Part 2-2 Imbedded game. prolog. Sometimes , it often seems that people act irrationally in some games they play, but the action is understood as rational when realize that the game is really part of a bigger game.
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Sometimes, it often seems that people act
irrationally in some games they play, but the
action is understood as rational when realize
that the game is really part of a bigger game.
The game in which people seem to act irrationally is imbedded or nested in a larger game.
if a game is a part of a larger game, then equilibrium strategy in the smaller game may depend on the larger game. The smaller game is said to be nested game within the larger.
if a nested game is a proper subgame of the larger game, then the nested game must be in equilibrium for the larger game to be in subgame perfect equilibrium. The smaller game is said to be imbedded in the larger.
Two-stage game. Second-stage game is a
2. the proper game with two pure strategy
Second-mover N can infer something（N reason that the A guess that N chooses the “SE”） from a choice that firs-mover A made in the first-stage, and this inference can solve the uncertainty in the coordination.
A 在first-stage選擇 “study”，向second-stage
mover N傳遞他在second stage 將選擇
故N之 best response 為 “SE”
When a game has an unsatisfactory outcome, the outcome may be changed via some method or arrangement of mechanism, for example, forward induction method, contract, etc.
Thus, the original game is nested or imbedded in a larger game, so that the outcome is changed from the original game.
First-stage player A uses forward induction. Player takes into account what second-stage player N will infer from his choice and the influence that inference can have on N’s choice.
Player N does as in A’s anticipation by forward induction.
2ndgame （subgame）is imbedded in the larger game. The larger game is the imbedding game. Subgame perfect equilibrium in the imbedding game will require that the imbedded game is in equilibrium. The reverse is not necessarily true.
1. Upper subgame：
（guard, armed）, payoff：（-5, 4）
2. Lower subgame：
（don’t guard, unarmed）, payoff：（-1, 0）
Outcome：GK： fake and don’t guard，GG：unarmed，Payoff：（-1, 0）
inefficient outcome with
player B engage a third party and post a bond of 2.
If he chooses “ grab” , he forfeits the bond; otherwise, he could be returned
美國可以透過駐軍來改變賽局(change the rules)
Strike game without Union
NE：（don’t concede, don’t strike），but
why are there strikes？
players ：employer and UTG
UTG’s payoff is proportional to his reputation of toughness.
UTG’s payoffs are quite different from those of the employees.
no pure strategy NE
why do employees affiliate with the UTG？
If employees affiliate with UTG., they give up the freedom to decide whether to strike.
UTG’s action set
Since lower-side game in Fig15.12 has no pure strategy equilibrium it must be an equilibrium in mixed strategy.
1/2, the employers make “concede” with