1 00:00:00,030 --> 00:00:01,509 in this video I'm going to tell you 在这个视频中，我要告诉你 2 00:00:01,709 --> 00:00:03,969 about how to define formally the 关于如何正式定义 3 00:00:04,169 --> 00:00:06,219 imperfect information extensive form and 不完善的信息广泛形式和 4 00:00:06,419 --> 00:00:08,140 how to reason about strategies in these 如何推理这些策略 5 00:00:08,339 --> 00:00:11,740 games so in the perfect information 游戏中的完美信息 6 00:00:11,939 --> 00:00:14,919 extensive form we have a player take an 广泛的形式，我们有一个球员采取 7 00:00:15,119 --> 00:00:16,900 action at every single choice node in 在每个选择节点上的动作 8 00:00:17,100 --> 00:00:19,749 the game and a consequence of that 游戏及其后果 9 00:00:19,949 --> 00:00:22,060 definition is that we're saying that 定义是我们在说 10 00:00:22,260 --> 00:00:23,919 players know what node they're in all 玩家知道他们在哪个节点 11 00:00:24,118 --> 00:00:26,350 the time and that means they know the 时间，这意味着他们知道 12 00:00:26,550 --> 00:00:28,179 whole history of all of the moves that 所有动作的整个历史 13 00:00:28,379 --> 00:00:31,269 have happened before in the game this is 在游戏中发生过，这是 14 00:00:31,469 --> 00:00:32,948 reasonable for some games like chess 对于象棋这样的游戏来说是合理的 15 00:00:33,149 --> 00:00:34,750 where you really do get to see what your 你真正在哪里看到你的 16 00:00:34,950 --> 00:00:36,719 opponent does in every different move 对手的动作各不相同 17 00:00:36,920 --> 00:00:39,099 it's not reasonable for games like 对于像这样的游戏是不合理的 18 00:00:39,299 --> 00:00:41,709 battleship where your play your opponent 您扮演对手的战舰 19 00:00:41,909 --> 00:00:43,329 can do something and you don't get to 可以做某事而你却无法 20 00:00:43,530 --> 00:00:46,178 see what it is and it matters to to what 看看它是什么，对什么都重要 21 00:00:46,378 --> 00:00:47,588 happens to you later in the game it can 在游戏的后面发生在你身上 22 00:00:47,789 --> 00:00:49,149 matter to your payoff it can matter to 对您的回报至关重要，对 23 00:00:49,350 --> 00:00:52,059 whether the game stops or continues so 游戏是停止还是继续 24 00:00:52,259 --> 00:00:55,748 in order to model this richer situation 为了模拟这种更丰富的情况 25 00:00:55,948 --> 00:00:57,428 where players aren't able to observe 玩家无法观察的地方 26 00:00:57,628 --> 00:00:59,858 everything that their opponents do we're 他们对手所做的一切 27 00:01:00,058 --> 00:01:03,099 going to add something new to the game - 将为游戏添加一些新内容- 28 00:01:03,299 --> 00:01:04,509 the game representation so we're going 游戏表示，所以我们要去 29 00:01:04,709 --> 00:01:06,418 to call it the imperfect information 称其为不完善的信息 30 00:01:06,618 --> 00:01:09,429 extensive form and the way this is going 广泛的形式以及前进的方向 31 00:01:09,629 --> 00:01:10,869 to work is we're going to take the old 上班是我们要把旧的 32 00:01:11,069 --> 00:01:13,450 definition that we had before but we're 我们以前有过的定义 33 00:01:13,650 --> 00:01:16,000 going to say that players consider some 会说玩家考虑一些 34 00:01:16,200 --> 00:01:17,738 choice nodes to be equivalent to each 选择节点等效于每个 35 00:01:17,938 --> 00:01:19,750 other so there's some choice nodes that 其他的还有一些选择节点 36 00:01:19,950 --> 00:01:22,359 