1. the repeated games with lack of information on one side Now we focus on

2. Repeated game future In any repeated game with incomplete information, player must take into account to what extent their actions reveal their private information, and to what extent this revelation will affect their future payoffs.

3. Game Classify Completely unrevealing strategy Completely revealing strategy Partially revealing strategy

4. Definition about the following example the utility matrix is game's ture state the occur prob of state A, noted by expected payoff(utility)

5. Completely unrevealing strategy given State A State B Player 1:know the true state, Player 2:know nothing, Player 1:plays U every time. Player 2:observing player 1's actions, that player 1 is playing U state may be A then will switch to playing R. Player 1 payoff ->

6. if player 1 ignores her private imformation, like play the average game!!!

7. expected payoff-> player 1 achieves average expected payoff of 0.25.

8. what we care about with repeated game we want to get utility for the long-term if player take advantage of her private information let player 2 know true state advantage player 1 get would be short- term. and not be enough to compensate for the long-term losses!!!

9. Completely revealing strategy given Player 1:know the true state, Player 2:know nothing, Player 1:play D if the state of the world is A; otherwise always play U Player 2:player 2 know true state No matter what strategy player 2 uses Player 1 payoff ->

10. Partially revealing strategy if we use Completely unrevealing strategy then…

11. player 2 can always play R and thus guarantee a payout of at most 0. reduce to average game

12. if we use Completely revealing strategy Always play M if the inferred state is A; otherwise always play L”. Again, player 2 is able to guarantee a maximum payout of 0.

13. another strategy Player 1: state is A, with p=0.75 play U p=0.25 play D; state is B, with p=0.25 play U p=0.75 play D; Player 2: assume state is A player 2 observes that player 1 is almost playing U, less play D ， guess the state

14. reduce to average game

15. player 1 achieves a payoff of 1. partially revealing this information, better then completely revealed her private information. completely ignored her private information.