Game tree ■Any node other than Player 1 a terminal node represents some player. Player 2 ■For a node other than Player 2 a terminal node,the edges that connect it with its successors represent the actions available to the player represented by the node 12
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 ■A path from the root Player 1 to a terminal node H represents a complete sequence of Player 2 Player 2 moves which determines the payoff at the terminal node 13
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 安
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 >In Out Incumbent's strategies Accommodate (if challenger plays In) Fight (if challenger plays In) ■Payoffs Normal-form representation Incumbent Accommodate Fight In 2,1 0, 0 Challenger Out 1, 2 1,2 15
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
Strategy and payoff In a game tree,a strategy for a player is represented by a set of edges. A combination of strategies (sets of edges), one for each player,induce one path from the root to a terminal node,which determines the payoffs of all players 16
Strategy and payoff ◼ In a game tree, a strategy for a player is represented by a set of edges. ◼ A combination of strategies (sets of edges), one for each player, induce one path from the root to a terminal node, which determines the payoffs of all players 16