# Iterative Games

More recently, I took a deep dive into game theory and was surprised to discover how useful game theory is. Most of the value of understanding game theory comes from one core idea: playing iterative games.

That is what we’ll discuss in this essay: What are iterative games and why do they matter? We’ll also look at some real-world implications (e.g., the incentives of a wedding planner and how iterative relationships build trust).

## Solving For Iterative Games

Game theory is the study of how rational decision-makers interact with one another. It attempts to explain human behaviour through the lens of mathematics and logic.

The focus of game theory is the stage game, which is the underlying game that is played. Stage games have rules and a point system which allow us to identify winners and losers. While there are many different types and styles of stage games, I will classify all stage games into two broad categories:

1.       Non-iterative games

2.       Iterative games

A non-iterative game is a stage game that is played only once by the participants.

An iterative game is a stage game that is repeated numerous times by the same participants, with the participants not knowing when the game will end.

The distinction between iterative and non-iterative games is small, but the implications on how people behave are significant. Non-iterative games lead to players acting “selfishly”. Iterative games result in players considering the impact of their actions (their “reputation”) on the future behaviours of other players. Concern for one’s reputation leads to cooperative behaviour.

To further explore this, I will use the classic Prisoner’s Dilemma game as the stage game.

#### The Prisoner’s Dilemma

Two criminals (A & B) are accused of a crime. They are held in separate rooms by the police and are unable to communicate. They each have two options: confession or silence. The possible outcomes and consequences of their decisions are the following:

1. Both confess: Two years in prison for each of them (1 point each)

2. A confesses; B remains silent: A will be set free (3 points); B will serve three years (0 points)

3. B confesses; A remains silent: B will be set free (3 points); A will serve three years (0 points)

4. Both remain silent: One year in prison for each of them (2 points each)

What should they do? What would you do?

The dominant strategy for each player is always to confess, even though this will lead to a sub-optimal outcome for both parties. [1]

Why?

Because each player’s best decision is to confess, regardless of what the other side does.

Let’s examine this from the perspective of player A:

• If B confesses, the best outcome for A is to confess. If B confesses and A stays silent, A will receive 0 points.

• If B remains silent, the best outcome for A is to confess, which would award A 3 points.

The structure of the game is set up in a way that incentives both parties to choose to protect themselves at the expense of the other participant. As a result, both are worse off than if they had cooperated in their decision-making, hence the dilemma.

#### Iterative Prisoner’s Dilemma

This is representative of many of the problems we face in life. If we were able to cooperate better in our decision-making with people, we would get better outcomes. But the question is how?

By playing repeatedly.

In one-off games, selfish strategies dominate. Each side is incentivized to think short-term based on the structure of the game. By pursuing a selfish outcome, each participant gets a worse score than if they were to cooperate because cooperation is not rational in this circumstance. There is no trust that your counterparty will reciprocate cooperative behavior. In fact, if you cooperate, your counterparty is incentivized to act selfishly to maximize their gain.

When you play multiple times, the incentive structures of the game shift towards cooperation.

Cooperative behaviors are much more likely when we interact with the same people repeatedly. This is for two reasons: 1) each round of cooperation compounds trust; and 2) you can punish selfish behavior.

Compounding trust:

When two people cooperate in a “game”, they build trust that the next time they see each other, they will cooperate. They establish a reputation as a cooperative participant.

What is interesting is that this is still rooted in self-interest. Through cooperation, the participant, as an individual, is better off over the long-run.

Punishment:

Iteration also allows you to punish people who act selfishly. If your counterparty acts selfishly you can retaliate or choose not to play any “games” with them in the future. Overtime, selfish actors will fare worse than cooperators.

Game theory models are simplifications of the real world. The strategies used to win the Prisoner’s Dilemma don’t map on perfectly to reality. But we can draw two life principles from game theory strategies:

1)      Play iterative games

2)      With cooperative people

Iterative games:

You want to play “games” (read: operate within systems) that are iterative in nature.

What influences the behaviors of people is the incentive structure of the systems they operate in. Having exposure to iterative games allows you to ensure that the incentive structure of the system nudge people towards cooperative behaviors. This leads to the best outcome for both parties.

Cooperative people:

Solving for iterative games is not enough. There will be people within iterative incentive structures who still think short-term.

You need to find the people who are cooperatively in iterative games. People who care about their reputation and understand that it is in everyone’s best interest to work together.

#### Don’t plan a wedding

My fiancée, Charlotte, and I are currently planning a wedding and have hired a wedding planner to help us. While our wedding planner theoretically works for us, I can’t help but see that her incentives are not perfectly aligned with ours.

Charlotte and I are transient to the wedding industry. We will be interacting with our planner and the numerous wedding vendors only once (hopefully…). Thus, our wedding planner and the vendors we work with are not incentivized to get us the best possible deal. If anything, they are incentivized to take care of each other at the expense of the transient couples they interact with. The planner and vendors are playing an iterative game with each other and a one-off game with us.

To be clear, I do not blame our planner, nor the vendors. They are acting perfectly rationally, and I would do the same in their shoes. The fault is my own for having exposure to a one-off game. But I am told that a “happy wife = happy life”, so the price is worth it?

#### Forget the contract

While at university I founded a start-up with one of my best friends.

Although our venture ended up failing, it taught me a lot about business relationships and finding long-term people. My co-founder acted incredibly fair and ethical throughout the whole process. Whenever we had disagreements or conflicts, he was cooperative and principled. My trust in him grew the more that we worked together.

The advantages of this are profound. If he ever approached me with a business or investment idea I would jump at the opportunity. I am not worried about getting ripped off, needing to hire a lawyer, or even having a formal contract drawn up prior to working with him. I know this person has integrity and understands that we are playing a long-term game. This frees us up to focus on taking bigger risks with more upside.

You build trust with cooperative people and trust is the foundation of any successful relationship.