The major purpose of this dissertation is to begin to experimentally study general equilibrium theory. Partial equilibrium analysis has been the focus of hundreds of experiments, and evidence abounds supporting the proposition that gains from trade will be realized in the market for a single good. Yet, in a general equilibrium context, almost no such documentation exists. Furthermore, general equilibrium theory is not amenable to testing via field data. Thus, at present, the theory that is the intellectual foundation of microeconomics remains untested. The natural starting point of such an investigation is the well-known Edgeworth Box environment. This involves conducting experiments within four major categories. In the first treatment, a two-person, two-good pure barter setting, subjects with given endowments effect trades over the goods. Information is incomplete but symmetric, with individuals having knowledge only of their own endowments and valuations. In the second treatment, prices are introduced to induce a budge constraint. Here, the experimenter acts as an auctioneer, adjusting prices based upon excess demand and supply. Third, the case of asymmetric information is considered, as subjects with full knowledge of both parties' endowments and valuations trade with the experimenter, who acts in a purely price-taking capacity. The final set of experiments extends the second treatment to an r-replication of the economy; here, price-taking behavior is the only individually rational strategy. The results of the barter experiments clearly support standard theoretical predictions, as all gains from trade are exhausted in virtually every case. However, one party usually captures most of these gains through superior bargaining ability. When prices are introduced there is often an initial attempt to behave strategically by at least one of the parties. However, in the limited information environment, it is rarely successful. Thus, the competitive equilibrium is almost always achieved. When information is asymmetric, however, the result is quite different; the majority of people do engage in strategic under-revelation of demand and are thus able to capture the maximum extra surplus available. The final treatment, that of the r-replication of the economy shows the surprising result that subjects in this environment cannot learn, in the alloted time, that behaving in a non-price-taking fashion is very costly.

The central goal of this dissertation is to develop a simple but powerful theory to handle a problem which arises in management situations where an optimally exploited, system at steady state is subjected to a set of continuous, persistent and unpredictable disturbances emanating from the system's environment. Such disturbances drive the system out of steady state. The question that arises in such a situation is whether there exists any additional control which can be imposed on the disturbed system in order to drive it back to the steady state and maintain it there for all future time? We show in this dissertation that such a control is possible provided bounds for the disturbances are known. We develop the additional control using concepts from reachability and the so-called Liapunov's "second method". We further develop some theory concerning certain problems which arise in generating the boundary of the reachable set, ∂R(•) using the controllability maximum principle. In generating ∂R(•) several boundary controls may be used to generate different parts of ∂R(•). We show that all the parts of ∂R(•) are polygonally connected. We also show that for a second-order system if an equilibrium point under constant control is hyperbolic and lies on ∂R(•), it is asymptotically stable. Further, in persistently disturbing a system, it is desirable to have some idea about the boundedness of the disturbed system. If the system is bounded then a boundary can be generated using controllability maximum principle. We give some theory and discussion on how to test such boundedness for linear, quasilinear and some cases of nonlinear systems. The last two chapters of this dissertation show how the theory is applied to a second-order system; in particular to a second-order grazing system.

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