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Journals / Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik / 2002 / Cilt: 3 - Sayı: 3

Stackelberg and Nash equilibrium situations in differential games with simple motions

Sade hareketli diferansiyel oyunlarda Stackelberg ve Nash denge durumları

Mammadağha MAMMADOV
Pages
427–432
Publication Date
2022-10-11
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Nash and Stackelberg equilibrium sets of motion conditions are given by static inequality relationships.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we consider a positional non antagonistic two person differential game with simple motions.
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Key Findings & Data:The payoff functions of both players are terminal.
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Conclusion & Impact:Nash and Stackelberg equilibrium sets of motion conditions are given by static inequality relationships.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, we consider a positional non antagonistic two person differential game with simple motions. The payoff functions of both players are terminal. First the Stackelberg solution (the Germeyer's hierarchic games) are examined. Existence of such solutions has been showed and their structure have been determined. A mathematical programming problem is defined to obtain the Stackelberg solutions. The set of Nash equilibrium situations are determined by intersection of two sets of Stackelberg solutions. Nash and Stackelberg equilibrium sets of motion conditions are given by static inequality relationships.

Özet

Çalışmada sade hareketli pozisyon diferansiyel oyunlar ele alınmıştır. Oyuncuların amaç (veya maliyet) fonksiyonları terminaldir (yani, hareketin son zamandaki durumunun fonksiyonudur). Önce Stackelberg çözümleri (Yu. B. Germeyyer'in hiyerarşi oyunları) incelenmiştir. Böyle çözümlerin varlığı gösterilmiş , yapısı açıklanmış ve çözümlerin bulunması için matematik programlama problemi yazılmıştır. Nash denge durumları ise Stackelberg çözümlerinin yardımı ile (iki Stackelberg çözümleri kümesinin kesişimi olarak) belirlenmektedir. Nash ve Stackelberg denge durumlarına uygun hareket kümeleri statik eşitsizlik ilişkilerinin yardımı ile verilmektedir.

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Cite This Article

MAMMADOV, M. (2022). Stackelberg and Nash equilibrium situations in differential games with simple motions. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik, Cilt: 3 - Sayı: 3, 427–432. https://ajindex.com/articles/438511

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References (4)

  1. Germeyer, Yu.,B. (1971). On Two-Person Games with Fixed Sequence of Moves. Dokl. Akad. Nauk SSSR 198, 1001-1004 (in Russian). Simaan, M. and J. Cruz (1973). On the Stackelberg Strategy in Nonzero-Sum Games. Journ. of Optim. Theory and Appl. 11(5). Germeyer, Yu. B. (1976). The Games with Nonopposite Interest. Nauka: Moscow (in Russian). Kononenko, A. F. (1976). On the Equilibrium Positional Strategy in Nonantagonistic Differential Games. Dokl. Akad. Nauk SSSR 231, 285-288 (in Russian). Kononenko, A. F. (1977). On Many-Step Conflicts with Information Exchange. Jurn. Vichislitelnoy Matem, i Matem. Fiziki 17(4), 922-934 (in Russian). Kononenko, A. F. (1980). The Structure of Optimal Strategy in Dynamic Control Systems. Jurn. Vichislitelnoy Matem, i Matem. Fiziki 20(5), 1105- 1116 (in Russian). Kononenko, A. F. and M. Mamedov (1990). Nonantagonistic Two-Person Linear - Quadratik Differential Games. Journ. Probl. Control and Inform. Theory 9(4), 297-312.
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  3. Krasovskiy, N. and A. Subbotin (1976).
  4. The Positional Differential Games, Nauka: Moscow (in Russian). Subbotin, A. I. (1987). Calculating The Value of Draw- Near Differential Game with Simple Motions.In: Upravleniye s Garantirovannim Rezultatom (Subbotin, A.,1. and A.F. Kleimenov, eds) 71-76. Inst. Math. Mech.: Sverdlovsk (in Russian).