The Gist

Withholding material information from people affects their ability to make informed decisions. The only reason to knowingly withhold this information is to affect someone’s decisions, which is inherently manipulative.

Note: “Material Information” is any information that might affect someone’s ability to make a fully-informed decision. I.e. the price of an extra scoop of ice cream is material information if I’m at an ice cream shop deciding what to get. The weather on the surface of Mars is not material information for this decision. It is information, but it does not affect what I will order at the ice cream shop.

Introduction to Game Theory

To understand how withholding material information affects people’s decision making, we must first understand how our decisions and the decisions of those around us manifest. Luckily, mathematicians and social scientists have developed a field to study that exact thing: game theory.

The Makings of a Game

In game theory, a game is scenario in which players make decisions in order to receive certain outcomes. The game can be broken into four primary parts:

• Players
• Strategies
• Information
• Payoffs

The Players are the decision makers in the game. They have different options and strategies available to them that lead to different outcomes. In Game Theory, they are assumed to be rational. This means that a player is going to make decisions to maximize their own payoffs based on the strategies and information available to them. (If you are wondering about how altruism plays into this, I will explain later. For now, just know that a rational player maximizes their own payoffs).

The Strategies are the different combinations of actions Players can take from the beginning to end of a game. If the game consists of multiple decisions and some decisions are dependent on the actions of other players, then a strategy is a full set of actions a player can take throughout the game.

Information is the set of things known about the player during the course of the game. If a player has “Complete Information” a player knows the payoffs for all players, who the players are, the rules of the game, and all available strategies for the players. “Incomplete Information” is a state of not knowing any one of these things. “Perfect Informaton” is when a player has knowledge of all the moves that were previously played in the game, and “Imperfect Information” is when this is not true.

Finally, we have Payoffs. This is the utility derived by each player when a particular outcome is reached. For example, you may gain utility from winning a game of chess. You may also lose utility from losing a game of chess. In poker, you may gain utility when you win a hand. Similarly, when you lose a hand of poker, you may lose utility.

With these established, we can now understand how a game theortic point of view illustrates the effect of withholding information on other people’s actions.

Game Theory Applied to Life

Illustrations of Game Theory in Life

In order to understand the argument of this post, I want to emphasize two of the four parts of a game.

Firstly, payoffs. At the end of the day, every decision we are making is for the sake of reaching certain payoffs. They are our primary motivators, defining both how and why we do the things we do. But it is easy to misunderstand payoffs, both in theory and in practice because they are measured through an intangible means: utility.

Utility is subjective to each player, and the utility each player derives from a certain outcome may look different from the material aspects of the game. For example, imagine you are a parent playing a game of Tag with your young kid in the park, and you are far faster than your kid. Materially, you win the game by continuing to run away from your child while they are the tagger. The longer you stay clear of getting tagged, the more you “win Tag”. On the surface, it may seem like your payoff is increased by “winning Tag” more, but that’s not true. In this scenario, you’re an experienced parent who knows that your kid will be sad and even give up if they are unable to Tag you for too long. Sure, you gain utility from winning sometimes and tagging your kid, but you also gain utility from knowing when to let yourself get tagged so your kid has an enjoyable afternoon. You altruistically care more about having fun with your kid than winning the game. Materially, you are losing if you get tagged every once in a while, but your payoff is a net positive if you do. In terms of game theory (and life), you are winning.

When I first introduced the concept of payoffs, I used a game of poker as an example, and I specifically said, “you may gain utility when you win a hand”. Emphasis now on the word “may“. When you win a hand of poker, you win chips or cash. Whether or not those things add utility to your life is subjective. The cash might bring you utility in the form of material purchasing power, but if you’re playing with mobsters who don’t like losing money, you may lose utility in the form of broken kneecaps from winning the same hand of poker. Whether or not the cash is worth more or less than your ability to walk is up to you, so you may gain utility when you win a hand of poker with mobsters, even if your knees are broken. But you may also lose utility, even though the material outcome (more cash, fewer working knees) is the same. The utility gained or lost is up to you.

Second, it’s important to understand information (or a lack thereof), and how it takes form in our day-to-day interactions. People may not know what options are available to them when they are making decisions, or how a particular outcome affects someone elses’ (or even their own) payoffs. Let’s take the game of poker with mobster’s example again. I may not have information on the people I’m playing with, such as their mob affiliation. I may not know that one of them breaking my kneecaps is a possible move they can make. I may not know if the money in the pot is currently large enough for them to decide it’s worthwhile to break my kneecaps. Each of these is a piece of missed information that makes me unable to play the game in a manner that is optimal to me. I may think I’m acting optimally by winning this hand, but in the grand scheme of things, I may later wish that I hadn’t.

