← Game Theory
第 1 章 · 20 分钟
The minimal object: strategies, outcomes, preferences
What an interaction is written as, and exactly what 'rational' means here.
概念地图
Formalising
Writing an interaction as players, strategies, outcomes and preferences.
深色为本章概念，浅色为其他章
陪练模式
不想只是读？让它带你走一遍。
导师把这一章拆成小步，每一步先问你，再讲；你用自己的话答，它先认下对的部分再纠偏。用你自己的 AI，对话只存在这台设备上。
Locus01
延伸阅读
von Neumann and Morgenstern · 1944 · Theory of Games and Economic Behavior
First wrote interactive decision as a formal object and solved zero-sum two-person games completely. They argued against treating economic behaviour as one agent optimising against nature; the cost is that nothing outside zero-sum had a solution concept then, so the book's reach was far narrower than its title.
Foundational
Nash · around 1950 · non-cooperative games and existence
Generalised the solution concept to any finite game and proved existence in mixed strategies. This let non-zero-sum games in; the cost is that equilibria are usually not unique, and half a century of refinement has been spent on that cost.
Turn
Schelling · 1960 · The Strategy of Conflict
Argued that with multiple equilibria what actually decides is shared salience and the ability to commit, not finer calculation. The most persistent counterexample to reading equilibrium as prediction.
Counterexample
Bonanno · the open textbook Game Theory
The subject of this course. It keeps definitions and theorems cleanly apart, and in doing so largely leaves the step 'what does this formal object represent' to the reader — which is the step this course pulls out and handles separately.
Subject of this course
机制02
Compression into four things
To turn an interaction into something computable you need only four items: who chooses, what each can choose, what each profile of choices yields, and how each ranks those yields. Write those four down and you have a strategic form. The step is a compression: tone, history and face are all discarded, and only those four survive. Nearly every failure later in this course traces back to something discarded that turned out to matter.
机制An interaction, through being compressed into four items, becomes a computable object.
可迁移性测试
Move it to a ticket queue: write down who waits, whether cutting in is possible, what a served ticket yields and how urgent each person is, and you can work out whether cutting in happens without reading anyone's face. The isomorphism breaks in that a queue's rules are fixed in code, while real participants can change theirs.
机制03
A plan covering every situation
Chapter 4 will show that the whole question of whether a threat is credible turns on one formal requirement, which is worth reading now. It sits in the word strategy, which here is not the everyday 'plan'. What matters is the reach of the requirement: it extends past the equilibrium path, into positions nobody expects to visit, and that is where all of chapter 4's reasoning will end up living. Formal fussiness it is not.
机制A complete plan, through specifying actions for situations never reached, makes the credibility of a threat decidable.
可迁移性测试
Move it to a contingency plan: what reassures people is not the fire drill but that the branches nobody expects are written down too, because that is what the other side reads to judge whether you would act. The isomorphism breaks in that a plan can be quietly rewritten later.
Derivation04
From four items to what 'rational' exactly means
What is being proved: the word 'rational' in this course commits to one thing only, far less than the everyday use.
The player set and each strategy set are given and finite
A hypothesis. Drop finiteness and chapter 6's existence theorem needs separate continuity conditions.
Each player has a complete and transitive ranking over outcomes (read: 'i finds at least as good as')
A hypothesis. Drop completeness and a best response may fail to exist; drop transitivity and 'better' can no longer be lined up.
Each player acts on their own ranking only
A hypothesis, and the one most often misread: it does not exclude altruism, which is written into the ranking itself.
推导 · 0 / 4
Worked derivation05
Altruism does not violate 'acts on their own ranking'
A would rather take one less than have B take two more. Does that contradict the third hypothesis?
First say what an outcome is, then look at what the ranking is defined over.
裂缝06
The boundary of this chapter's claims
争议地形07
本书主张
Compressing an interaction into players, strategies, outcomes and preferences is the right starting point, and what is discarded can be added back to the model when needed.
另一种看法
The behavioural and evolutionary line holds that what is discarded — limited computation, learning, imitation, framing — is not a second-order correction but changes the equilibrium itself; evolutionary game theory replaces best response with replicator dynamics, and its stable points do not coincide with the Nash set.
分歧扎在
The disagreement is rooted in whether best response is the right primitive for behaviour, not in the mathematics. Both accept that strategic form is a clear notation; they differ on whether what it compresses away can be handled as a correction.
什么证据能裁决
What would settle it is where repeated play converges: have participants play the same game repeatedly with feedback and see whether long-run frequencies land on the Nash equilibrium or on the stable point of the replicator dynamics. The two predictions differ in some games (an asymmetric rock–paper–scissors, for instance) and can be told apart directly.
The evidence points to 'it depends on the game': where the equilibrium is unique and the game is dominance solvable the two agree, and with multiple equilibria or cyclic structure the evolutionary prediction fits better. What is missing is a way to separate learning speed from population composition — both shift the convergence point.
Boundary and counterexample08
The compression commitment as a testable specification
The modelling commitment under test: a real interaction can be represented by a fixed quadruple of players, strategies, outcomes and stable rankings.
Hypothesis dropped: the ranking stays fixed within one situation
The key to the compression; if the interaction itself changes preferences, the quadruple no longer represents it.
The counterexample in that case: the same person, on the same material outcome, choosing oppositely under different descriptions
No single ranking can then represent both choices.
The observable this commitment maps onto: repeated choices by one participant over the same material outcome set
The pairs must be identical in material outcome and differ only in presentation.
What counts against it: systematic reversal on the paired items, above a pre-registered threshold
The threshold is fixed in advance on how much reversal costs the quadruple its representativeness.
Pre-registered failure condition: reversal above threshold, or reproducible cycling in choices
Either counts as the commitment failing.
推导 · 0 / 3
接口09
Which slot it hangs on
挂在哪个槽位The conclusion you already hold is probably 'game theory assumes people are rational and selfish, so it does not apply to real people' — a judgement about range of application. This chapter goes at its first half.
Does this chapter (a) replace the content of the 'rational and selfish' premise, or (b) constrain your judgement about where game theory applies?
慢变量Register two slow variables: how many of your interactions you could actually write the full quadruple for, and in how many of those the participants' preferences shifted along the way. Look at the second first.
小结10
本章小结
01Strategic form is a compression: only players, strategies, outcomes and preferences survive.
02A utility function is notation for a ranking; any order-preserving transformation gives the same preferences.
03'Rational' here means taking a best response — no foresight, no correct beliefs, no selfishness.
04A strategy must cover unreached situations, or the credibility of a threat cannot be decided.
05The only step carrying observational risk is the commitment that rankings are stable, not any mathematical result.
提取练习 · 合上书，先自己答一遍。
?Is 'a utility function just writes the ranking as numbers' (a) true by definition or (b) a modelling commitment about reality?
?Does A preferring to take one less so B takes two more violate (a) the third hypothesis or (b) nothing at all?
Forced choice11
B · Identify the tag
' if and only if ' — what kind of step is that?
二选一
Forced choice12
D · Judge the interface
Which one hangs on a slot in your existing structure?
二选一
读到这里，把它记为已读。