Mental Models & Product #1: Game Theory
I’m not going to lie — since the pandemic and starting this new product role at Indigo, finding the motivation to learn beyond performing had been tough. While I love my job and the on-the-go learning that I’ve been doing every single day, my “constant learner” brain had been itching to do something more.
In the spirit of continuous improvement in the product craft and with the Ontario stay-at-home orders and rising covid cases being a blocker to doing anything else other than staying at home, I’m here to find my spark again. One area that I’ve been itching to dig into (and relevant to my field) are different mental models. In my previous role, I spent a lot of time reading up on what mental models are. Shane Parrish did an amazing job at breaking down mental models in Farnam Street which I would highly recommend as an excellent read.
What is a mental model?
A mental model is “ a representation of how [we think the world] works”. It’s a framework, a concept, a worldview that we carry around in our minds that help guide our behaviours and perception.
Why are mental models important in product thinking?
The more models we have in our heads as product thinkers, the bigger the toolbox we will have. As a product manager, there are many times we are required to make great decisions quickly. The more we train up and learn new mental models in our minds, the more we will be equipped to view the world objectively. Most of us, however, are specialists. And in product, while specialization is important in giving us an intimate understanding to shape/grow a feature, it is important for us to also have a broad perspective to communicate with stakeholders, understand our customers’ needs, and anticipate/bet on future trends. By minimizing our “blind spots” in cultivating a 360 way of thinking, we can confidently say we made the best decision at the time with the information we had.
Introducing… Game Theory.
What better way to start this series than the classic mental model of understanding how trust and relationships work?
Game theory is the study of mathematical models of strategic interaction among rational decision-makers (wiki)
A good example of game theory would be observing the game of chess: the other player’s move continuously influences the strategy and the game. Another example would be when multiple companies are competing with each other: just like the game of chess, the actions of one company influences the actions of the other competing companies. An example would be if a make-believe grocery store Floormart lowers the price of pop per can, the other competing make-believe company Grocer Basics might be forced to do the same to meet demands.
Game theory essentially involves the strategic interaction (known as strategy) between two or more participants (known as players) that results in a set of circumstances (known as the game) — arriving at either a good or bad outcome for the players (known as payoff). It consists of the following assumptions:
- All players know the rules of the game.
- All players are rational decision makers.
- All players will strive to maximize their payoffs in the game (acting according to their personal self-interest).
(source: investopia)
One of the simplest games in game theory is called sequential games. A classic example would be when one firm acts and another firm responds (like the Floormart and Grocer Basics example above). Sequential games are made when players make moves at different times or in turn. This means that:
- Players who move later in the game have additional information about the actions of other players or market reactions.
- Players who move first can often influence the game.
- Players make next action conditionally based on additional information received during the game.
While sequential games ignore the fact that strategic situations are often extremely dynamic, it allows for better forecasting and planning, that will lead to better decision making.
Sequential games (also called dynamic games) are a form of the non-cooperative game theory, which would be my current focus. A clear example of difficulties that arise from non-cooperative games would be a concept we used to learn a lot about in business school called the prisoner’s dilemma.
Imagine that Alice and Bennett are suspected committing a robbery together, so they are ushered into a dark room, isolated and forced to confess. Now, prison is clearly not a fun place to be in, so each of their goal is to get the shortest possible prison sentence for themselves. The catch is, they would have to decide whether to confess without knowing the other’s decision.
Both of them were given the consequences of their decision:
- If both confesses, both go to jail for 5 years.
- If one confesses, and the other one doesn’t, confessor goes free (for turning state evidence) and the other one goes to jail for 10 years.
- If no one confesses, they are released and free.
The irony of this problem is that if Alice and/or Bennett acts selfishly and does not cooperate with the other (one of them confesses), they do worse than if they were to act unselfishly and cooperate together (both of them stay silent).
This dilemma has been seen in real-life situations: two shops engaging in a price war, nations competing in an arms race, or even farmers increasing their crop productions.
For the best outcome to happen, players need to start cooperating, which introduces another theory called the Theory of Moves. According to the Theory of Moves, shifts in outcomes can be largely predicted on how the play starts:
- Play starting non-cooperatively will cause players to be stuck, which will result in players staying in a non-cooperative outcome.
- Play starting cooperatively will cause player to not defect given that defecting will result in both of them ending up in a worse outcome, which will result in players staying in a cooperative outcome.
- Play starting at one of the win-lose outcomes (one of the players are starting with the best outcome) will result in a causal effect based on the decision the best player makes. Knowing that it is in the best player’s interest, as well as their opponent, to act graciously to avoid the non-cooperative outcome that will result in the next-worst outcome for the both of them, which will result in players defaulting to a cooperative outcome.
(source: britannica)
These mentioned above are the opposite of a zero-sum game. A zero-sum game are games that result in quantifiable gain of one party that are of equal weight to the loss of the other party.
The last important concept of game theory is Nash equilibrium, where two or more competitors will not benefit by changing its existing course. Let’s revisit the oversimplified example of Floormart and Grocer Basics.
