ISSN:
1432-5217
Keywords:
Key words. Singular perturbation, stochastic game, continuous-time Markov chain, lexicographical optimization, averaging, aggregation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract. We consider the problem of the perturbation of a class of linear-quadratic differential games with piecewise deterministic dynamics, where the changes from one structure (for the dynamics) to another are governed by a finite-state Markov process. Player 1 controls the continuous dynamics, whereas Player 2 controls the rate of transition for the finite-state Markov process; both have access to the states of both processes. Player 1 wishes to minimize a given quadratic performance index, while player 2 wishes to maximize or minimize the same quantity. The problem above leads to the analysis of some linearly coupled set of quadratic equations (Riccati equations). We obtain a Taylor expansion in the perturbation for the solution of the equation for a fixed stationary policy of the player 2. This allows us to solve the game or team problem as a function of the perturbation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s001860000050
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