A <Emphasis Type="Italic">d</Emphasis>-person Differential Game with State Space Constraints |
| |
Authors: | S Ramasubramanian |
| |
Institution: | (1) Stat. Math. Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore, 560 059, India |
| |
Abstract: | We consider a network of d companies (insurance companies, for example) operating under a treaty to diversify risk. Internal and external borrowing
are allowed to avert ruin of any member of the network. The amount borrowed to prevent ruin is viewed upon as control. Repayment
of these loans entails a control cost in addition to the usual costs. Each company tries to minimize its repayment liability.
This leads to a d -person differential game with state space constraints. If the companies are also in possible competition a Nash equilibrium
is sought. Otherwise a utopian equilibrium is more appropriate. The corresponding systems of HJB equations and boundary conditions
are derived. In the case of Nash equilibrium, the Hamiltonian can be discontinuous; there are d interlinked control problems with state constraints; each value function is a constrained viscosity solution to the appropriate
discontinuous HJB equation. Uniqueness does not hold in general in this case. In the case of utopian equilibrium, each value
function turns out to be the unique constrained viscosity solution to the appropriate HJB equation. Connection with Skorokhod
problem is briefly discussed. |
| |
Keywords: | d-person differential game State space constraints Nash equilibrium Utopian equilibrium Dynamic programming principle System of HJB equations Constrained viscosity solution Semicontinuous envelope Deterministic Skorokhod problem Drift Reflection |
本文献已被 SpringerLink 等数据库收录! |
|