a player I isn't able to tell apart and 我无法分辨的球员 37 00:01:22,560 --> 00:01:24,579 that's going to mean they're not able to 这将意味着他们无法 38 00:01:24,780 --> 00:01:26,168 completely figure out the history of 完全弄清楚历史 39 00:01:26,368 --> 00:01:27,879 where they are in the tree because 他们在树上的位置是因为 40 00:01:28,079 --> 00:01:28,988 they're not going to know which of 他们不会知道哪个 41 00:01:29,188 --> 00:01:30,730 several choice nodes they're out when 几个选择节点 42 00:01:30,930 --> 00:01:33,278 they have to take a choice and we're 他们必须做出选择，我们 43 00:01:33,478 --> 00:01:35,319 going to do this by taking the set of 通过采取一组来做到这一点 44 00:01:35,519 --> 00:01:36,909 choice nodes for a given player and 给定玩家的选择节点，以及 45 00:01:37,109 --> 00:01:39,789 putting them into equivalence classes so 将它们放在等价类中 46 00:01:39,989 --> 00:01:42,099 what that means is kind of schematically 这意味着是示意性的 47 00:01:42,299 --> 00:01:44,558 if these are some different choice nodes 如果这些是一些不同的选择节点 48 00:01:44,759 --> 00:01:48,009 in the game that all of course belong to 在游戏中，所有当然都属于 49 00:01:48,209 --> 00:01:50,259 the same player we might say these are 我们可能会说这些球员是 50 00:01:50,459 --> 00:01:52,599 one equivalence class these are another 一个等价类，这是另一个 51 00:01:52,799 --> 00:01:54,399 equivalence class and these are a third 等值课程，这是第三 52 00:01:54,599 --> 00:01:56,528 equivalence class and what that would 等效类以及那会是什么 53 00:01:56,728 --> 00:01:58,899 mean is the player wouldn't know which 意思是玩家不会知道哪个 54 00:01:59,099 --> 00:02:00,789 of these two choice nodes 这两个选择节点中的一个 55 00:02:00,989 --> 00:02:03,278 I he was at when he was asked to make a 当他被要求制作一个 56 00:02:03,478 --> 00:02:06,159 choice but he would know that he was at 选择，但他会知道他在 57 00:02:06,359 --> 00:02:07,689 one of these two and not one of these 这两个之一，而不是其中之一 58 00:02:07,890 --> 00:02:08,679 two because they're in different 两个，因为他们是不同的 59 00:02:08,878 --> 00:02:11,649 equivalence classes so let's say that a 等价类，所以说 60 00:02:11,848 --> 00:02:13,640 little bit more formally 正式一点 61 00:02:13,840 --> 00:02:16,969 so to formally define an imperfect 从而正式定义一个不完美 62 00:02:17,169 --> 00:02:19,610 information extensive form game we start 我们开始的信息丰富的形式游戏 63 00:02:19,810 --> 00:02:21,920 with a perfect information extensive 拥有完善的信息 64 00:02:22,120 --> 00:02:23,719 form game which we've already learned 我们已经学过的形式游戏 65 00:02:23,919 --> 00:02:26,270 how to define before and then we're 如何定义之前，然后我们 66 00:02:26,469 --> 00:02:27,800 going to add this ingredient of 要添加这个成分 67 00:02:28,000 --> 00:02:31,310 equivalence classes so we're going to 等价类，所以我们将 68 00:02:31,509 --> 00:02:34,910 add this element I which is a set of 添加这个元素我是一组 69 00:02:35,110 --> 00:02:37,069 equivalent set of sets of equivalence 等价的等价集 70 00:02:37,269 --> 00:02:40,009 classes one for every player so for 为每个玩家分配一个，因此 71 00:02:40,209 --> 00:02:42,860 player one we have the set of 玩家一，我们有一套 72 00:02:43,060 --> 00:02:44,330 