A Numerical Toolbox to Solve N-Player Affine LQ Open-Loop Differential Games

作者：Michalak Tomasz^*; Engwerda Jacob; Plasmans Joseph

来源：Computational Economics, 2011, 37(4): 375-410.

DOI：10.1007/s10614-011-9257-z

• Linear quadratic differential games
• Riccati equations
• Cooperative games
• Noncooperative games
• Coalition structures
• Numerical computation

We present an algorithm and a corresponding MATLAB numerical toolbox to solve any form of infinite-planning horizon affine linear quadratic open-loop differential games. By rewriting a specific application into the standard framework one can use the toolbox to calculate and verify the existence of both the open-loop non-cooperative Nash equilibrium (equilibria) and cooperative Pareto equilibrium (equilibria). In case there is more than one equilibrium for the non-cooperative case, the toolbox determines all solutions that can be implemented as a feedback strategy. Alternatively, the toolbox can apply a number of choice methods in order to discriminate between multiple equilibria. The user can predefine a set of coalition structures for which they would like to calculate the non-cooperative Nash solution(s). It is also possible to specify the relative importance of each player in any coalition structure. Furthermore, the toolbox offers plotting facilities as well as other options to analyse the outcome of the game. For instance, it is possible to disaggregate each player's total loss into its contributing elements. The toolbox is available as a freeware from the authors of this paper.

• 出版日期2011-4