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親愛的您，這裡是LearningYard新學苑！
今天小編為大家帶來三方演化博弈知識的溫故知新。
歡迎您的通路！
Share interest, spread happiness, increase knowledge, and leave beautiful.
Dear, this is the LearingYard Academy!
Today, the editor brings you a reviewing the past and understanding the new knowledge of three party evolutionary game theory.
Welcome to visit!
1 内容摘要（Content summary）
今天小編将從“思維導圖、精讀内容、知識補充”三個闆塊，解讀分享三方演化博弈知識的溫故知新。
Today, the editor will interpret and share the reviewing the past and understanding the new knowledge of three party evolutionary game theory from the three sections of "mind map, intensive reading content, and knowledge supplement".
2 思維導圖（Mind mapping）
3 精讀内容（Intensive reading content）
早期小編對三方演化博弈及相關知識進行了學習，但彼時并未進行三方演化博弈文章的實際寫作，故學習時對于重點知識的把握不是很到位，且部分知識早已遺忘，故今日重新将其拿起，重走修行路，希望拾起舊憶的同時能有新的收獲。
In the early days, I studied the three-party evolutionary game and related knowledge, but I didn't actually write the three-party evolutionary game article at that time. Therefore, I didn't grasp the key knowledge very well when I was learning, and some of the knowledge had long been forgotten. So today I picked it up again and walked the path of cultivation again, hoping to pick up old memories and gain new gains.
在很多三方演化博弈的文章中，作者通常将建構好的模型以支付矩陣的形式寫出，來展示參與博弈的三者間的博弈關系和博弈政策組合。實際上還有一種更加直覺的表現形式，三方演化博弈收益樹，将博弈政策組合以樹狀圖的形式展現，能更為友善地看出三者間的政策關系。
In many articles on three-party evolutionary games, the author usually writes the constructed model in the form of a payment matrix to show the game relationship and game strategy combination between the three parties involved in the game. In fact, there is a more intuitive form of expression, the three-party evolutionary game benefit tree, which shows the game strategy combination in the form of a tree diagram, which can more easily see the strategic relationship between the three.
模型參數假設部分，根據博弈參與方之間的現實邏輯關系，以及各自的收益與成本來設計模型使用的參數。通常一個參與方有兩種政策可以選擇，參數假設要在這兩種政策選擇下根據不同情況設定不同的參數，使其符合邏輯，并滿足我們的模組化需要。
In the model parameter assumption part, the parameters used by the model are designed according to the actual logical relationship between the game participants, as well as their respective benefits and costs. Usually a participant has two strategies to choose from. The parameter assumption is to set different parameters according to different situations under these two strategy choices to make it logical and meet our modeling needs.
模型分析部分，首先要進行的就是計算模型參與方各自選擇不同政策時的期望收益及綜合平均收益，再由此計算出參與方政策選擇的複制動态方程。計算複制動态方程時，根據以往學者的總結，有一個固定的公式可以套用，但實際計算時可将該公式進行簡化，以使計算更加友善快捷。
In the model analysis part, the first thing to do is to calculate the expected returns and comprehensive average returns of the model participants when they choose different strategies, and then calculate the replication dynamic equation of the strategy selection of the participants. When calculating the replication dynamic equation, according to the summary of previous scholars, there is a fixed formula that can be applied, but the formula can be simplified in actual calculation to make the calculation more convenient and quick.
在對模型進行具體分析時，可将公式中的部分内容進行重新假設，以便更好地表達。分析模型時要計算較多的導數，判斷函數的增減性，此部分容易将自己繞暈，需多觀察，慢分析。
When analyzing the model in detail, some of the contents in the formula can be re-assumed for better expression. When analyzing the model, more derivatives need to be calculated to judge the increase and decrease of the function. This part is easy to confuse yourself, so you need to observe more and analyze slowly.
4 知識補充（Knowledge supplement）
什麼是演化博弈及複制動态方程？
What is evolutionary game and replication dynamic equation?
演化博弈論是一種研究自然界中遺傳進化和社會進化等現象的數學模型。其中複制動态方程是演化博弈論中的一種重要工具，它描述了參與博弈的個體在演化過程中如何選擇政策的變化規律。
Evolutionary game theory is a mathematical model that studies phenomena such as genetic evolution and social evolution in nature. Among them, the replication dynamic equation is an important tool in evolutionary game theory, which describes the changing law of how individuals participating in the game choose strategies during the evolution process.
今天的分享就到這裡了。
如果您對今天的文章有獨特的想法，
歡迎給我們留言，
讓我們相約明天，
祝您今天過得開心快樂！
That's all for today's sharing.
If you have a unique idea about the article,
please leave us a message,
and let us meet tomorrow.
I wish you a nice day!
參考資料：
翻譯：ChatGPT 4
文字：
演化博弈論的複制動态方程 - 百度文庫 (baidu.com)
[三方演化博弈零基礎教學]理論部分_哔哩哔哩_bilibili
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