Part 2-1 Sequential game

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# Part 2-1 Sequential game - PowerPoint PPT Presentation

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.

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### 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 extensive form and the game tree
• A game tree is a “directed graph” and has a “transitive precedence relation” Kreps ＆ Wilson（1982）：

definition of building block

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 starting node is a node with no predecessors.

A end node or end point is a node with no

successors.

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.

deter entry
• strategic setting

Players：incumbent：S

New entry：P

Move sequence：sequential

first mover：S, action set：﹛擴廠, 不擴廠﹜

second mover：P, action set：﹛Build,don’t﹜

Subgame：承襲自一特定完全訊息節點，包含所有Subgame：承襲自一特定完全訊息節點，包含所有

• Proper subgame（完整子賽局）：一個不等於整個

• Commitment structure：sequential game中，所有

proper subgame的集合，均為此sequential

game的承諾結構。

• SPNE：A game is in SPNE iff every subgame is in a

Nash equilibrium

an equilibrium in which the players always,

consistently, anticipate their rivals’ decision in

this way.

Backward induction(倒推法)

• Basicsubgame(基本子賽局)：一個不包含任何其他完整子賽局的子賽局，即稱之。
• Complex subgame(複雜子賽局) ：一個包含任何其他完整子賽局的子賽局，即稱之。

node2所包含之訊息集無法分割，整個賽局不包含任

The concept of subgame and sequential game
• Recalling 14.1

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

Step1：找出基本子賽局（特點：已無向下

Step2：找出各基本子賽局之NE

induced game

Step3：找出induced game之NE

1. 一原賽局一序列的均衡即構成

SPNE

2.逆推法乃是重複剔除dominated

strategy 在extensive game 之應用

1. S廠最適選擇“ build”

2. SPNE ：(S,P)：(B, (BD, DB))

Outcome：S 建廠，P不建

• strategic setting

H’s action set：﹛C,B﹜，

C：前進新迦太基，B：貝特河

P’s action set： ﹛L,C﹜，L：前進拉米尼

SPNE：（B, （CL,BC））

Outcome：H選B，P選C

NE and SPNE

a price war is not credible threat because it is not an equilibrium in the basic subgame.

• Every subgame perfect equilibrium is a NE,

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

subgame.

Note 1：

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

different“ subgames”.

the term “perfectness” reflects the idea of

sequential rationality.

Note 2：backward induction 不適用於無限賽

information game）

The two-stage centipede game has just one proper subgame, and it is basic.

• There is possible that SPNE of the sequential

game in extensive form may have inefficient

outcome.

SPNE：（Friday, Robison）：

Outcome：Friday 選，payoff 5,

Robison’s payoff 0

social dilemma

• Interpretation：為何需要法律保障之契約機制？