The economics literature distinguishes the quality of a game’s information (perfect vs. imperfect) from the completeness of a game’s information (complete vs. incomplete). Perfect information means that every player is perfectly informed of all the actions that happened in the game, including the starting state of the game. Complete information means that players possess all relevant information about their opponents, including their objectives, their possible actions, and their preferences. In economics, games are classified according to these two dimensions:
经济学文献从游戏的信息(完全与不完全)的完整性区分了游戏的信息质量 (完美与不完美)。 完美的信息意味着每个玩家都可以完美地了解游戏中发生的所有动作，包括游戏的开始状态。 完整的信息意味着玩家拥有有关对手的所有相关信息，包括他们的目标，他们可能采取的行动以及他们的偏好。 在经济学中，游戏根据以下两个方面进行分类：
In the previous article, we talked about social deduction games — a genre of game where the influence currency (specifically, social influence) is used to mediate the initial imbalance between the power and information currencies of two teams. The information in social deduction games is imperfect and incomplete because while the rules, the objectives, and the possible information in the game are common knowledge, some players have no knowledge of the starting state of the game, or of which actions were taken by which players. Effectively, the “good” team in a social deduction game starts somewhere in the bottom-left quadrant and the “bad” team starts somewhere in the top-right quadrant; the bad team then tries to thwart the good team’s attempts to reach information parity.
在上一篇文章中，我们讨论了社交演绎游戏-一种游戏类型，其中影响力货币(特别是社会影响力)用于调解两个团队的力量和信息货币之间的初始失衡。 社交演绎游戏中的信息是不完美且不完整的，因为尽管游戏中的规则，目标和可能的信息是常识，但有些玩家却不知道游戏的开始状态或采取了哪些行动。玩家。 实际上，社交演绎游戏中的“好”团队从左下象限开始，而“差”团队则从右上象限开始。 坏团队然后试图挫败好团队达到信息均等的尝试。
In this article, we discuss perfect information games — the right half of our diagram. As it so happens, almost all of these games also have complete information. Perfect incomplete information games are (unsurprisingly) rare, but they do exist and I will touch on them in future articles.
在本文中，我们讨论了完美的信息游戏-图的右半部分。 碰巧的是，几乎所有这些游戏也都具有完整的信息。 完美的不完整信息游戏很少(毫无疑问)，但是它们确实存在，我将在以后的文章中进行介绍。
热身 (Warming Up)
Many beloved perfect information games started off as war games designed to help military generals sharpen their strategic thinking. Chess, xiangqi, and shogi likely have a common ancestor in chaturanga, a game played in the Gupta Empire in the 6th century AD. Chaturanga translates to “having four parts”, referring to the four divisions of an army — infantry, cavalry, chariotry, and elephantry — and involves encircling the enemy king (“checkmate” translates to “the king is dead” or “the king is helpless”, from the Persian shah mat). Go, also an encirclement game (but of territory, not of a particular piece), was created much earlier in China (possibly as early as 2000 BC) and eventually became xiangqi’s upper-class cousin, played by elites. These games have stood the test of time and are as much cultural artifacts as they are games. They have captivated generation after generation as players continue to uncover new insights about the games’ strategic depth — insights whose discovery is being accelerated today by artificial intelligence projects like AlphaGo. War games aside, though, “perfect information” is less a genre of game and more a specific property of the game’s information currency.
