Equilibrium stacks for a non-cooperative game defined on a product of staircase-function continuous and finite strategy spaces

• Autorzy: Romanuke Vadim

Identyfikatory

DOI

10.7862/rf.2023.4

• Języki publikacji: EN

Abstrakty

EN

A method of solving a non-cooperative game defined on a product of staircase-function strategy spaces is presented. The spaces can be finite and continuous as well. The method is based on stacking equilibria of “short” non-cooperative games, each defined on an interval where the pure strategy value is constant. In the case of finite non-cooperative games, which factually are multidimensional-matrix games, the equilibria are considered in general terms, so they can be in mixed strategies as well. The stack is any combination (succession) of the respective equilibria of the “short” multidimensional-matrix games. Apart from the stack, there are no other equilibria in this “long” (staircase-function) multidimensional-matrix game. An example of staircase-function quadmatrix game is presented to show how the stacking is fulfilled for a case of when every “short” quadmatrix game has a single pure-strategy equilibrium. The presented method, further “breaking” the initial staircase-function game into a succession of “short” games, is far more tractable than a straightforward approach to solving directly the “long” non-cooperative game would be.

Słowa kluczowe

EN

game theory; payoff functional; staircase-function strategy; non-cooperative game; equilibrium stack; multidimensional-matrix game

PL

teoria gier; funkcja wypłaty; gra niekooperacyjna; gra macierzowa

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2023
• Tom: Vol. 46
• Strony: 79--114
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Romanuke Vadim

• Faculty of Mechanical and Electrical Engineering, Polish Naval Academy, Gdynia, Poland

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).