LAUSR

The theory of dynamic games has progressed very much in the last decades, and these models are now used in many areas which span from economics to engineering applications, from decisionmodels in social sciences to computer science. Just to quote two typical examples, the allocation of investments in dynamic industry models or the optimal policy design in (multicountry) macroeconomic settings can be formulated as a dynamic game, the optimization of traffic flow on a network (which could be a road network or an Internet network) can also be formulated as a dynamic game. These new formulations have to be made effective via a quantitative solution of dynamic games models because realistic models in these fields are in general analytically intractable, clearly their treatment requires the use of numerical methods to obtain reliable approximate optimal strategies for the players. Another important issue is that these solutions should also be implemented in a reasonable amount of time in order to be really useful (just think at the regulation of informations flows on the Internet). This is the main motivation to develop new algorithms and approximation schemes which could help in their numerical solution and to analyze their efficiency and complexity. It is also important to remind that the numerical solution of game problems is a rather difficult task, even for simple models. These problems often involve nonlinear terms and the space dimension is usually rather high either because of the number of players or because of the complexity of the state space. For example, for pursuit-evasion games when we have two players the space state is doubled unless one can use reduced coordinates expressing the position of one player in a reference system attached to the second player. This will imply to solve a problem in R2d if every player lives in Rd . For other types of games when the