Trigger Strategies

Trigger strategies are an essential topic in repeated games. Players can decide in each round and consider the result from the last rounds.

In most of the games considered here, participants have to decide whether to cooperate or to defect. The question is how previous decisions influence (trigger) future decisions.

There are a few well-studied trigger strategies, such as:

• Dove
• Hawk
• Grim trigger
• Tit for Tat
• Tit for two Tats
• Tester
• Pavlov
• Random

The problem is that most of the strategies are not subgame perfect.

Dove

The dove strategy means to play always cooperative. While this is a very simple strategy, it is vulnerable to exploitation.

Hawk

The hawk strategy means always to play defective.

Grim Trigger

In a grim trigger strategy, the player starts cooperatively. But as soon as the other player defects, the player defects for the rest of the game.

The advantage is that one can enforce cooperation from the first round on. Besides, the strategy is easy to understand and simple to apply. However, the disadvantage is that it is not subgame perfect for all discount factors.

It might result in very low returns.

Tit for Tat

Tit for Tat is a forgiving strategy. Player 1 starts cooperating. If the other player defects, player 1 defects too in the following round. If the other player keeps defecting, player 1 keeps defecting too. But as soon as the other player starts to cooperate again, player 1 cooperates in the next round too.

The advantage is that it takes “regret” into account. If a player makes a mistake and realizes that, the game can continue cooperatively. It also punishes defecting behavior making the strategy credible as long as there is no end to the game. Besides, the strategy is easy to understand and simple to apply.

The disadvantage is that it is vulnerable to misunderstandings. Suppose both players play Tit for Tat. But player 1 defects in round 1 without noticing it. This causes an echo effect (or ping pong). This strategy is not subgame perfect, making it profitable to defect in the last round.

Player	Strategy
A	C	D	C	D	C
B	D	C	D	C	D

Tester

In this strategy, player 1 starts uncooperatively in the first two rounds. Does the other player react uncooperative, then play two rounds cooperative and then Tit for Tat.

If the other player continues cooperating, the Tester-player plays alternatingly cooperative and uncooperative.

Pavlov

The strategy is: win – stay, lose – shift.

The first round is cooperative. What is considered as win or lose depends on the game. Typically, if both cooperate it is considered as a win. Also if the Pavlov player defects and the other player cooperates, this is considered a win. If both defect or the Pavlov player cooperates and the other player defects, this is considered as lose and causes a shift in strategies.

Majority

In this strategy, the player defects in the first round. The player defects in all following rounds if the opponent defects more than the player.

An alternative is to start cooperating and defect if the opponent defects more than the player.

Evaluation

There is no best trigger strategy. However, in many cases, the Tit for Tat strategy proved to be a sound strategy. It can be observed in nature too.

Some best practices might be:

• Don’t be jealous. Take only your pay-offs into account and not the pay-offs of others.
• Don’t be the first who defects.
• Return the favor. If someone defects, defect too. If someone cooperates, cooperate too.
• Don’t be too complicated. If nobody understands your strategy, nobody can follow it.