equivalence classes or let's say for 等价类，或者说 73 00:02:44,530 --> 00:02:47,240 player I we have a set of equivalence 玩家，我有一组等效 74 00:02:47,439 --> 00:02:51,080 classes numbered from 1 to K sub I so 从1到K子类的编号 75 00:02:51,280 --> 00:02:52,670 these are all different equivalence 这些都是等价的 76 00:02:52,870 --> 00:02:55,118 classes and each one of these classes is 类，这些类中的每一个是 77 00:02:55,318 --> 00:02:57,560 some number of different choice notes 一些不同的选择笔记 78 00:02:57,759 --> 00:03:00,770 one or more choice notes and these are 一个或多个选择说明，这些是 79 00:03:00,969 --> 00:03:02,270 going to be different choice nodes that 将成为不同的选择节点 80 00:03:02,469 --> 00:03:04,819 that player isn't able to tell apart so 该玩家无法分辨，所以 81 00:03:05,019 --> 00:03:06,649 if every one of these equivalence 如果这些等价的每一个 82 00:03:06,848 --> 00:03:08,780 classes contains only one choice node 类仅包含一个选择节点 83 00:03:08,979 --> 00:03:10,430 we're back with the perfect information 我们回来了，完美的信息 84 00:03:10,629 --> 00:03:12,649 case and if any of these equivalence 情况，以及是否有这些等同物 85 00:03:12,848 --> 00:03:14,569 classes contains more than one thing 类包含不止一件事 86 00:03:14,769 --> 00:03:16,280 then we have something new we have a 然后我们有了新的东西 87 00:03:16,479 --> 00:03:17,689 game where the player doesn't quite know 玩家不太了解的游戏 88 00:03:17,889 --> 00:03:20,450 what's going on all the time now in 现在一直在发生什么 89 00:03:20,650 --> 00:03:22,340 order to make this definition work we 为了使这个定义可行，我们 90 00:03:22,539 --> 00:03:24,170 need to add a couple of restrictions so 需要添加一些限制，所以 91 00:03:24,370 --> 00:03:26,390 that it makes sense so we want to say 这很有意义，所以我们想说 92 00:03:26,590 --> 00:03:31,099 that if and if two different choice 如果，如果两个不同的选择 93 00:03:31,299 --> 00:03:32,960 nodes are part of the same equivalence 节点是同等的一部分 94 00:03:33,159 --> 00:03:35,569 class then first of all they have to 上课，那么他们首先要 95 00:03:35,769 --> 00:03:37,730 belong to the same player they have to 属于他们必须同一个球员 96 00:03:37,930 --> 00:03:39,349 be labeled with the same player because 被标记为同一个玩家，因为 97 00:03:39,549 --> 00:03:41,118 if they're not you'd be able to tell 如果不是，您将能够告诉他们 98 00:03:41,318 --> 00:03:42,800 them apart because they different 他们分开是因为他们不同 99 00:03:43,000 --> 00:03:44,270 players would be acting so the player 玩家会表演，所以玩家 100 00:03:44,469 --> 00:03:46,009 kind of when he shows up he would know 当他出现时，他会知道 101 00:03:46,209 --> 00:03:48,710 which player he was he would really not 他是哪个球员，他真的不会 102 00:03:48,909 --> 00:03:50,060 be confused about all of the nodes in 对中的所有节点感到困惑 103 00:03:50,259 --> 00:03:52,730 the equivalence class and the second 等价类和第二类 104 00:03:52,930 --> 00:03:55,610 restriction we have is that the two 我们有两个限制 105 00:03:55,810 --> 00:03:57,319 choice nodes have to have the same set 选择节点必须具有相同的集合 106 00:03:57,519 --> 00:03:59,180 of available actions because if the 可用操作，因为如果 107 00:03:59,379 --> 00:04:01,310 player can't tell them apart he has