Part 2-3 Repeated Game

prolog

• Intuition ： the role of repeated play

• Folk theorem( 無名氏定理 ) ： The wildly held intuition that noncooperative

games played repeatedly may often have cooperative equilibria.

One-off game ： noncooperative solution cooperative solution using sequential game to test the intuition

intuition can be very misleading when repeated play has an end point.

play repeated

Camper’s Dilemma(simultaneous game)

NE ：（ don’t, don’t ） exhibits social dilemma.

two stage game ： the same simultaneous game plays twice

• two stage game ： Four basic proper subgame. Applying backward induction, the SPNE is （ don’t,

don’t ）• N-round We extend this reasoning to N stages. As long as

the N is limited number of time, the best-response strategy in last round is always the noncooperative “ don’t” strategy as in first round. That says no cooperative strategy will ever played.

• 玩有限次的重複賽局：當一次賽局有一純策略納許均衡時，則此納許均衡被重複玩就是重複賽局的子賽局完美均衡。

Pressing game（ sequential game ）

SPNE ：（ N, （ PN, NN ）） Outcome ： A takes “N”

• two-round repeated game

• two-round repeated game If A persuade the B to take “ care” by threatening to retaliate. A might, for example,

response to a “no care” strategy by taking “ no pressing” the following round. Suppose A takes a Tit- for-Tat strategy rule ： 「 The player’s strategy in this round

depends on the opponent’s choice in last round」

• Is the Tit-for-Tat strategy a credible threat and promise ？

Credibility is associated with SPNE Note ：本期合作之目的乃在營造次期合作 的氣氛，若無次期，本期即無合作 之必要。

• Is the threat credible ？： light gray oval If B1 takes “no care”, then A2 takes “ no

pressing”• Since -1>-2, the threat is credible.

• Is the promise credible ？： dark gray oval

If B1 takes “ care”, then A2 takes “pressing” The “no pressing” is A2’s best response because

he anticipates that B2 will take “no care” in this round.

The “no care” is B2’s best response since there is no next round.

So, the promise is incredible.

• player A cannot play a Tit-for-Tat rule on 2nd round, last round.

SPNE ： as in one round

• Extension ： T round, limited number of times Tnd round ：不合作 T-1nd round ：不合作 … 1st round ：不合作

Folk theorem is not applicable to noncooperative games that repeated a definite number of times.

非合作均衡策略重複 T 次乃是此重複賽局唯一的 SPNE

the Chain store Paradox

Since retaliation is not subgame perfect on the last play, any threat to retaliation will not be credible.

The payoff depends on the motivation

恐嚇取財的挾持賽局

以殺人為目的的挾持賽局