself cannot generate macroscopic cycles, but when combined with deterministic dynamics which constrain the system to a closed circular manifold, gives rise to global quasicycles in the population densities. Finally, we examine a spatially extended system comprising many such patch populations, exploring the emergence of synchronisation between the different cycles. By a stability analysis of the global synchronised state, we probe the relationship between the synchronicity of the metapopulation and the magnitude of the coupling between patches due to species migration. In all cases, we conclude that the nature of the demographic noise can play a pivotal role in the macroscopically observed dynamical behaviour of the system.

Many evolutionary game theory papers have obtained their results when the bounded rationality which creates change vanishes. In our first chapter we consider whether such results are actually a good reflection of a population whose bounded rationality is small yet persistent. Our model consists of a two type population with three stable equilibria. Firstly we find that results from the standard vanishing noise approach can be very different from those obtained when noise is small but constant. Secondly when the results differ the small and persistent noise approach selects an equilibrium with a co-existence of conventions. Our second chapter generalises the model of our first chapter to a population of many player types and several stable equilibria. Firstly we produce the characteristics of the long run equilibria under vanishing noise analysis. Secondly we find that the introduction of a small neutral group into a divided society can produce a welfare improving switch in the long run equilibrium towards social co-ordination. Our third chapter combines the model of the second chapter with the message of the first. We show numerically that the long run location of a heterogenous population with extremely low levels of bounded rationality can be completely different to the equilibria selected through vanishing noise analysis. We also show that such an event is not a rare occurrence and find that over a third of populations are misrepresented by stochastic stability. Our final chapter conducts a review of the literature on social threshold models. We give a thorough description of each paper and discuss the main assumptions that drive the key results.

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Graduation date: 2005