A semi-infinite approach for solving Nash games with off-the-shelf solvers
Tyler Gardner, Matthew W. Harris · 2025
Static and dynamic two-player Nash games are investigated and reformulated into semi-infinite programs. A custom algorithm that leverages off-the-shelf solvers is used to solve the programs, and hence, the games. The approach is tested on four benchmark problems. All four problems are successfully solved. When using a local solver, it is observed that the algorithm works consistently with different initial guesses. When using a global solver, initial guesses are not required. A dynamic linear quadratic game with hundreds of variables is investigated. The solution obtained from the semi-infinite program is compared with the theoretical closed-loop solution. The objective values differ by less than 0.1 percent. Finally, control constraints are added to the dynamic game. Again, the semi-infinite approach successfully solves the problem though no theoretical solution exists for comparison.