to 玩家无法将他们分开，他必须 108 00:04:01,509 --> 00:04:03,920 know what to do and it's the only 知道该怎么办，这是唯一的 109 00:04:04,120 --> 00:04:07,730 restrictions so let's look at an example 限制，让我们来看一个例子 110 00:04:07,930 --> 00:04:09,800 game here and see what the equivalence 在这里比赛，看看等效 111 00:04:10,000 --> 00:04:13,640 classes are so in this game player one 在这个玩家中上课是这样的 112 00:04:13,840 --> 00:04:15,319 has two different equivalence classes 有两个不同的等价类 113 00:04:15,519 --> 00:04:18,740 this is one equivalence class and this 这是一个等价类 114 00:04:18,939 --> 00:04:21,649 is another equivalence class so in other 是另一个等价类，所以在其他 115 00:04:21,848 --> 00:04:23,569 words we're going to use a dotted line 我们将使用虚线的单词 116 00:04:23,769 --> 00:04:25,968 here to connect together choice nodes 这里将选择节点连接在一起 117 00:04:26,168 --> 00:04:26,750 that belong to 属于 118 00:04:26,949 --> 00:04:28,850 the same equivalence class and what we 相同的等价类以及我们 119 00:04:29,050 --> 00:04:30,259 want to say in this game is that player 想在这场比赛中说的是那个球员 120 00:04:30,459 --> 00:04:33,110 1 moves and if he goes right then the 1移动，如果他走对，则 121 00:04:33,310 --> 00:04:34,850 game is just going to end and they're 游戏即将结束，他们 122 00:04:35,050 --> 00:04:36,500 just going to get a each of half of one 只会得到一半的一半 123 00:04:36,699 --> 00:04:39,949 if he goes left then they're going to 如果他走了，那他们将 124 00:04:40,149 --> 00:04:41,449 get to make player two is going to get 成为第二个玩家 125 00:04:41,649 --> 00:04:44,420 to make a choice and player 2 is going 做出选择，而玩家2将会 126 00:04:44,620 --> 00:04:47,360 to go either A or B and then player 1 is 去A或B然后玩家1是 127 00:04:47,560 --> 00:04:50,030 going to get to move a second time but 打算再去一次，但是 128 00:04:50,230 --> 00:04:51,470 player 1 isn't going to get to observe 玩家1不会观察 129 00:04:51,670 --> 00:04:54,829 the move that player 2 took and so he's 玩家2采取的行动，所以他是 130 00:04:55,029 --> 00:04:56,590 going to have to take the same action 将不得不采取相同的行动 131 00:04:56,790 --> 00:04:58,550 regardless of whether he said this 不管他是否这么说 132 00:04:58,750 --> 00:05:00,620 choice noted this choice node and indeed 选择记录了这个选择节点，实际上 133 00:05:00,819 --> 00:05:02,689 you can see we've labeled it the same 您可以看到我们已将其标记为相同 134 00:05:02,889 --> 00:05:05,780 way so if he says he wants to go left he 这样，如果他说他想离开他 135 00:05:05,980 --> 00:05:06,980 would have to go left it from both of 将不得不从两个 136 00:05:07,180 --> 00:05:10,460 these notes and just to complete the 这些笔记，只是为了完成 137 00:05:10,660 --> 00:05:11,360 answer to my question what are the 回答我的问题是什么 138 00:05:11,560 --> 00:05:12,980 equivalence classes for player 2 玩家2的等效课程 139 00:05:13,180 --> 00:05:15,560 well player 2 only has one choice node 玩家2只有一个选择节点 140 00:05:15,759 --> 00:05:17,030 actually there's a typo here there 其实这里有错字 141 00:05:17,230 --> 00:05:20,180 shouldn't be a 2 player 2 has only one 不应该是2位玩家2位只有一位 142 00:05:20,379 --> 00:05:21,470 choice node and so he has only one 选择节点，所以他只有一个 