Nonsmooth Optimization and Related Topics pp 307-325 | Cite as

# Constrained Well-Posed Two-Level Optimization Problems

## Abstract

A two-level optimization problem corresponding to a two-player game in which player 1 has the leadership in playing the game is considered. Let *K* _{1} and *K* _{2} be the sets of admissible strategies for the two players. Player 1 (called the leader) and player 2 (called the follower) must select strategies *v* _{1} ∈ *K* _{1} and *v* _{2} ∈ *K* _{2} respectively, in order to minimize their objective functionals *J* _{1} and *J* _{2}. It is supposed that player 1 knows everything about player 2 but player 2 knows only the strategy announced by player 1. So, more precisely, player 1 chooses first an optimal strategy knowing that player 2 will react by playing optimally and that his choice cannot be affected by player 1. This concept, introduced by Von Stackelberg in 1939 [24] in the context of static economic competition has been presented in a control theoretic framework by Chen and Cruz (1972) and Simaan and Cruz (1973). A great deal of papers have been devoted to these problems in static and dynamics games (a good list of references can be found in [3], particularly on dynamic cases, and in [1] for application to economic models).

## Keywords

Differential Game Dynamic Game Stackelberg Game Lower Level Problem Stackelberg Equilibrium## Preview

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