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<dc:title xml:lang="pl"><![CDATA[Convergence method, properties and computational complexity for Lyapunov games]]></dc:title>
<dc:creator><![CDATA[Clempner, Julio B.]]></dc:creator>
<dc:creator><![CDATA[Poznyak, Alexander S.]]></dc:creator>
<dc:subject xml:lang="pl"><![CDATA[Lyapunov game]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[Lyapunov equilibrium point]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[best reply]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[repeated games]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[forward decision process]]></dc:subject>
<dc:description xml:lang="pl"><![CDATA[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.]]></dc:description>
<dc:description xml:lang="pl"><![CDATA[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.]]></dc:description>
<dc:description xml:lang="pl"><![CDATA[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.]]></dc:description>
<dc:publisher><![CDATA[Zielona Góra: Uniwersytet Zielonogórski]]></dc:publisher>
<dc:contributor><![CDATA[Korbicz, Józef (1951- ) - red.]]></dc:contributor>
<dc:contributor><![CDATA[Uciński, Dariusz - red.]]></dc:contributor>
<dc:date><![CDATA[2011]]></dc:date>
<dc:type xml:lang="pl"><![CDATA[artykuł]]></dc:type>
<dc:identifier><![CDATA[http://www.zbc.uz.zgora.pl/repozytorium/Content/46921/AMCS_2011_21_2_11.pdf]]></dc:identifier>
<dc:identifier><![CDATA[https://zbc.uz.zgora.pl/repozytorium/dlibra/publication/55020/edition/46921/content]]></dc:identifier>
<dc:identifier><![CDATA[oai:zbc.uz.zgora.pl:46921]]></dc:identifier>
<dc:source xml:lang="pl"><![CDATA[AMCS, Volume 21, Number 2 (2011)]]></dc:source>
<dc:source xml:lang="pl"><![CDATA[https://www.amcs.uz.zgora.pl/?action=paper&paper=556]]></dc:source>
<dc:language><![CDATA[eng]]></dc:language>
<dc:relation><![CDATA[oai:zbc.uz.zgora.pl:publication:55020]]></dc:relation>
<dc:rights xml:lang="pl"><![CDATA[Biblioteka Uniwersytetu Zielonogórskiego]]></dc:rights>
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