Section: New Results

Stochastic Differential Games

In many situations, controls are chosen by several agents who interact in various ways. To handle such cases one may use the theory of SDGs. This applies to model uncertainty problems, which can be regarded as a zero-sum game between the agent and the "market" and risk minimization, with risk represented via dynamic risk measures. More general non-zero sum games, involving several players, possibly with asymmetric information or delay will be studied.

An interesting new application of the theory of stochastic differential games, is the issue of Public Private Partnership which is a mechanism for a community to outsource the construction of public equipment. The community agrees to pay a rent to the contractor in order to cover the depreciation of the equipment, the maintenance costs and the financial costs. We want to model such partnerships and to compute and compare Nash equilibria and Stackelberg equilibria when the community is the leader. We would also like to investigate whether the community aversion to debt may lead it to enter such a partnership even this is more costly than constructing and managing the equipment by itself.