Game tree If a node x is a successor of another node y then y is called a predecessor of Ⅹ, In a game tree, any node X2 other than the root has a unique predecessor ■ Any node that has no successor is called a termina/ node which is a possible end of the game ■ EXample4:X4,%,x,X, Xa are terminal nodes
Game tree ◼ If a node x is a successor of another node y then y is called a predecessor of x. ◼ In a game tree, any node other than the root has a unique predecessor. ◼ Any node that has no successor is called a terminal node which is a possible end of the game ◼ Example 4: x4 , x5 , x6 , x7 , x8 are terminal nodes 11 x0 x1 x2 x3 x4 x5 x6 x7 x8
Game tree a Any node other than Player a terminal node H represents some pla ayer. Player 2 Player 2 ■ For a node other than a terminal node the H T H T edges that connect it with its successors represent the actions available to the player represented by the node
Game tree ◼ Any node other than a terminal node represents some player. ◼ For a node other than a terminal node, the edges that connect it with its successors represent the actions available to the player represented by the node 12 Player 1 Player 2 H T -1, 1 1, -1 H T Player 2 H T 1, -1 -1, 1
Game tree Player ■ A path from the root to a terminal node H presents a complete sequence ot Player 2 Player 2 moves which determines the payoff H T H T at the terminal node
Game tree ◼ A path from the root to a terminal node represents a complete sequence of moves which determines the payoff at the terminal node 13 Player 1 Player 2 H T -1, 1 1, -1 H T Player 2 H T 1, -1 -1, 1
Strategy a strategy for a player is a complete plan of actions It specifies a feasible action for the player in every contingency in which the player might be called on to act What the players can possibly play, not what they do play ■Cf: static games
Strategy ◼ A strategy for a player is a complete plan of actions. ◼ It specifies a feasible action for the player in every contingency in which the player might be called on to act. ◼ What the players can possibly play, not what they do play. ◼ Cf: static games 14
Entry game Challenger's strategies n Out ■ Incumbents strategⅰes Accommodate(if challenger plays In) Fight (if challenger plays In ■ Payoffs Normal-form representation Incumbent Accommodate Fight 1 0 0 Challenger Out 21 2 1 2
Entry game Incumbent Accommodate Fight Challenger In 2 , 1 0 , 0 Out 1 , 2 1 , 2 15 ◼ Challenger’s strategies ➢ In ➢ Out ◼ Incumbent’s strategies ➢ Accommodate (if challenger plays In) ➢ Fight (if challenger plays In) ◼ Payoffs ◼ Normal-form representation