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Complete vs. Incomplete Information Distinction

Why It Matters

When information is complete, strategic analysis focuses on equilibrium given known payoffs. When incomplete, a new dimension emerges: players use actions to signal their private information (signaling) or design mechanisms to elicit it (screening), and they update beliefs about opponents based on observed actions. Many real-world strategic failures stem from assuming complete information when uncertainty exists (leading to adverse selection, signaling failures) or over-complicating complete information situations by modeling unnecessary uncertainty.

The Key Move

For any strategic situation:

  1. Ask: do all players know each other's payoffs/preferences/costs?
  2. If yes, it's complete information - focus on equilibrium analysis with known payoffs.
  3. If no, identify what's unknown: preferences, costs, capabilities, alternatives?
  4. Model as incomplete information game where actions reveal information.
  5. Check whether players have incentives to misrepresent (separate signaling equilibria from pooling equilibria).
  6. Look for screening mechanisms that elicit private information.
  7. Apply Bayes' rule: update beliefs about opponent types based on their observed actions.

Classic Application

Job market signaling (Spence model). Employers have incomplete information about worker productivity. Workers know their own ability but can't directly communicate it (cheap talk isn't credible). Costly signal: education. High-ability workers can acquire education more easily (lower cost) than low-ability workers. Employers observe education and infer productivity. Separating equilibrium: high-ability workers get education, low-ability workers don't, because the cost-benefit ratio differs by type. Education's value is in signaling ability, not necessarily increasing it - this explains why firms value degrees even when job doesn't use specific knowledge.

Surprising Application

Restaurant pricing and quality uncertainty. Customers have incomplete information about food quality before ordering. Restaurants know their own quality. Signaling mechanism: high prices. High-quality restaurants can sustain high prices (repeat customers, word-of-mouth) while low-quality restaurants can't (customers don't return). Price becomes a quality signal in equilibrium - expensive restaurants are more likely to be good because low-quality restaurants can't profitably mimic the price. This explains why artificially lowering prices can backfire (sends low-quality signal) and why new restaurants often price high initially (establishing quality signal). Non-obvious because we think of price as cost-based, but it's also an information-revelation mechanism.

Failure Modes

Assuming incomplete information when it's actually complete - over-complicating situations where preferences are known. Not identifying the private information dimension - what specifically is unknown? Ignoring pooling equilibria - sometimes all types choose the same action, so no information is revealed. Treating signals as costless - effective signals must be differentially costly across types. Missing adverse selection - when one side has private information, the informed side's participation decision reveals information about the distribution of types.

Go Deeper

Spence, "Job Market Signaling," Quarterly Journal of Economics 87(3), 1973; Gibbons, Game Theory for Applied Economists, Chapter 3

  • Adverse Selection - Information Economics: Reasoning Under Asymmetry and Uncertainty
  • Signaling - Information Economics: Reasoning Under Asymmetry and Uncertainty