- Floormart and Grocer Basics both sell pop at $1/can. They each sell 200 cans daily. After subtracting expenses from the $200 of revenue, they are left with $100 of pure profit. They each pocket $0.50 for every sale.
- One day, Floormart was thinking to offer their pop at $0.80/can. That’s $0.30 profit per can. If they wanted to meet their minimum of $100 of profit, they would have to sell at least 334 cans. Floormart’s cheaper price will attract 134 of Grocer Basic’s customers so that they can make the same amount of profit as they did before.
- They both know that Grocer Basic is not going to stand for that and will decide to compete (lower prices) as well.
- If they did that, both of them would then earn lesser than they were initially earning.
- Since both companies are rational decision makers, they came to the same conclusion that they are better off continuing to sell their pop at $1/can. This is the state of Nash equilibrium, where two or more competitors decide they are better off by not changing their strategy.
The games that I have listed are part of a much larger list of commonly studied games (check out this extensive list on wiki). Basically, game theory is a vast area of study with many variations of application, which can be studied in depth, but I hope you get the general idea.
Ok cool, but how does it relate to Product?
Game theory is ideal for strategic situations where competitive or individual behaviours can be modelled. In the broader scope of product, it can be a really good mechanism to decide whether to exit or enter a specific market. In a cross-collaboration sense, it can be a really good tool to understand how various stakeholders can act in different circumstances. It can help us, product managers, provide timely guidance as we tackle difficult, unprecedented decisions.
Similar to the overarching description of game theory, the key is to analyze a range of scenarios based on decisions by reasonable actors (stakeholder groups, other competing priorities), and to clearly present the advantages and disadvantages of each option, providing informed support to prioritization decisions made.
As someone who works in the eCommerce space, market expectations and trends move very quickly which require me to work with a ton of uncertainties daily (case in point — a global pandemic). To move away from corporate decision making that stems from gut feelings and assumptions (which usually increases the probability of multiple band-aid fixes after shipping a product, or a complete re-do of recently-built features), game theory can help provide clear information to decision-making. But only if we have a set of detailed inputs to make the usage of this theory practical and more predictable.
(source: mckinsey)
Of course as product managers, we are constantly faced with practical, dynamically evolving business problems beyond a neat simulation like the prisoner’s dilemma. The main takeaway, however, from lessons learned in game theory is that even if people or companies rationally follow their own self-interest, the best outcome is hard to reach when they can’t or don’t cooperate.
(source: thequintessentialmind)
In product, there is a common phrase for the need to “keep stakeholders happy”. However, that is not going to happen all the time unless we want a bloated backlog filled with new feature requests that no one wants. Instead, product is about helping our stakeholders achieve their goals and agendas.
For example, engineers want to know what the vision of the product is and how their work is helping the team get there. Executives want to know how the product roadmap is contributing to the success of the company’s strategy. The marketing team wants to know how the product can benefit the customer and find ways to measure their strategy. Everyone is essentially acting according to their personal self-interest.
Naturally, everyone will want to have a say in how your product should look based on their idea of success — you are the essential connection between the multiple functions. As a recap, one of game theory’s key assumption is that everyone is a rational decision maker. So as the connection between the different (sometimes competing) groups, we need to know our stuff. We need to have a deep understanding of the multiple facets of a product (our customers, the functionality of the product, business strategy, to name a few) that is backed by real data (key word is real, not vanity metrics).
In product, we need to facilitate rationality amongst our stakeholders through sharing our knowledge openly (for example, our team is setting up a weekly dashboard for our portfolio’s performance that will be shared to the broader group) and making ourselves accessible for questions (for example, setting up regular one-on-one sessions with stakeholders).
Everyone wants a “yes” but no one wants a “no”.
“Not saying no to internal stakeholders is the worst outcome for our customers” is a statement that I am constantly reminding myself on a daily basis. How do we foster collaboration among the different groups without compromising on the value of the product?
- Acknowledge the request
- Show empathy for their goals
- Provide context for existing priorities and decision-making process
Saying “no” does not mean you are pitting stakeholder groups against each other, but instead, finding ways to foster strong alliances despite competing priorities.
By creating a simple checklist when making a challenging decision or nurturing relationships, this can train our minds to a default first principles thinking by breaking down complicated problems into basic elements.
- Are the actors in this situation rational?
- Are we able to reach Nash equilibrium?
- Are they acting according to their self-interest?
- Do they understand the rules of the game?
If most of the game theory parameters are not met, there is an option to either:
- Rationality: Pause the conversation and postpone the decision to allow difficult feelings to subside.
- Rules of game: Reframe the conversation by exploring which user or customer problem the proposed solution would help address.
- Self-interest: Ask clarifying and probing questions to check that we have correctly understood what was said and encourage the actors to provide more information.
- Nash equilibrium: Having a stakeholder map will help us to see how the various stakeholders are connected, understanding the power vs. interest dynamic, and paint the broader picture.
The key takeaway is that instead of focusing on ways to split the difference, game theory will help us build successful products through stepping away from weak compromises and instead be a mechanism to improving internal alignment around data-driven decisions.