143 00:05:21,670 --> 00:05:26,060 equivalence class so how should we 等值课程，那么我们应该如何 144 00:05:26,259 --> 00:05:27,860 define the pure strategies for each 为每个定义纯策略 145 00:05:28,060 --> 00:05:29,689 player in this game what's going to make 这个游戏的玩家将要做什么 146 00:05:29,889 --> 00:05:31,960 sense as a definition of pure strategies 感觉是纯粹策略的定义 147 00:05:32,160 --> 00:05:36,259 well intuitively remember before what we 直观地记得我们之前 148 00:05:36,459 --> 00:05:38,750 said was that we had the cross-product 说是我们有交叉产品 149 00:05:38,949 --> 00:05:42,079 of all of the different action sets for 的所有不同操作集中 150 00:05:42,279 --> 00:05:44,480 each player we don't want that here 我们不想在这里的每个球员 151 00:05:44,680 --> 00:05:45,860 because we don't want for it to be 因为我们不希望它成为 152 00:05:46,060 --> 00:05:47,900 possible for player 1 to do something 玩家1可以做某事 153 00:05:48,100 --> 00:05:49,639 different in this choice node and in 在这个选择节点和 154 00:05:49,839 --> 00:05:52,310 this choice node so instead what we're 这个选择节点，所以我们是 155 00:05:52,509 --> 00:05:55,879 going to use as a definition is that the 用作定义是 156 00:05:56,079 --> 00:05:58,220 pure strategies for player I are the 我是玩家的纯策略 157 00:05:58,420 --> 00:06:00,230 cross-product of the action sets in 动作的叉积 158 00:06:00,430 --> 00:06:02,960 every different equivalence class that 每个不同的等价类 159 00:06:03,160 --> 00:06:05,990 he has and so player one's pure 他有，所以玩家是纯粹的 160 00:06:06,189 --> 00:06:09,230 strategies here are going to be a choice 这里的策略将是一个选择 161 00:06:09,430 --> 00:06:11,960 here and independently a choice here so 在这里，这里是一个独立的选择 162 00:06:12,160 --> 00:06:14,300 player one could take the action LL or 玩家可以采取行动LL或 163 00:06:14,500 --> 00:06:17,870 he could take the action RL or you could 他可以采取行动RL，也可以 164 00:06:18,069 --> 00:06:21,500 take the action L R or RR so player one 采取LR或RR的动作，让玩家一 165 00:06:21,699 --> 00:06:24,319 here has four different pure strategies 这里有四种不同的纯策略 166 00:06:24,519 --> 00:06:26,420 rather than eight as he would have if we 而不是他的八倍 167 00:06:26,620 --> 00:06:30,660 didn't have this equivalence class here 这里没有这个等效课程 168 00:06:33,009 --> 00:06:36,740 so in the imperfect information normal 所以在不完美的信息中正常 169 00:06:36,939 --> 00:06:38,800 form we have a more powerful 形式我们有一个更强大的 170 00:06:39,000 --> 00:06:40,939 representation than we did in the 代表性比我们在 171 00:06:41,139 --> 00:06:44,240 perfect information case and one way we 完美的信息案例和我们的一种方式 172 00:06:44,439 --> 00:06:46,009 can see that is we can represent any 可以看到那是我们可以代表任何 173 00:06:46,209 --> 00:06:47,420 normal form game in this representation 此表示形式的普通形式游戏 174 00:06:47,620 --> 00:06:49,460 which you may recall we couldn't do with 您可能还记得我们无法做到的 175 00:06:49,660 --> 00:06:52,280 perfect information games so here I'm 完美的信息游戏，所以我在这里 176 00:06:52,480 --> 00:06:54,650 showing you how to represent the TCP 向您展示如何表示TCP 177 00:06:54,850 --> 00:06:56,379 back-off game or in other words the 