{"id":40989,"date":"2024-09-25T10:30:05","date_gmt":"2024-09-25T10:30:05","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d9%86%d8%a7%d9%88%d8%a8-%d8%af%d8%b1-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%87%d8%ac-%d9%86%d8%b2%d8%af\/"},"modified":"2024-09-25T10:30:06","modified_gmt":"2024-09-25T10:30:06","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d9%86%d8%a7%d9%88%d8%a8-%d8%af%d8%b1-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%87%d8%ac-%d9%86%d8%b2%d8%af","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d9%86%d8%a7%d9%88%d8%a8-%d8%af%d8%b1-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%87%d8%ac-%d9%86%d8%b2%d8%af\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062a\u0646\u0627\u0648\u0628 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0647\u062c-\u0646\u0632\u062f\u06cc\u06a9 \u0628\u06cc\u0646 \u0648 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u06cc \u062d\u0644 NE \u0646\u0627\u0645\u062a\u0642\u0627\u0631\u0646 \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u062f\u0648 \u0646\u0641\u0631\u0647 \u0628\u0627 \u062c\u0645\u0639 \u0635\u0641\u0631"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPeriodicity in Hedge-myopic system and an asymmetric NE-solving paradigm for two-player zero-sum games<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062a\u0646\u0627\u0648\u0628 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0647\u062c-\u0646\u0632\u062f\u06cc\u06a9 \u0628\u06cc\u0646 \u0648 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u06cc \u062d\u0644 NE \u0646\u0627\u0645\u062a\u0642\u0627\u0631\u0646 \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc \u0647\u0627\u06cc \u062f\u0648 \u0646\u0641\u0631\u0647 \u0628\u0627 \u062c\u0645\u0639 \u0635\u0641\u0631<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nXinxiang Guo, Yifen Mu, Xiaoguang Yang<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n25<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nDynamical Systems,\u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u067e\u0648\u06cc\u0627 ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 7 March, 2024; originally announced March 2024. , MSC Class: 91A05; 91A25; 91A68<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 7 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u06a9\u0644\u0627\u0633 MSC: 91A05 \u061b91A25 \u061b91A68<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

In this paper, we consider the $n \\times n$ two-payer zero-sum repeated game in which one player (player X) employs the popular Hedge (also called multiplicative weights update) learning algorithm while the other player (player Y) adopts the myopic best response. We investigate the dynamics of such Hedge-myopic system by defining a metric $Q(\\textbf{x}_t)$, which measures the distance between the stage strategy $\\textbf{x}_t$ and Nash Equilibrium (NE) strategy of player X. We analyze the trend of $Q(\\textbf{x}_t)$ and prove that it is bounded and can only take finite values on the evolutionary path when the payoff matrix is rational and the game has an interior NE. Based on this, we prove that the stage strategy sequence of both players are periodic after finite stages and the time-averaged strategy of player Y within one period is an exact NE strategy. Accordingly, we propose an asymmetric paradigm for solving two-player zero-sum games. For the special game with rational payoff matrix and an interior NE, the paradigm can output the precise NE strategy; for any general games we prove that the time-averaged strategy can converge to an approximate NE. In comparison to the NE-solving method via Hedge self-play, this HBR paradigm exhibits faster computation\/convergence, better stability and can attain precise NE convergence in most real cases.<\/p>\n

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\u06a9\u0646\u06cc\u0645.\u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u06cc \u0648\u06cc\u0698\u0647 \u0628\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0627\u0632\u067e\u0631\u062f\u0627\u062e\u062a \u0645\u0646\u0637\u0642\u06cc \u0648 NE \u062f\u0627\u062e\u0644\u06cc \u060c \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc \u062f\u0642\u06cc\u0642 NE \u0631\u0627 \u062a\u0648\u0644\u06cc\u062f \u06a9\u0646\u062f.\u0628\u0631\u0627\u06cc \u0647\u0631 \u0628\u0627\u0632\u06cc \u06a9\u0644\u06cc \u060c \u0645\u0627 \u062b\u0627\u0628\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u0633\u062a\u0631\u0627\u062a\u0698\u06cc \u0645\u062a\u0648\u0633\u0637 \u0632\u0645\u0627\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u06cc\u06a9 NE \u062a\u0642\u0631\u06cc\u0628\u06cc \u0647\u0645\u06af\u0631\u0627 \u0634\u0648\u062f.\u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u0627 \u0631\u0648\u0634 \u062d\u0644 NE \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0628\u0627\u0632\u06cc \u062e\u0648\u062f \u067e\u0631\u0686\u06cc\u0646 \u060c \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u06cc HBR \u0645\u062d\u0627\u0633\u0628\u0627\u062a\/\u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u0633\u0631\u06cc\u0639\u062a\u0631 \u060c \u062b\u0628\u0627\u062a \u0628\u0647\u062a\u0631 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u0648 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062f\u0631 \u0628\u06cc\u0634\u062a\u0631 \u0645\u0648\u0627\u0631\u062f \u0648\u0627\u0642\u0639\u06cc \u0628\u0647 \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc NE \u062f\u0642\u06cc\u0642 \u0628\u0631\u0633\u062f.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

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