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).
| Type | I=Red, U=Red | I=Red, U=Blue | I=Blue, U=Red | I=Blue, U=Blue |
|---|---|---|---|---|
| social | 2, 3 | 0, 0 | 1, 1 | 3, 2 |
| solitary | 0, 3 | 2, 0 | 3, 1 | 1, 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).