← Game Theory
第 7 章 · 20 分钟
Reverse audit: checking the modelling commitments of chapters 1–6
The audit covers chapters 1 to 6, including right conclusions reached wrongly.
概念地图
Nash equilibrium
A profile in which nobody gains by moving alone.
本章不引入新概念，图为全书脉络
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Locus01
延伸阅读
Friedman · 1953 · the methodology of positive economics
Argued that a theory is worth what its predictions are worth and that the realism of its assumptions does not matter. He argued against judging models by how lifelike their assumptions are; the cost is that the standard fails exactly where a structure has to be carried to a new setting — out-of-distribution extrapolation is what needs the assumptions to be right.
Foundational
Rubinstein · early 2000s · the self-criticism of the 'economic fables' line
Called game-theoretic models fables: they clarify thinking, they do not predict the world. This argued against using solution concepts directly as forecasting tools; the cost is that calling them fables makes them hard for any observation to refute.
Revision
Chapters 1 to 6 of this course
The subject of the audit. The third block (derivation) and fifth block (boundary) of each chapter are the entry points, with the focus on whether that chapter's one modelling claim stands.
Under audit
机制02
Formal soundness conceals modelling risk
The mathematics never goes wrong. That is the nature of a formal subject and also where it most easily misleads: a whole chapter of derivation can be flawless while the step that ties it to reality — what this course calls the modelling commitment — does not hold at all. Seeing a tight derivation, a reader tends to credit that tightness to this step as well. Marking the claim out in every chapter is what lets it face inspection on its own.
机制A flawless derivation, through making the whole chapter look sound, spares the one risky commitment from inspection.
可迁移性测试
Move it to a financial model: every formula is correct and the cell reading 'fifteen per cent growth for five years' was guessed. Trusting the sheet because the formulas are tight is the same error. The isomorphism breaks in that the guessed cell is at least visible.
机制03
A solution concept read as a prediction
Chapter 3 said equilibrium is a consistency condition rather than a prediction; chapter 4 said backward induction solves for consistency rather than behaviour. The misuse has one shape: an answer to 'which situations are self-consistent' read as an answer to 'what will happen'. This course books it as solution-concept misreading. The test is simple: did this use rule out any specific observable outcome?
机制A consistency condition, through being read as a prediction, leaves the analyst believing the model excluded what it did not.
可迁移性测试
Move it to a type checker: passing the check says the program is free of one class of error, not that it does what you wanted. Reading 'passed' as 'behaves correctly' is the same shape. The isomorphism breaks in that a type system documents its guarantee, while a solution concept's guarantee has to be read out of the definition yourself.
Derivation04
Counting the categories in chapters 1–6
This aggregates the tags across the first six chapters and derives one conclusion: the observational risk of this course sits on six modelling claims, and everything else is definition and established results.
Chapters 1 to 6 have 4 derivation steps each, 24 in total
Counting rule: only the steps inside each chapter's third block, not the boundary or debate sections.
Twelve are tagged [definition] and six are tagged [assumption]
Definitions and established results carry no observational risk; assumptions are hypotheses, and dropping one makes the claim false.
Six are tagged [modelling], one per chapter
In a formal subject this is the only class observation can refute.
推导 · 0 / 4
裂缝05
The boundary of this chapter's claims
争议地形06
本书主张
This course's position: in a formal subject the only thing worth arguing about is the modelling commitment, and the tightness of the mathematics guarantees nothing about the applicability of a conclusion.
另一种看法
The fables line holds that the value of a game-theoretic model was never prediction but clarification — it supplies a language for discussing interaction. By that standard, pressing on modelling commitments applies the wrong yardstick.
分歧扎在
The disagreement is rooted in what the model is for. If it is only for clarifying concepts, the fables position holds; if it is for designing mechanisms, pricing or regulation, the modelling commitment decides the consequences directly. This course aims at the second and therefore takes the first position — a choice made by the goal, not a refutation of the fables view.
什么证据能裁决
What would settle it is a survey of use: what share of actual citations of these solution concepts go into concrete design (auction rules, contract terms, regulatory thresholds) rather than discussion. A low share supports the fables position; a substantial share entering design makes the commitments something that must be checked.
The evidence points to a substantial share entering design: auction and matching mechanisms really are built on solution concepts, and their performance can be assessed afterwards. What is missing is a systematic record of failures — the successful mechanisms are cited repeatedly and the failures are rarely written down.
Boundary and counterexample07
The solution-concept misreading commitment as a testable specification
The modelling commitment under test: a consistency condition read as a prediction leaves analysts believing the model excluded what it did not.
Hypothesis dropped: users know that a solution concept gives only consistency
If users already know this, the misreading does not occur and the mechanism cannot be tested.
The counterexample: an analysis of a multi-equilibrium game presenting a unique 'prediction' with no stated selection basis
The definition says nothing about which equilibrium, so a unique prediction must have borrowed something from outside the model.
The observable: whether published analyses of multi-equilibrium cases state a selection basis
It must be a multi-equilibrium case; with a unique equilibrium there is no misreading.
What counts against it: the share stating a selection basis exceeds a pre-registered threshold
The threshold is fixed in advance and not adjusted afterwards.
Pre-registered failure condition: the share above threshold, or inter-coder agreement below the acceptable level
The second voids the test.
推导 · 0 / 3
接口08
Which slot it hangs on
挂在哪个槽位The conclusion you already hold is probably 'a conclusion derived mathematically is more reliable' — a judgement about where reliability comes from. This chapter goes at which layer it applies to.
Does this chapter (a) replace 'mathematical conclusions are more reliable', or (b) constrain it: the formal part is reliable and all the risk sits in the correspondence step?
慢变量Register two slow variables: how many of the models you have used lately let you point at their modelling-commitment sentence, and in how many that sentence is simply absent. Look at the second first.
小结09
本章小结
01Of 24 derivation steps in chapters 1–6, twelve are definitions, six are assumptions, and six modelling claims carry the observational risk.
02The tightness of the formal part does not carry over to the step saying what the object represents.
03Solution-concept misreading has one shape: consistency read as prediction, which with several solutions must borrow from outside.
04'The original makes no such commitment; supplied for the sake of application' must be booked separately from a real defect.
05Choosing to inspect modelling commitments is a choice made by the goal, not a refutation of the fables view.
提取练习 · 合上书，先自己答一遍。
?Is 'risky steps equal the total minus definitions minus assumptions' (a) classification arithmetic or (b) a modelling commitment about reality?
?Is giving a unique prediction for a three-equilibrium game with no stated basis (a) a computational error or (b) solution-concept misreading?
Forced choice10
A · Identify the mechanism
Which of these is a mechanism?
二选一
Forced choice11
C · Locate the crack
In which situation does this audit give a confident and wrong answer?
二选一
读到这里，把它记为已读。