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Bayes–Nash Equilibrium

Build the normal form of an incomplete-information game and find its equilibria. Work through each exercise, check it instantly, and use the explanation to close any gaps.

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An incomplete-information game

The informed player chooses Red or Blue after learning whether their type is social or solitary. The uninformed player chooses without seeing the type. Each type initially has probability ½. Payoffs are (informed, uninformed).

TypeI=Red, U=RedI=Red, U=BlueI=Blue, U=RedI=Blue, U=Blue
social2, 30, 01, 13, 2
solitary0, 32, 03, 11, 2

A strategy for the informed player is a pair (social action, solitary action). Each normal-form cell is uninformed expected payoff, (social payoff, solitary payoff).

1. Build the normal form

Uninformed \ informed(R,R)(R,B)(B,R)(B,B)
Red
Blue

2. Find the equilibrium

3. Shift the prior

If the social type's probability rises to 5/6, how does the equilibrium set change?

Choose one