The Zero-Sum Discrete-Time Feedback Linear Quadratic Dynamic Game: From Two-Player Case to Multi-Player Case

The two-person zero-sum discrete-time feedback linear quadratic dynamic game is considered. A method that provides a saddle-point for the zero-sum discrete dynamic game is developed to derive a necessary and sufficient condition under which the game has a feedback saddle-point solution. Existence solutions, which are described in terms of a sequence of nonnegative definite algebraic Riccati matrices, are constructed. Next, a generalization of such a game to a multi-player case is studied. Using the results in a two-person case, the characterization of a feedback saddle-point solution for the multi-player game is derived

Uncertainty in a Fishery Management Game

In this paper we analyze the consequences of taking noise into account in a simple twoperson fishery management game.Both a stochastic and deterministic formulation are considered.Compared to the noise-free model it is shown that the used stochastic frameworkhas no implications for the equilibrium actions, whereas in the deterministic formulation as well the number of as the equilibrium actions themselves depend on the model parameters.The various equilibrium actions predicted using the deterministic frameworkseem to be quite plausible.

Robust Dynamic Programming in N Players Uncertain Differential Games

In this paper we consider a non-cooperative N players differential game affected by deterministic uncertainties. Sufficient conditions for the existence of a robust feedback Nash equilibrium are presented in a set of min-max forms of Hamilton–Jacobi–Bellman equations. Such conditions are then used to find the robust Nash controls for a linear affine quadratic game affected by a square integrable uncertainty, which is seen as a malicious fictitious player trying to maximize the cost function of each player. The approach allows us to find robust strategies in the solution of a group of coupled Riccati differential equation. The finite, as well as infinite, time horizon cases are solved for this last game. As an illustration of the approach, the problem of the coordination of a two-echelon supply chain with seasonal uncertain fluctuations in demand is develope