And that is the key here. In game theory, we assume everybody is rational. Each player is trying to maximize their payoffs based on the information available to them. In other words, each person, if given all the available, material information, will work towards the outcome that gives them the most utility (highest payoff). So, the only reason to purposely withhold material information from someone is because doing so might affect the way the other person behaves.

The Effect of Withholding Information

There are a number of ways we can withhold information.

First, we can withhold the options another person has available to them. You may want to go out to dinner with your roommate after work, so you may not tell your roommate that you guys have food at home. Your roommate may not realize eating at home is an option, leading them to agree to meet you at a restaraunt after work, even though their preference may have been a homecooked meal.

Alternatively, we may withhold how an action may affect another person’s payoffs. You may go to the pool with your friend and want them to join you in the water. The water is cold, and you know they might not join you if they know how cold it is. You withhold information about the temperature of the water, and when they jump in, you have the payoff of your friend’s company in the water. That said, they may have a lower payoff because they’re in frigid water they would have otherwise avoided.

Finally, you may withhold information about how something affects your outcomes and payoffs. You may be a guest at a dinner party, but you don’t want to impose or feel like a burden on your hosts. As the night progresses, you get more and more thirsty, but there no cups set up at the dinner party. It would be beneficial to you to drink water, and the host (if they knew you were thirsty) might even prefer to be “bothered” so they could get you water, but you, assuming yourself to be nothing but a burden if you ask for what you need, hide the fact that you want water from your host. Because of an assumption you made about someone else’s payoffs, you withhold material information that may have led to the host gladly getting you a drink for the evening.

The intent behind and manner of withholding information may be different on a case by case basis, but they ultimately have the same effect. They have the ability to change the decisions made by those around you, potentially leading them to act in ways that are suboptimal to the things they want.

If we truly believed the people we are interacting with to be rational and that all of the information we have is true, then giving them access to all of the material information we have available would allow them to act optimally. Thus there are two primary motivations for us, as rational individials, to willingly withhold material information:

• We do not believe the other person is rational, and wish to stop them from choosing a suboptimal payoff for themselves
• We want the other person to potentially act suboptimally because it increases our own payoff

Regardless of the motivation, the outcome is the same. A person is potentially led to take a different course of actions (aka “a player chooses a different strategy”) based on our choice to keep material information from them. In other words, “withholding information” is a tool that we use to manipulate the actions of those around us, making it inherently manipulative.

Disclaimer

In the past when I have brought this argument to people’s attention, I’ve gotten a lot of backlash from it. I have since realized that their needs to be a connotative disclaimer for the argument because the wording of the thesis, though accurate, is a bit abrasive.

The word “manipulative” has a strong negative connotation with it. People think that it’s inherenly a bad thing motivated by bad intentions, but that’s not true. For example, in the “needing water at a dinner party” scenario, we fail to express our thirst, thus stopping the host from having the option to get out drinks to quench our thirst, because we do not want to impose. We believe an imposition will negatively affect the host. Our intentions by not relaying information related to our need are positive, even if in reality, the host would experience a higher payoff by addressing our unmet need and being an attentive host. That said, there is also a reality where the host is irked by our imposition and has to choose between being a bad host or putting in labor to get water they did not want to get. In this case, your expectation that they would have a higher payoff from you not relaying your thirst is correct (again, a manipulation, but this time with a positive outcome and positive intent).

Another situation could be trying to help someone we believe is acting irrationally. Take for example, a child, who we may deem to be myopic about their health because they do not foresee the health ailments that come with bad habits. The child may want to eat ice cream and cake every night for dinner instead of healthier options, even if we express to them that those foods are bad for the health in the long run. Given the time between today and the long-term health implications of their decision, the payoff to them for this food today and tomorrow and the next day may make it seem like they should eat the cake, but this is because they are not “acting rationally” and taking into account the negative payoff that will ensue when their health declines and they have medical expenses related to these choices. Even when they understand the long-run payoffs, they may forfeit the higher long-run payoffs for the joy of ice cream and cake every night. Just as a parent may withhold ice cream from the child to help the child reach a better long-term payoff, withholding information can work similarly when other’s are suspected of acting irrationally.

