Part 2-1 Sequential game. prolog. 出 招有先後順序 The relationship of interaction between players in the dynamic game represent at the order of move, but not simultaneous move as in static game. Extensive form Nash equilibrium 是完全訊息靜態賽局解之基本概念 SPNE 是完全訊息動態賽局解之基本概念.
The relationship of interaction between players in the dynamic game represent at the order of move, but not simultaneous move as in static game.
A node is a point in the game at which some player or Nature takes an action, or the game ends.
A successor to node X is a node that may occur later in the game if X has been reached.
Apredecessor to node X is a node must be reached before X can be reached.
A end node or end point is a node with no
A branch is one action in a player’s action set
at particular node.
A path is a sequence of nodes and branches
from the starting node to an end node.
first mover：S, action set：﹛擴廠, 不擴廠﹜
second mover：P, action set：﹛Build,don’t﹜
an equilibrium in which the players always,
consistently, anticipate their rivals’ decision in
Node PA、Node PB 之訊息集均為sinslelton，之後的分支均各為一完整子賽局，因此，開始於initial node S 的賽局，稱為複雜子賽局（complex subgame）。
think forward, reason backward
strategy 在extensive game 之應用
若到達PB：P廠最適選擇 “ build”
1. S廠最適選擇“ build”
2. SPNE ：(S,P)：(B, (BD, DB))
H’s action set：﹛C,B﹜，
P’s action set： ﹛L,C﹜，L：前進拉米尼
a price war is not credible threat because it is not an equilibrium in the basic subgame.
but not every NE is subgame perfect.
SPNE is a refinement of NE
A strategy profile is a SPNE if
i. it is a NE for the entire game; and
ii. its relevant action rules are a NE for every
A strategy profile is a perfect equilibrium if it
remains an equilibrium on all possible paths,
includes not only the equilibrium path but
all the other paths, which branch off into
the term “perfectness” reflects the idea of
The two-stage centipede game has just one proper subgame, and it is basic.
game in extensive form may have inefficient
Outcome：Friday 選，payoff 5,
Robison’s payoff 0
若無契約約束，opportunism 發生，social optimum無法達到。