Constrained Well-Posed Two-Level Optimization Problems

  • J. Morgan
Part of the Ettore Majorana International Science Series book series (EMISS, volume 43)

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 1K 1 and v 2K 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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • J. Morgan
    • 1
  1. 1.Dept. of Mathematics and ApplicationsUniv. of NaplesNaplesItaly

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