许多备受喜爱的完美信息游戏开始于战争游戏，旨在帮助军事将领们提高其战略思维。 国际象棋，象棋和将棋在加图兰加可能是一个共同的祖先，该游戏是在公元6世纪古普塔帝国玩的。 乔图兰加(Chaturanga)译为“具有四个部分”，指的是陆军的四个师–步兵，骑兵，战车和大象–包括包围敌方国王(“将军”翻译成“国王已死”或“国王已死”)。无助”， 来自波斯语shah mat )。 围棋，也是一种包围游戏(但不是领土，而是一块领土)，是在中国更早( 可能早在公元前2000年 )创造的，并最终成为了由精英们扮演的象棋的上流表弟。 这些游戏经受了时间的考验，并且与游戏一样具有许多文化产物。 随着玩家不断发现有关游戏战略深度的新见解，他们一代又一代着迷。这些见解如今已被AlphaGo等人工智能项目所加速。 但是，除了战争游戏以外，“完美信息”不是游戏的一种，而是游戏信息货币的一种特定属性。
One consequence of having a perfect information game is that if the game mechanics allow players to directly interact, the game must be turn-based. If players were allowed to act simultaneously, then players would not have perfect knowledge of all previous actions in the game. Because perfect information games are often turn-based, the actions in these games (and the resulting game states) are amenable to being visually represented as trees. If you’ve ever taken an advanced course in game theory, probability, economics, or computer science, you’ll have seen diagrams like these:
拥有完善的信息游戏的一个后果是，如果游戏机制允许玩家直接互动，则游戏必须基于回合制。 如果允许玩家同时行动，那么玩家将不会完全了解游戏中的所有先前动作。 由于完美的信息游戏通常是基于回合制的，因此这些游戏中的动作(以及最终的游戏状态)都可以直观地表示为树。 如果您曾经学习过博弈论，概率论，经济学或计算机科学方面的高级课程，那么您将看到如下图：
We’ll avoid getting into the weeds of specific game trees in this article, but the one relevant concept here is the notion of a branching factor. For an individual node (game state) in the tree, the branching factor is the number of new nodes generated from the original one; each possible action you can take from that node gives rise to a new “branch” and a new resulting node. We are usually interested in the average or effective branching factor of a typical node at a given level of the tree.
在本文中，我们将避免涉及特定游戏树的杂草，但是此处一个相关的概念是分支因子的概念。 对于树中的单个节点(游戏状态)，分支因子是从原始节点生成的新节点数。 您可以从该节点执行的每个可能操作都会产生一个新的“分支”和一个新的结果节点。 我们通常对树的给定级别上典型节点的平均或有效分支因子感兴趣。
The difficulty of a perfect information game is directly proportional to its average branching factor. Perfect information games can take years to master and are notoriously difficult. Not because players lack meaningful information, but because they are overwhelmed by the burden of understanding its implications. You can only think so many moves ahead.
完美信息游戏的难度与它的平均分支因子成正比。 完美的信息游戏可能需要花费数年才能掌握，而且非常困难。 不是因为玩家缺乏有意义的信息，而是因为他们不堪理解其含义的负担。 您只能认为前进的步伐很多。
In the first article of this series, we discussed how currencies that never differ in quantity across teams can be excluded from our analysis. Since all players have access to exactly the same information in perfect information games by definition, information is not a relevant currency here. We are therefore left to grapple with just power and influence.
在本系列的第一篇文章中 ，我们讨论了如何从团队中排除数量上永不相同的货币。 根据定义，由于所有玩家都可以在完美的信息游戏中获得完全相同的信息，因此这里的信息不是一种重要的货币。 因此，我们只剩下权力和影响力。
Because we are by and large talking about turn-based games, one power currency that deserves attention is turn order.
In games with two teams, there is often a slight advantage associated with going first. This is especially true in games with high branching factors like chess and go, where small advantages accumulate like compound interest over several levels of the game tree to create winning states. Different games compensate for this known power imbalance in various ways — players may play multiple games as both sides in competitive settings, the advantaged side may be given a handicap, or the win condition for the advantaged side may be altered altogether. For example, in armageddon chess, the player with the White pieces is given more time on their clock, but Black wins the game if they secure at least a draw (while White has to win outright).
在有两支球队的比赛中，先发通常会带来一点优势。 在象棋和围棋之类具有高分支因子的游戏中尤其如此，在这种情况下，小的利益会像在多个游戏树级别上的复利一样积累，以创建获胜状态。 不同的游戏以各种方式补偿这种已知的力量失衡-玩家可以在竞争环境中作为双方玩多场游戏，可以给优势方让分，或者可以完全改变优势方的获胜条件。 例如，在世界末日象棋中，拥有白色棋子的玩家有更多的时间来计时，但如果黑人至少赢得平局，则黑棋将赢得比赛(而白棋必须完全获胜)。
In games with three or more teams, the advantage of a particular position in the turn order becomes complicated to assess, especially if players can form impromptu, implicit agreements to eliminate other players first. Multiplayer variants of perfect information games have an even larger branching factor than their two-team counterparts, but they can be a great way to introduce a cooperative dynamic to games that makes turn order more irrelevant.
The most prominent power currency is the resources of the game itself — typically your pieces. In games like Ludo, Othello, and Go, all pieces move in the same way and therefore have equal value. Points are accumulated based on the particular arrangement of the pieces on the board (the theme generally being “capture territory”), not on the inherent value of the pieces themselves.
