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Tytuł: Convergence method, properties and computational complexity for Lyapunov games

Autor:

Clempner, Julio B. ; Poznyak, Alexander S.

Data wydania:

2011

Typ zasobu:

artykuł

Współtwórca:

Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.

Tytuł publikacji grupowej:

AMCS, Volume 21 (2011)

Abstract:

We introduce the concept of a Lyapunov game as a subclass of strictly dominated games and potential games. The advantage of this approach is that every ergodic system (repeated game) can be represented by a Lyapunov-like function. A direct acyclic graph is associated with a game. The graph structure represents the dependencies existing between the strategy profiles. By definition, a Lyapunov-like function monotonically decreases and converges to a single Lyapunov equilibrium point identified by the sink of the game graph. ; It is important to note that in previous works this convergence has not been guaranteed even if the Nash equilibrium point exists. The best reply dynamics result in a natural implementation of the behavior of a Lyapunov-like function. Therefore, a Lyapunov game has also the benefit that it is common knowledge of the players that only best replies are chosen. By the natural evolution of a Lyapunov-like function, no matter what, a strategy played once is not played again. ; As a construction example, we show that, for repeated games with bounded nonnegative cost functions within the class of differentiable vector functions whose derivatives satisfy the Lipschitz condition, a complex vector-function can be built, where each component is a function of the corresponding cost value and satisfies the condition of the Lyapunov-like function. The resulting vector Lyapunov-like function is a monotonic function which can only decrease over time. Then, a repeated game can be represented by a one-shot game. The functionality of the suggested method is successfully demonstrated by a simulated experiment.

Wydawca:

Zielona Góra: Uniwersytet Zielonogórski

Identyfikator zasobu:

oai:zbc.uz.zgora.pl:46921

DOI:

10.2478/v10006-011-0026-x

Strony:

349-361

Źródło:

AMCS, Volume 21, Number 2 (2011) ; kliknij tutaj, żeby przejść

Jezyk:

eng

Prawa do dysponowania publikacją:

Biblioteka Uniwersytetu Zielonogórskiego

Temat i słowa kluczowe:

Lyapunov game Lyapunov equilibrium point best reply repeated games forward decision process

Kolekcje, do których przypisany jest obiekt:

Data ostatniej modyfikacji:

2024-11-05

Data dodania obiektu:

2018-08-24

Liczba wyświetleń treści obiektu:

150

Wszystkie dostępne wersje tego obiektu:

https://zbc.uz.zgora.pl/repozytorium/publication/55020

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Nazwa wydania Data
Convergence method, properties and computational complexity for Lyapunov games 2024-11-05

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Adres

Biblioteka Uniwersytetu Zielonogórskiego
al. Wojska Polskiego 71
65-762 Zielona Góra

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(+48) 68 328 21 55

E-Mail

repozytorium@uz.zgora.pl

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