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Alexander Haider:
"Rational utilization of a common resource by multiple agents";
Supervisor: V.M. Veliov; E105-4, 2014; final examination: 2014-01-20.

The behaviour of multiple agents who utilise one common resource
will be investigated in this thesis, where di erent growth
models for the resource are taken into account. The agents'
utility depends on the stock of the resource, their extraction
rate and their technological level, which can be increased with
investments. The influence of how much one agent is futureoriented
will be the key point for the optimal control strategies.
The main focus is on the one agent problem, how the
optimal solution of this one agent changes if a second agent is
introduced, and at last, how the optimal outcome of these two
agents can be increased, if instead of a full competition on the
market the agents mutually agree on a certain commitment
strategy in order to jointly extract the resource optimally. It
will turn out that in any case a certain commitment is of bene
t for both agents and will increase their output compared to
the non-commitment strategy. Solutions will be obtained by
applying Pontryagins Maximum Principle and the concept of
Nash equilibria in a di erential game setup and the obtained
numerical solutions for the two agent cases are explicitly given
and analysed.

optimal control, differential games

http://publik.tuwien.ac.at/files/PubDat_224635.pdf