最突出的动力货币是游戏本身的资源 -通常是您的作品。 在Ludo，Othello和Go等游戏中，所有棋子都以相同的方式移动，因此具有同等的价值。 积分是根据棋子在棋盘上的特定排列(主题通常是“捕获区域”)而不是棋子本身的内在价值来累积的。
In games like checkers, chess, and shogi, pieces can move in different ways and therefore have different values. A numerical value might be assigned to the value of the pieces, but experts frequently disagree on what the correct values should be, especially if they are tangential to the game’s win condition (the theme generally being “capture your opponent’s most important piece”).
Most perfect information games start with equal resources for all teams. This simplifies the analysis of power considerably and makes the values of individual pieces less relevant because anything I can do to you, you can do to me. As the game progresses, the balance of power shifts, and in most situations, a decisive power advantage should lead to victory. However, power imbalances matter more in games which feature higher variance between the abilities of individual pieces. For example, in chess, the total power of your team is almost always decreasing, and the queen dominates every other piece by far. In such an ecosystem, it is almost impossible to recover from a significant power imbalance short of an immense amount of compensation in your influence currency. Contrast this with shogi, where pieces can reenter the game after they are captured, and the most powerful piece is only the rook. This often leads to mutual checkmating attacks even in the presence of significant power imbalance.
对于所有团队来说，最完美的信息游戏都以平等的资源开始。 这大大简化了功率分析，并使各个零件的价值不那么相关，因为我对您可以做的一切，您都可以对我做。 随着比赛的进行，力量的平衡会发生变化，在大多数情况下，决定性的力量优势应该会导致胜利。 但是，功率不平衡在游戏中更为重要，因为游戏的各个部分的能力之间存在较大差异。 例如，在国际象棋中，您的团队的总实力几乎总是在下降，而女王/王后则一直统治着其他所有领域。 在这样的生态系统中，几乎不可能从重大的电力失衡中恢复过来，而没有影响货币的巨额补偿。 与将棋相比，将棋子可以在被捕获后重新进入游戏，而最强大的棋子只是新手。 即使存在严重的功率不平衡，这也经常导致相互验证攻击。
Nevertheless, different teams in perfect information games can start with different resources — or accumulate different resources along the way. Consider some variants of chess:
Or consider other genres of games altogether, like Bananagrams — a Scrabble-like game where you must use your own stash of lettered tiles to build a valid crossword before anyone else, while drawing additional tiles from a communal pile — and Monopoly. Because players can see everyone’s tiles in real time but can only interact with their own, Bananagrams is one of those rare perfect information games that is not turn-based. Players start off with different resources (i.e. different letters) and continue to receive different resources throughout the game, but the game is balanced around the fact that the English language contains enough words to accommodate most combinations of letters. Similarly, players in Monopoly accumulate different resources (money, properties, houses, hotels) along the way. The game is balanced around when these resources are dispensed, and what benefits are afforded to players who own a particular set of color groups, utilities, etc.
或完全考虑其他类型的游戏，例如Bananagrams(类似Scrabble的游戏)，在这种游戏中，您必须使用自己的带字母的积木藏起来，在其他任何人之前构建有效的填字游戏，同时从公共堆中获取其他积木和垄断。 由于玩家可以实时看到每个人的图块，但只能与自己的图块交互，因此Bananagrams是那些罕见的非回合制完美信息游戏之一。 玩家以不同的资源(即不同的字母)开始，并在整个游戏中继续获得不同的资源，但是游戏围绕以下事实进行了平衡：英语包含足够的单词以容纳大多数字母组合。 同样，“垄断”中的参与者在此过程中积累了不同的资源(金钱，财产，房屋，酒店)。 游戏在分配这些资源的时间以及拥有一组特定颜色组，实用程序等的玩家所能享受的收益方面保持平衡。
Just to drive the point home, these games are still perfect information games because all of these resources are known about from the beginning of the game. Players can plan around them — even when randomness plays a role in a player’s actions.
The last power currency worth mentioning is time. A player can spend endless amounts of time contemplating their move in a game with a high branching factor, so time is a very pragmatic currency for managing the duration of a game and encouraging more daring play. Typically time is implemented as a currency for the win condition: players lose if they run out of the time before their opponents (think chess clocks and increments, or the byoyomi system in go).
最后一个值得一提的动力货币是时间 。 玩家可以花费大量时间来考虑在分支因子较高的游戏中的移动，因此时间是管理游戏持续时间并鼓励更大胆游戏的非常实用的货币。 通常情况下，时间是作为获胜条件的一种货币来实现的：如果玩家在对手之前的时间用完了，他们就会输钱(想想国际象棋的钟表和增量，或者在使用byoyomi系统)。
Unlike in social deduction games, where the influence currency is immediately accessible because of our innate familiarity with the “rules” of social interaction, influence in a perfect information game can be inscrutable to the novice. That is not to say that social influence is any less complex or multifaceted, but understanding influence in games where everything is known is a lifelong endeavor with many peaks to traverse and a near-infinite skill cap. To put this in perspective, consider two facts: 1) any decent AI for a perfect information game can easily defeat the human world champion in that game, and 2) the best AIs still lose to each other because they do not fully understand the influence currency.
与社交演绎游戏不同，在社交演绎游戏中，由于我们天生就熟悉社交互动的“规则”，因此可以立即获得影响力货币，而对于新手来说，在完美的信息游戏中的影响力是难以理解的。 这并不是说社会影响力没有那么复杂或多方面，而是要了解在一切已知的游戏中的影响力是一项毕生的努力，需要穿越许多高峰，并且技能上限几乎是无限的。 为了正确理解这一点，请考虑以下两个事实：1)一款完美的信息游戏中任何一款像样的AI都可以轻易击败该游戏中的人类世界冠军； 2)最好的AI仍然会彼此失去，因为它们无法完全理解其影响力。货币。
At its core, your understanding of influence comes down to your ability to look at the current state of the game and assess how well each team is doing, what each team’s plan should be, and why. Perfect information games test how reliable your heuristics are for navigating and pruning the morass of possible actions you could take when you invariably find yourself in a part of the game tree that you’ve never encountered before — which is almost guaranteed to happen every time you play. Getting better at these games involves assessing myriad factors about a game state. Not just who has more resources (power imbalance), but who has more “space”, whose pieces are better “developed”, who has the “initiative”, who is “attacking” and “defending”, who is making better use of their “tempi”, and so on — where all these terms mean something specific in different games and are highly context dependent.
从本质上讲，您对影响力的理解取决于您查看游戏当前状态并评估每个团队的表现，每个团队的计划应该是什么以及为什么的能力。 完美的信息游戏可以测试您的试探法在导航和修剪各种杂物时的可靠性，而这些杂物总是会出现在您从未遇到过的游戏树的一部分中时，几乎可以保证每次您都会遇到这种情况玩。 在这些游戏中变得更好涉及评估有关游戏状态的众多因素。 不仅谁拥有更多的资源(权力失衡)，谁拥有更多的“空间”，谁拥有更好的“开发”能力，谁拥有“主动性”，谁拥有“进攻”和“捍卫”能力，谁就能更好地利用他们的“ tempi”，依此类推-所有这些术语都表示不同游戏中的特定内容，并且高度依赖于上下文。
The critical skill in these games is knowing when and how to trade power for influence. This is something AI has been enlightening us on for a long time, especially so in recent years with the advent of neural-network AIs. These AIs do not rely on human-given heuristics. Instead, they build up their own positional understanding by playing games against themselves millions of times. I’ll discuss AlphaGo and AlphaZero in more detail in the next article.
这些游戏中的关键技能是知道何时以及如何用力量交换影响力。 这是AI长期以来一直启发我们的事情，尤其是近年来随着神经网络AI的出现。 这些AI不依赖于人类赋予的启发式算法。 相反，他们通过与自己进行数百万次比赛来建立自己的位置理解。 在下一篇文章中，我将更详细地讨论AlphaGo和AlphaZero。
下次之前... (Before next time…)
In perfect information games, players are armed with the power currencies of turn order, resources, and time as they wade through a deluge of possible actions whose consequences cannot be calculated to endgame. Perfect information games compensate for the irrelevance of the information currency with a richness and inexhaustible depth in their influence currency.
With our introduction to social deduction games and perfect information out of the way, we have set the stage for a deeper exploration of the implications of the market economy framework. In the next article I will talk about the art of actually winning these kinds of games by carefully managing your power and influence currencies, which I will analogize to cash and unrealized gain in a stock market.