【正文】 er 1’s choice, player 2 chooses to show Head or Tail ? Both players know the following rules: ? If two pennies match (both heads or both tails) then player 2 wins player 1’s penny. ? Otherwise, player 1 wins player 2’s penny. Player 1 Player 2 H T 1, 1 1, 1 H T Player 2 H T 1, 1 1, 1 June 11, 2021 73347 Game TheoryLecture 16 8 Dynamic games of plete and imperfect information ? Imperfect information ? A player may not know exactly Who has made What choices when she has an opportunity to make a choice. ? Example: player 2 makes her choice after player 1 does. Player 2 needs to make her decision without knowing what player 1 has made. June 11, 2021 73347 Game TheoryLecture 16 9 Imperfect information: illustration ? Each of the two players has a penny. ? Player 1 first chooses whether to show the Head or the Tail. ? Then player 2 chooses to show Head or Tail without knowing player 1’s choice, ? Both players know the following rules: ? If two pennies match (both heads or both tails) then player 2 wins player 1’s penny. ? Otherwise, player 1 wins player 2’s penny. Player 2 Player 1 Player 2 H T 1, 1 1, 1 H T H T 1, 1 1, 1 June 11, 2021 73347 Game TheoryLecture 16 10 Information set ? Gibbons’ definition: An information set for a player is a collection of nodes satisfying: ? the player has the move at every node in the information set, and ? when the play of the game reaches a node in the information set, the player with the move does not know which node in the information set has (or has not) been reached. ? All the nodes in an information set belong to the same player ? The player must have the same set of feasible actions at each node in the information set. June 11, 2021 73347 Game TheoryLecture 16 11 Information set: illustration Player 1 L R Player 2 L’ R’ 2, 2, 3 Player 2 L’ R’ 3 L” R” 3 L” R” 3 L” R” 3 L” R” 1, 2, 0 3, 1, 2 2, 2, 1 2, 2, 1 0, 1, 1 1, 1, 2 1, 1, 1 an information