不确定性下的战略：期望、信息价值与期权
引入| English | 释义 | 拼音 |
|---|---|---|
| expected value/ekˈspektɪd ˈvæljuː/ | 期望值 | qī wàng zhí |
| scenario | 情景 | qíng jǐng |
| EVPI | 完全信息期望价值 | wán quán xìn xī qī wàng jià zhí |
| real option | 实物期权 | shí wù qī quán |
| trigger | 触发条件 | chù fā tiáo jiàn |
Three futures, one expected value
- The founder does not know whether the festival doubles, stalls or dies - and adapting is not a plan. Uncertainty has arithmetic.
- Scenario 情景 payoffs: grows 45k (p 0.5), stalls 18k (p 0.3), dies -12k (p 0.2). Expected value 期望值: $22.5 + 5.4 - 2.4 = 25.5$k.
The ceiling on knowing
- EVPI: with perfect information you act only on the good outcomes: $0.5 \times 45 + 0.3 \times 18 = 27.9$k.
- The information is worth $27.9 - 25.5 = 2.4$k - the most ANY study may cost. A 6k consultant study is unbuyable at any quality.
EV: 0.5 x 45 + 0.3 x 18 + 0.2 x (-12) = ? (one decimal)
难度 2/5 · 今日首次完成可获 140 金币及少量额外奖励
25.5k.
Match each tool to its number in the case.
难度 2/5 · 今日首次完成可获 140 金币及少量额外奖励
Four numbers, four different decisions.
Options beat forecasts
- Stage the cafe: an 8k pilot. Real option 实物期权 arithmetic: $0.3 \times 70 + 0.7 \times (-2) - 8 = 11.6$k against 7.0 unstaged - staging adds +4.6 by cutting the tail.
- A trigger 触发条件 writes the review in daylight: pre-orders 20% below plan by week 4 and the expansion option lapses unexercised.
Forecast, option, or trigger?
Route each tool to what it actually is.
With perfect information: 0.5 x 45 + 0.3 x 18 = 27.9. The EVPI?
难度 2/5 · 今日首次完成可获 140 金币及少量额外奖励
27.9 - 25.5 = 2.4k.
Staged: 0.3 x 70 + 0.7 x (-2) - 8 = ? (one decimal)
难度 2/5 · 今日首次完成可获 140 金币及少量额外奖励
11.6k against 7.0 unstaged: +4.6 for an 8k pilot.
A consultant offers the festival-demand study for 6k. The EVPI arithmetic says:
难度 1/5 · 今日首次完成可获 100 金币及少量额外奖励
One subtraction kills it; the nearly-free app data is the better spend.
Three uncertainty slips
- Reading the EV as a forecast. It is a weighted average of futures that will not happen.
- Buying information above its EVPI.
- Confusing flexibility with indecision. An option has a price, a trigger and an expiry.
Staging adds value mainly by:
难度 1/5 · 今日首次完成可获 100 金币及少量额外奖励
The head stays; the tail goes - that is what options buy.
The EV of 25.5k is a forecast of this year’s result.
难度 1/5 · 今日首次完成可获 100 金币及少量额外奖励
It is a weighted average of futures - none of which is 25.5.
An option without a trigger, price and expiry is procrastination.
难度 1/5 · 今日首次完成可获 100 金币及少量额外奖励
Flexibility with a rule; otherwise it is indecision with a name.
Recap
- EV 25.5; EVPI 2.4 - the ceiling on research.
- Staged: 11.6 against 7.0 for an 8k pilot; the tail is where options pay.
- Write the trigger before the uncertainty resolves.