退避游戏或换句话说 178 00:06:56,579 --> 00:06:59,480 prisoner's dilemma game in imperfect 不完美的囚徒困境游戏 179 00:06:59,680 --> 00:07:01,910 information extensive form so how does 信息扩展形式，如何 180 00:07:02,110 --> 00:07:04,610 this work well first of all player 1 首先玩家1运作良好 181 00:07:04,810 --> 00:07:06,770 gets to decide whether to cooperate or 决定是否合作或 182 00:07:06,970 --> 00:07:09,920 defect and after that player 2 gets to 缺陷，然后玩家2进入 183 00:07:10,120 --> 00:07:12,680 decide whether to cooperate a defect now 现在决定是否合作缺陷 184 00:07:12,879 --> 00:07:15,230 of course in the prisoner's dilemma you 当然在囚徒困境中 185 00:07:15,430 --> 00:07:16,610 don't get to see what the other person 不要去看对方 186 00:07:16,810 --> 00:07:18,620 chose to do when you take your own 选择自己去做时 187 00:07:18,819 --> 00:07:20,420 action so it might sound like a problem 行动，所以听起来好像是个问题 188 00:07:20,620 --> 00:07:23,120 that player 2 gets to move second but 玩家2获得第二 189 00:07:23,319 --> 00:07:25,910 player 2 isn't able to tell which action 玩家2无法判断哪个动作 190 00:07:26,110 --> 00:07:28,100 player 1 took and so although our game 玩家1参加了比赛，尽管我们的比赛 191 00:07:28,300 --> 00:07:29,900 representation says that he goes second 表示说他屈居第二 192 00:07:30,100 --> 00:07:31,460 it doesn't really make a difference that 它并没有真正改变 193 00:07:31,660 --> 00:07:33,949 he goes second because because he's not 他获得第二名是因为他没有 194 00:07:34,149 --> 00:07:36,350 informed of what player 1 did and then 告知玩家1的行为，然后 195 00:07:36,550 --> 00:07:38,329 once both of them take their actions we 他们俩一旦采取行动，我们 196 00:07:38,529 --> 00:07:40,520 end up with some payoff so if they go C 最终得到一些回报，所以如果他们去C 197 00:07:40,720 --> 00:07:43,250 D and they end up with this payoff here D，他们最终在这里得到了回报 198 00:07:43,449 --> 00:07:44,569 and these are the same payoffs that we 这些是与我们相同的收益 199 00:07:44,769 --> 00:07:47,569 have in the game matrix notice that we 在游戏矩阵中注意到我们 200 00:07:47,769 --> 00:07:49,819 could have things work the same way if 可以让事情以相同的方式运作，如果 201 00:07:50,019 --> 00:07:52,759 we put player 2 at the root node and 我们将播放器2放在根节点上， 202 00:07:52,959 --> 00:07:55,579 player 1 down here below because time 玩家1在这里的下方，因为时间 203 00:07:55,779 --> 00:07:59,159 isn't really playing a role in this game 在这个游戏中并没有真正扮演角色 204 00:07:59,730 --> 00:08:02,629 so I what I told you on the previous 所以我以前告诉过你的 205 00:08:02,829 --> 00:08:04,819 slide was how to start with a normal 幻灯片是如何从正常开始 206 00:08:05,019 --> 00:08:06,560 form game and make an extensive form 形式游戏并进行广泛的形式 207 00:08:06,759 --> 00:08:09,439 game out of it I can also still do the 游戏出来，我仍然可以 208 00:08:09,639 --> 00:08:11,000 thing that we talked about with the 我们谈论的东西 209 00:08:11,199 --> 00:08:13,069 perfect information extensive form which 完善的信息广泛形式 210 00:08:13,269 --> 00:08:14,660 is to start with an extensive form game 从一个广泛的形式游戏开始 211 00:08:14,860 --> 00:08:16,340 and make a normal form game out of it 然后用它制作一个普通的形式游戏 212 00:08:16,540 --> 