That said, I use the example of a parent and child because assuming someone is acting irrationally is paternalistic. It stems from an idea that you know more or know better than somebody else about their own preferences, payoffs, etc… Then, you take actions or control material information in a way that puts them on a path that you believe provides better payoffs for them. Again, this is not to take a moral stance on it, just as I am not saying withholding information for the sake of manipulating somebody’s actions is “wrong”. Nevertheless, paternalistic tendencies toward manipulating somebody’s actions because you believe you know better than them can be condescending.

This is all to say, there are numerous reasons one may choose to withhold information from others, but that does not necessarily mean they are done with ill-intent nor that they are harmful, but it does mean there is intent to manipulate somebody’s choices in a way that aligns with your view of a better future. So I do not mean to say that withholding material information is “bad”. I simply mean to explain how doing so is inherently manipulative.

Closing Thoughts

I came up with this notion of withholding information being manipulative after taking a Game Theory for Economists course in my senior year of college. I remember a friend told me about how they were feeling in regards to a situation related to another friend of theirs. They confided in me that something their friend was doing was bothering them and I said, “why don’t you tell him?” Like a flash in my mind, I saw a game theory decision matrix for their exact problem and thought “there’s a good chance her friend would be eager to solve the problem she’s presenting, but until he knows there’s an issue, the problem will remain unsolved.” She said, “but what if he doesn’t want to solve the problem,” and I said “you are deciding his actions for him rather than letting him decide that for himself.”

That’s when it occurred to me that withholding information inhibits people from making decisions, and her making that decision for her friend was manipulating him into a scenario he might not want to be in where he is causing her distress in their friendship.

The point of this post is to argue that this relationship between information and action is always true. Withholding information inhibits people from making informed decisions. I hope that by understanding this, we can live in a world where we are all making and allowing others to make informed decisions that help each other the most. I hope that we can all be altruistic enough and expect that others also have our best interest at heart, and their payoffs are higher when ours are. But I don’t know if that’s the world we live in.

When I was in my Game Theory class, my professor said something that has really stuck with me. He said: “It does not matter what the game is. Never let anybody else know your payoff structure.” The implication being that when somebody else knows our payoff structure, they have the capacity to use it their advantage. Knowing what decisions we will make to maximize our payoffs, they can make decisions to maximize their own, even at the cost of ours.

Based on his statement, I’ve recently started designing a board game to help illustrate the effect of assuming bad-actors on people’s need to withhold information. I won’t go into the rules of the game here, but there’s a particular mechanic that I want to highlight.

The game has 25 unique win-condition cards that can be given to players at the start of the game. Some of these cards, but not all of them, require other players to lose in order for you to win. We’ll call these the “competitive win-conditions”. When players begin the game, their win-conditions are kept secret from the other players. Players are given the option to reveal their win conditions at any time during the game if they so choose, but they never have to. From this we derive 3 cases:

• Case 1: We play the game and someone has a competitive win-condition

In this scenario, the players are encouraged to keep their win-conditions a secret throughout the course of the game. Someone else’s winning is dependent on someone else losing, thus revealing your own win condition makes it easier for them to derail your victory and secure it for themself.

• Case 2: We play the game having taken out all competitive win-conditions cards before the game starts (ie we know nobody has a competitive win-condition).

In this scenario, the game becomes a cooperative game. All players can feel safe to reveal their win-conditions, and everybody is able to work together to try and make sure everybody can meet their win conditions.

• Case 3: We play the game with competitive win-conditions as an option, but nobody ends up getting a competitive win-condition. (ie anybody could benefit from others losing, but it so happens that nobody does).

In this scenario, the players are still encouraged to keep their win-conditions a secret throughout the course of the game. Even though nobody at the table is incentivized to make somebody else lose, players do not know that. As a result, they keep their win-conditions to themselves to keep themselves safe.

The game illustrates the dangers of both having bad-actors that need others to lose in order to win, and the mere danger of simply expectating those bad-actors to potentially exist. It doesn’t matter if the world is empty of bad-actors if we still expect them to be there. I believe we live in a world where we don’t need others to lose in order for us to win. We have simply created systems where this is the case. But if we approach each other with more cooperation, more altruistic compassion, and an expectation that everybody else is doing the same thing, we don’t have to keep hiding our win-conditions. Society can be a cooperative game.

I would like to leave this post with a quote from the 2011 movie Our Idiot Brother that has really stuck with me throughout the years. When I feel cynicle and think about the effect my withholding of information has on others, this quote reminds me of the enlightening perspective around hope, transparency, and the goodness of humanity held by the film’s protagonist Ned.

I like to think that if you put your trust out there; if you really give people the benefit of the doubt, see their best intentions, people will rise to the occasion.

– Ned