ECOS2001 Chap.11 Dynamic Games & Asymmetric Information
Dynamic Games & Asymmetric Information
The final block adds timing and hidden information. Sequential games are drawn as game trees and solved by backward induction, giving the subgame-perfect Nash equilibrium and ruling out non-credible threats (the classic entry-deterrence result). Repeated games can sustain collusion: firms behave as one monopoly, and a grim-trigger strategy supports cooperation in equilibrium if players are patient enough.
The information half uses Bayes' rule and conditional expectations: adverse selection (the lemons market) where conditional-expectation pricing drives out good types, signalling (e.g. education) and screening that can separate types, and moral hazard where hidden actions create an incentive-versus-insurance trade-off.
What this chapter covers
- 01
Game trees and backward induction to the subgame-perfect equilibrium (SPNE)
- 02
Non-credible threats: a Nash equilibrium that is not subgame-perfect
- 03
Repeated games and collusion; the grim-trigger patience condition
- 04
Bayes' rule and conditional expectation E[X | A]
- 05
Adverse selection / the lemons market (conditional-expectation pricing)
- 06
Signalling, screening (separating vs pooling) and moral hazard
Conditional expectation in a lemons-style labour market
- 1 markIdentify the qualifying types: θ ≤ 5 covers θ = 2 (prob 0.3) and θ = 5 (prob 0.5).
- 1 markConditional probability denominator: P(θ ≤ 5) = 0.3 + 0.5 = 0.8.
- 2 marksNumerator (probability-weighted abilities in the set): 2·0.3 + 5·0.5 = 0.6 + 2.5 = 3.1.
- 1 markConditional expectation: E[θ | θ ≤ 5] = 3.1 / 0.8 = 3.875.
- 1 markAdverse selection: if the firm pays only the conditional average 3.875, the genuine θ = 5 workers (worth more than the wage) withdraw, lowering the average of those who stay and pushing the wage down further — the good types are driven out.
Key terms
- Backward induction
- Solving a sequential game from the last decision back to the first, choosing the optimal action at each node; it yields the subgame-perfect equilibrium.
- Subgame-perfect Nash equilibrium (SPNE)
- A Nash equilibrium that is optimal in every subgame, so it rules out non-credible threats; in finite games it is found by backward induction.
- Grim-trigger strategy
- A repeated-game strategy of cooperating until any defection, then punishing forever; it sustains collusion when players are patient enough (a high enough discount factor).
- Adverse selection
- A pre-contract information problem where the informed side's type is hidden, so price-equals-average drives out the best types — the lemons market, formalised with conditional expectations.
Dynamic Games & Asymmetric Information FAQ
What is the difference between a Nash equilibrium and a subgame-perfect equilibrium?
A Nash equilibrium only requires no profitable unilateral deviation given the others' fixed strategies, which can rely on threats that would never actually be carried out. Subgame-perfection (backward induction) additionally requires optimal play in every subgame, eliminating those non-credible threats — for example, in entry deterrence, fighting is a Nash threat but not subgame-perfect.
What is the difference between adverse selection and moral hazard?
Adverse selection is a hidden-type problem before the contract (you cannot tell good risks from bad), addressed by signalling and screening. Moral hazard is a hidden-action problem after the contract (effort cannot be observed), addressed by designing incentives that trade off insurance against motivation.
Exam move
Practise backward induction on small game trees, always asking which Nash equilibria survive as subgame-perfect, and rehearse the grim-trigger patience condition. For the information half, drill Bayes' rule and conditional expectations until the numerator/denominator setup is automatic, and be ready to explain adverse selection, signalling and moral hazard in plain words.
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