00:08:19,189 and the way this works is exactly the 而它的工作方式正是 213 00:08:19,389 --> 00:08:21,590 way I did before so I take all of the 我以前做的方式，所以我把所有 214 00:08:21,790 --> 00:08:23,750 pure strategies for player 1 and I make 我和玩家1的纯策略 215 00:08:23,949 --> 00:08:26,090 them into rows I take all of the pure 他们成排，我把所有的纯 216 00:08:26,290 --> 00:08:27,770 strategies for player 2 and I make them 玩家2的策略，我让他们 217 00:08:27,970 --> 00:08:30,020 into columns and then this gives me my 列，然后这给了我我的 218 00:08:30,220 --> 00:08:31,610 matrix and for every cell of the matrix 矩阵以及矩阵的每个单元格 219 00:08:31,810 --> 00:08:35,179 I say well if player 1 took this pure 我说好，如果玩家1接受了 220 00:08:35,379 --> 00:08:37,189 strategy and player 2 took this pure 策略和玩家2采取了这种纯 221 00:08:37,389 --> 00:08:39,439 strategy what payoff would result and I 策略会带来什么回报，我 222 00:08:39,639 --> 00:08:41,209 put that into this cell of the matrix 把它放到矩阵的这个单元格中 223 00:08:41,409 --> 00:08:45,240 and I fill in the whole matrix that way 然后我以这种方式填写整个矩阵 224 00:08:45,320 --> 00:08:48,539 and once I have the matrix like that 一旦我有了这样的矩阵 225 00:08:48,740 --> 00:08:51,508 then then I'm kind of done my definition 然后我就完成了定义 226 00:08:51,708 --> 00:08:53,370 of mixed strategies is exactly what it 混合策略正是它的目的 227 00:08:53,570 --> 00:08:54,508 was before it's just the mixed 之前只是混合 228 00:08:54,708 --> 00:08:56,389 strategies in the induced normal form 归纳法则形式的策略 229 00:08:56,589 --> 00:08:58,828 the definition of best response in Nash 纳什最佳反应的定义 230 00:08:59,028 --> 00:09:00,299 equilibrium for imperfect information 不完美信息的平衡 231 00:09:00,500 --> 00:09:02,339 extensive form games again just kind of 广泛的形式游戏再次只是一种 232 00:09:02,539 --> 00:09:04,859 leverage the induced normal form and so 利用归纳的范式等等 233 00:09:05,059 --> 00:09:06,419 all of those concepts that you already 您已经拥有的所有这些概念 234 00:09:06,620 --> 00:09:09,628 understand from from normal form games 从普通形式的游戏中了解 235 00:09:09,828 --> 00:09:12,389 carry over directly to imperfect 直接结转不完美 236 00:09:12,589 --> 00:09:14,490 information games and so for example we 信息游戏，例如我们 237 00:09:14,690 --> 00:09:16,649 know from Nash's theorem that a Nash 从纳什定理知道纳什 238 00:09:16,850 --> 00:09:18,508 equilibrium always exists for every 每个人总是存在均衡 239 00:09:18,708 --> 00:09:20,429 imperfect information extensive form 不完善的信息广泛形式 240 00:09:20,629 --> 00:09:22,529 game because I can make a finite normal 游戏，因为我可以做有限的法线 241 00:09:22,730 --> 00:09:25,589 form game out of it now it's going to be 从中形成形式的游戏 242 00:09:25,789 --> 00:09:28,469 the case that this transformation can 这种转变可以 243 00:09:28,669 --> 00:09:30,448 make the game exponentially bigger as it 使游戏成倍增长 244 00:09:30,649 --> 00:09:32,549 could before even with the perfect 甚至可以做到完美 245 00:09:32,750 --> 00:09:34,438 information case but for example for 信息案例，但例如 246 00:09:34,639 --> 00:09:36,029 existence of equilibrium that doesn't 不存在的均衡 247 00:09:36,230 --> 00:09:39,719 