In this paper a numerical procedure based on a genetic algorithm (GA) evolution process is given to compute a Stackelberg solution for a hierarchical n+1-person game. There is a leader player who enounces a decision before the others, and the rest of players (followers) take into account this decision and Solve a Nash equilibrium problem. So there is a two-level game between the leader and the followers, called Stackelberg–Nash problem. The idea of the Stackelberg-GA is to bring together genetic algorithms and Stackelberg strategy in order to process a genetic algorithm to build the Stackelberg strategy. In the lower level, the followers make their decisions simultaneously at each step of the evolutionary process, playing a so called Nash game between themselves. The use of a multimodal genetic algorithm allows to find multiple Stackelberg strategies at the upper level. In this model the uniqueness of the Nash equilibrium at the lower-level problem has been supposed. The algorithm convergence is illustrated by means of several test cases.

A Hierarchical Multi-modal Hybrid Stackelberg-Nash GA for a Leader with Multiple Followers Game

D'AMATO, EGIDIO;DANIELE, ELIA;MALLOZZI, LINA;TANCREDI, SIMONE
2012

Abstract

In this paper a numerical procedure based on a genetic algorithm (GA) evolution process is given to compute a Stackelberg solution for a hierarchical n+1-person game. There is a leader player who enounces a decision before the others, and the rest of players (followers) take into account this decision and Solve a Nash equilibrium problem. So there is a two-level game between the leader and the followers, called Stackelberg–Nash problem. The idea of the Stackelberg-GA is to bring together genetic algorithms and Stackelberg strategy in order to process a genetic algorithm to build the Stackelberg strategy. In the lower level, the followers make their decisions simultaneously at each step of the evolutionary process, playing a so called Nash game between themselves. The use of a multimodal genetic algorithm allows to find multiple Stackelberg strategies at the upper level. In this model the uniqueness of the Nash equilibrium at the lower-level problem has been supposed. The algorithm convergence is illustrated by means of several test cases.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/452795
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact