Python 中异常值的简单标度概率

Question

我正在创建一个虚拟拍卖游戏，我需要比现在更复杂的 NPC 行为。基本上，每个项目都有一个基本价格（bp），并且该项目的起始出价（sb）将以此范围（或非常类似的东西）计算：0.8bp<= sb <= 1.1bp. The opposing NPC bidders need to judge how reasonable the current bid is, compared to the base price and/or starting value, and, with some outlying behavior (i.e. betting when it seems a little irrational), bid reasonably on the current item. Put simply, it should bid aggressively on the item when the bid is lower or around the base price, and frugally bid on the item if it's high above the base price, or just give up.

问题是，我真的不知道该怎么做。不仅如此，这将主要在 TI-84 Plus CE 计算器上运行，因此外部库和模块必须非常有限（本质上只是随机）。如果您附上您提供的任何公式/代码的简短（或详细）解释，那就太好了，因为我很想了解更多相关信息。

Answer 1

以下是您入门的答案：

import random
from dataclasses import dataclass


@dataclass
class Npc:
    i: int
    alpha = 2
    beta = 0.25
    bid_percent_increase_min = 1.01
    bid_percent_increase_max = 1.03
    percent_thresh_for_mandatory_bid = 0.75

    def bet(self, cb, bp):
        r = (
            random.gammavariate(self.alpha, self.beta)
            + self.percent_thresh_for_mandatory_bid
        )
        if r >= cb / bp:
            return (
                random.uniform(
                    self.bid_percent_increase_min, self.bid_percent_increase_max
                )
                * cb
            )
        return 0


@dataclass
class Auction:
    item_name: str
    bp: float
    npcs: int = 5
    starting_bid_percent_min = 0.8
    starting_bid_percent_max = 1.1

    def __call__(self, *args, **kwargs):
        # 0.8bp <= sb <= 1.1bp
        cb = (
            random.uniform(self.starting_bid_percent_min, self.starting_bid_percent_max)
            * self.bp
        )
        print(f"Auction starting for {self.item_name.title()} (BP: ${self.bp:.2f})")
        print(f"\tStarting bid: ${cb:.2f}")
        bettors = [Npc(i) for i in range(self.npcs)]
        while len(bettors) > 1:
            for j, bettor in enumerate(bettors):
                b = bettor.bet(cb, self.bp)
                if b > cb:
                    print(
                        f"\t\tCurrent bid: ${cb:.2f} | Bettor {bettor.i} bids ${b:.2f}"
                    )
                    cb = b
                else:
                    print(f"\tBettor {bettor.i} left")
                    bettors.pop(j)
        print(
            f"Winning bid: ${cb:.2f} | Bettor {bettors[0].i} won the {self.item_name.title()}!"
        )


if __name__ == "__main__":
    items = [
        ("apple", 1.30),
        ("water bottle", 9.99),
        ("tv", 189.99),
        ("laptop", 1499.99),
    ]
    for item_name, bp in items:
        Auction(item_name, bp)()
        print("\n")

输出示例：

Auction starting for Apple (BP: $1.30)
    Starting bid: $1.23
    Bettor 0 left
        Current bid: $1.23 | Bettor 2 bids $1.25
        Current bid: $1.25 | Bettor 3 bids $1.28
        Current bid: $1.28 | Bettor 4 bids $1.30
        Current bid: $1.30 | Bettor 1 bids $1.32
    Bettor 2 left
    Bettor 4 left
        Current bid: $1.32 | Bettor 1 bids $1.34
        Current bid: $1.34 | Bettor 3 bids $1.35
        Current bid: $1.35 | Bettor 1 bids $1.39
        Current bid: $1.39 | Bettor 3 bids $1.43
        Current bid: $1.43 | Bettor 1 bids $1.47
    Bettor 3 left
Winning bid: $1.47 | Bettor 1 won the Apple!


Auction starting for Water Bottle (BP: $9.99)
    Starting bid: $10.63
    Bettor 0 left
        Current bid: $10.63 | Bettor 2 bids $10.77
        Current bid: $10.77 | Bettor 3 bids $11.00
    Bettor 4 left
        Current bid: $11.00 | Bettor 1 bids $11.27
        Current bid: $11.27 | Bettor 2 bids $11.50
        Current bid: $11.50 | Bettor 3 bids $11.75
    Bettor 1 left
        Current bid: $11.75 | Bettor 3 bids $11.92
        Current bid: $11.92 | Bettor 2 bids $12.20
        Current bid: $12.20 | Bettor 3 bids $12.36
    Bettor 2 left
Winning bid: $12.36 | Bettor 3 won the Water Bottle!


Auction starting for Tv (BP: $189.99)
    Starting bid: $171.10
        Current bid: $171.10 | Bettor 0 bids $174.12
        Current bid: $174.12 | Bettor 1 bids $177.67
        Current bid: $177.67 | Bettor 2 bids $180.92
        Current bid: $180.92 | Bettor 3 bids $183.20
        Current bid: $183.20 | Bettor 4 bids $186.78
    Bettor 0 left
        Current bid: $186.78 | Bettor 2 bids $189.89
    Bettor 3 left
        Current bid: $189.89 | Bettor 1 bids $192.56
    Bettor 2 left
        Current bid: $192.56 | Bettor 1 bids $196.38
        Current bid: $196.38 | Bettor 4 bids $200.25
        Current bid: $200.25 | Bettor 1 bids $206.24
    Bettor 4 left
Winning bid: $206.24 | Bettor 1 won the Tv!


Auction starting for Laptop (BP: $1499.99)
    Starting bid: $1404.03
    Bettor 0 left
        Current bid: $1404.03 | Bettor 2 bids $1431.79
        Current bid: $1431.79 | Bettor 3 bids $1450.59
        Current bid: $1450.59 | Bettor 4 bids $1491.00
        Current bid: $1491.00 | Bettor 1 bids $1508.36
    Bettor 2 left
        Current bid: $1508.36 | Bettor 4 bids $1550.88
        Current bid: $1550.88 | Bettor 1 bids $1589.62
        Current bid: $1589.62 | Bettor 3 bids $1613.55
        Current bid: $1613.55 | Bettor 4 bids $1650.92
    Bettor 1 left
        Current bid: $1650.92 | Bettor 4 bids $1684.26
        Current bid: $1684.26 | Bettor 3 bids $1715.78
        Current bid: $1715.78 | Bettor 4 bids $1750.79
    Bettor 3 left
Winning bid: $1750.79 | Bettor 4 won the Laptop!

这里我使用了gamma分布，PDF看起来像这样（偏移0.75）：

如果从此分布中抽取的随机值大于（当前出价/底价），则 NPC 进行投注。这意味着什么：

• 当前出价低于0.75*bp时总是进行投注
• 当当前出价超过底价时，投注的可能性就会降低（其中存在一些非理性因素）

您显然可以使用

alpha

和

beta

值以及其他一些参数，以更好地适应您的特定情况。