Non-cooperative inventory games for defective items and quantity discounts using strategic complementarity
In this paper, the mathematical analysis for obtaining the equilibrium of the inventory games under strategic complementarities, the existence of defective items, and quantity discounts have been analyzed. The inventory system consists of many buyers who order a single type of product from one suppl...
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Croatian Operational Research Society
2025-01-01
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| Series: | Croatian Operational Research Review |
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| Online Access: | https://hrcak.srce.hr/file/473264 |
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| author | Rubono Setiawan |
| author_facet | Rubono Setiawan |
| author_sort | Rubono Setiawan |
| collection | DOAJ |
| description | In this paper, the mathematical analysis for obtaining the equilibrium of the inventory games under strategic complementarities, the existence of defective items, and quantity discounts have been analyzed. The inventory system consists of many buyers who order a single type of product from one supplier. They compete with each other as a player in a non-cooperative game with strategic complementary. They maximize a supermodular payoff function and take into account some fraction of defective items from a lot of the arrival products. The concept of supermodular games is used to obtain the equilibria of these problems. A new existence theorem of Nash equilibrium in a specific condition has been proved. The optimum analysis has been justified for two conditions, that is the condition without discount and another without it. The numerical computations are provided using Python programming. At the end, the numerical result shows that elements of the Nash equilibrium set can be altered when discounts are considered. A quantity discount policy can be used by the supplier to prevent players from choosing the least Nash equilibrium. |
| format | Article |
| id | doaj-art-1e53b717af514f9e8a1e07560dae13ea |
| institution | Kabale University |
| issn | 1848-0225 1848-9931 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Croatian Operational Research Society |
| record_format | Article |
| series | Croatian Operational Research Review |
| spelling | doaj-art-1e53b717af514f9e8a1e07560dae13ea2025-02-04T14:05:03ZengCroatian Operational Research SocietyCroatian Operational Research Review1848-02251848-99312025-01-01161536410.17535/crorr.2025.0005Non-cooperative inventory games for defective items and quantity discounts using strategic complementarityRubono Setiawan0Department of Mathematics Education, Universitas Sebelas Maret, Jawa Tengah, IndonesiaIn this paper, the mathematical analysis for obtaining the equilibrium of the inventory games under strategic complementarities, the existence of defective items, and quantity discounts have been analyzed. The inventory system consists of many buyers who order a single type of product from one supplier. They compete with each other as a player in a non-cooperative game with strategic complementary. They maximize a supermodular payoff function and take into account some fraction of defective items from a lot of the arrival products. The concept of supermodular games is used to obtain the equilibria of these problems. A new existence theorem of Nash equilibrium in a specific condition has been proved. The optimum analysis has been justified for two conditions, that is the condition without discount and another without it. The numerical computations are provided using Python programming. At the end, the numerical result shows that elements of the Nash equilibrium set can be altered when discounts are considered. A quantity discount policy can be used by the supplier to prevent players from choosing the least Nash equilibrium.https://hrcak.srce.hr/file/473264complementaritydefectivelatticesupermodular |
| spellingShingle | Rubono Setiawan Non-cooperative inventory games for defective items and quantity discounts using strategic complementarity Croatian Operational Research Review complementarity defective lattice supermodular |
| title | Non-cooperative inventory games for defective items and quantity discounts using strategic complementarity |
| title_full | Non-cooperative inventory games for defective items and quantity discounts using strategic complementarity |
| title_fullStr | Non-cooperative inventory games for defective items and quantity discounts using strategic complementarity |
| title_full_unstemmed | Non-cooperative inventory games for defective items and quantity discounts using strategic complementarity |
| title_short | Non-cooperative inventory games for defective items and quantity discounts using strategic complementarity |
| title_sort | non cooperative inventory games for defective items and quantity discounts using strategic complementarity |
| topic | complementarity defective lattice supermodular |
| url | https://hrcak.srce.hr/file/473264 |
| work_keys_str_mv | AT rubonosetiawan noncooperativeinventorygamesfordefectiveitemsandquantitydiscountsusingstrategiccomplementarity |