Bayesian Nash Examples

Game Theory · Axiom Academy

EXAMPLE Bayesian Nash Examples Unit 5 - Games with Incomplete Information Players: Two firms (Firm 1 and Firm 2) choosing prices (High or Low) Incomplete Information: Firm 1 doesn't know Firm 2's cost structure Type A (High Cost): occurs with probability Type B (Low Cost): occurs with probability Actions: Each firm can set price High (H) or Low (L) Excellent work! You've completed this Bayesian Nash equilibrium example. Here's what we learned: Type-Contingent Strategies: In Bayesian games, each player type must have a specified action. Firm 2's strategy specifies what Type A does and what Type B does. Expected Payoff Calculation: Players with incomplete information compute expected payoffs by weighting each type's payoff by the probability of that type occurring. Best Response for Each Type: Each type of each player must be playing a best response to the strategies of all other player types, given the beliefs. Bayesian Nash Equilibrium: A BNE is a strategy profile where each type of each player maximizes expected utility given their beliefs about other players' types and the strategies of those types. Incomplete Information Matters: The equilibrium can differ significantly from complete information Nash equilibria because players must account for uncertainty about opponent types. This systematic approach works for any Bayesian game: identify types, write type-contingent payoffs, calculate expected values, find best responses for each type, and verify mutual best responses!

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