Incomplete Information Summary

Game Theory · Axiom Academy

SUMMARY Incomplete Information Summary Unit 5: Key concepts from games with incomplete information, beliefs, and strategic uncertainty. Incomplete Information: Players are uncertain about opponents' payoffs, types, or characteristics Types: Private information that characterizes a player (e.g., cost, valuation, preference) Common Prior: All players share the same probability distribution over types Why It Matters: Models real-world situations where players have private information (auctions, negotiations, markets) Bayesian Nash Equilibrium (BNE): Strategy profile where each type maximizes expected payoff given beliefs Beliefs: Probability assessments about opponents' types and actions Expected Payoffs: Players compute payoffs weighted by probabilities of different types Key Property: No player wants to deviate given their beliefs and information Signaling: Informed player (sender) takes action observed by uninformed player (receiver) Perfect Bayesian Equilibrium (PBE): Strategies are sequentially rational and beliefs updated via Bayes' rule Sequential Rationality: Actions are optimal at every information set given beliefs Belief Consistency: Beliefs updated using observed actions and equilibrium strategies Separating Equilibrium: Different types choose different actions, fully revealing their type Pooling Equilibrium: Different types choose the same action, revealing no information Semi-Separating: Some types pool while others separate (partial revelation)

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