matter now lastly you might wonder what 现在很重要，您可能想知道 248 00:09:39,919 --> 00:09:41,818 happens if I take both of these 如果我把这两个都发生 249 00:09:42,019 --> 00:09:43,318 transformations that I've shown you and 我向您展示的转换和 250 00:09:43,519 --> 00:09:45,568 I apply them together so for example I 我将它们一起应用，例如 251 00:09:45,769 --> 00:09:46,649 could start with an imperfect 可能从不完美开始 252 00:09:46,850 --> 00:09:48,929 information extensive form game make it 信息丰富的游戏形式 253 00:09:49,129 --> 00:09:50,849 into a normal form game and then make 变成普通形式的游戏，然后制作 254 00:09:51,049 --> 00:09:52,349 that back into an imperfect information 回到不完美的信息 255 00:09:52,549 --> 00:09:55,349 extensive form game again so you might 再次进行广泛的形式游戏，因此您可能 256 00:09:55,549 --> 00:09:57,059 wonder do I end up with the same game 我不知道我最终会玩同样的游戏吗 257 00:09:57,259 --> 00:10:00,628 and the answer is no I won't because I 答案是不，我不会，因为我 258 00:10:00,828 --> 00:10:02,818 might have a game tree which is pretty 可能有一个漂亮的游戏树 259 00:10:03,019 --> 00:10:06,109 deep and it could have all kinds of 深，它可能有各种各样的 260 00:10:06,309 --> 00:10:08,758 different equivalence classes it could 可以使用的不同等价类 261 00:10:08,958 --> 00:10:09,959 have all kinds of different sequential 有各种不同的顺序 262 00:10:10,159 --> 00:10:12,089 moves by the different players and when 由不同玩家移动，以及何时 263 00:10:12,289 --> 00:10:14,099 I make it into a normal form game I'm 我把它变成普通的形式游戏 264 00:10:14,299 --> 00:10:16,740 going to get this flat table and then 要得到这张桌子，然后 265 00:10:16,940 --> 00:10:18,839 when I take a flat table and turn that 当我拿一张平桌子转身 266 00:10:19,039 --> 00:10:21,959 into an extensive form game it's going 进入广泛的形式游戏 267 00:10:22,159 --> 00:10:23,399 to be an extensive form game that only 成为一个广泛的形式游戏， 268 00:10:23,600 --> 00:10:26,578 has two levels with all this stuff in 有两个级别的所有这些东西 269 00:10:26,778 --> 00:10:30,419 one big equivalence class and so it's 一个大等价类，所以 270 00:10:30,620 --> 00:10:31,769 going to be an extensive form game that 将是一个广泛的形式游戏， 271 00:10:31,970 --> 00:10:32,938 looks different from the one that I 看起来和我的不同 272 00:10:33,139 --> 00:10:36,209 started with but what is important is 首先开始，但重要的是 273 00:10:36,409 --> 00:10:37,469 that it's going to have the same 它将具有相同的 274 00:10:37,669 --> 00:10:39,359 strategy spaces the same sets of pure 策略空间相同的纯集合 275 00:10:39,559 --> 00:10:41,549 strategies from both agents and it's 两家代理商的策略， 276 00:10:41,750 --> 00:10:42,659 going to have the same set of Nash 将具有相同的纳什集 277 00:10:42,860 --> 00:10:45,179 equilibria so although these games might 平衡，所以尽管这些游戏可能 278 00:10:45,379 --> 00:10:46,769 look different from the perspective of 从不同的角度看 279 00:10:46,970 --> 00:10:48,508 how they explicitly talk about time 他们如何明确谈论时间 280 00:10:48,708 --> 00:10:50,039 they're going to be strategically 他们将在战略上 281 00:10:50,240 --> 00:10:52,889 equivalent games and that's it for this 等效的游戏，仅此而已 282 00:10:53,089 --> 00:10:58,089 video 视频