Game Theory: A Simple Strategy That Will Change Your Life Forever

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You’re twenty-three years old. You just moved into a modest two-bedroom apartment

with a roommate—a neutral acquaintance you’re  splitting costs and responsibilities with. To

ensure everything is fair and cordial, you both  establish who does what in the apartment—when and

who takes out the trash, cleans the floors  and counters, does the dishes, and so on.

You determine you’ll each do the dishes once  a week. You take Sunday. They take Wednesday.

Soon, the first Sunday comes around, and, as  planned, you do the dishes. Then the first

Wednesday comes, and your roommate does them.  This continues for a couple of weeks. Then,

on one Wednesday, after coming home late from  work, you find the dishes piled up in the sink.

You don’t say anything. In your generous  nature, you assume it’s a one-off thing,

and your roommate will just do them the next day. When that Sunday comes, however, the pile of

dishes is twice as high, spilling out of the  sink and onto the surrounding countertop. They

never did them. You want to tell your roommate  that they should do the dishes today, but they

aren’t home—and haven’t been all day. And so, you  do them. This keeps things on schedule anyway.

When the following Wednesday comes, your  roommate does the dishes. All is well and

back to normal. That is until the following  Wednesday, when again, late into the evening,

you find the sink filled with dishes. You go to  your roommate and ask them what’s going on. They

assure they will do them. You accept this. The  next day, however, the dishes are still there,

pilled even higher. And then the next day. And  the next day. You realize there’s a problem.

When that Sunday comes, you wonder what you  should do. Do the dishes or leave the already

giant pile to grow bigger? What precedent  have you set? What precedent will you set?

Can you reset things? What if you don’t do the  dishes, and then your roommate still doesn’t

do them? The kitchen will remain a constant  mess. Alternatively, what if you do do them,

and soon you’re always doing them every time?  Who are you dealing with here, and how can you

deal with them most effectively? You wonder what  decision—based on what strategy—you should make.

*** This is a version of a famous thought experiment

in game theory known as the prisoner’s dilemma—a  situation where two people would be better off

cooperating, but each person has some incentive  to go against the other. In both not cooperating,

however, both end up worse off. In this case, the  individual incentive is not spending time doing

the dishes. The outcome is either a messy kitchen  and messy roommate situation or a clean one.

Broadly, game theory is the mathematical study  of decision making and strategies in situations

where outcomes depend on others’ choices. More  specifically, it examines the nature and effects

of how conflict and cooperation among rational  decision-makers can lead to optimal or suboptimal

payoffs. In essence, it is a science of strategy. In social situations, in business, in economics,

and in politics—in every interaction—whether  between as little as two people or as many as

nations, decisions are constantly being made  that affect everyone involved. As individuals

and collectives, we each possess the power to  not only change our own circumstances but also

the circumstances of others—of the world. These  decisions and their outcomes can be as benign as

who does the dishes in an apartment to as critical  as whether a country and its citizens survive.

Game theory suggests that every decision made with  a particular aim can, in principle, be represented

and understood as a mathematical model. In other  words, with a clear goal and defined constraints,

a rationally right choice can always be  determined. More yet, an optimal strategy

can be determined across multiple choices. And  through various computer programs and simulations,

researchers in the field of game theory have  actually found a strategy (or an approach and

temperament) that, under many conditions in  society and nature, has proven to consistently

be extremely effective. And surprising to many in  the field, the strategy is profoundly simple. Even

more compelling, it is hopeful. It is something  that each of us can apply to our own lives.

Before going any further, it’s important to note  that in the context of game theory, a “game” is

not how we conventionally think of one—though  it can also include traditional games. Rather,

“game” simply refers to any interaction that  occurs between multiple decision-makers,

where the outcome and payoff of the interaction  for each individual depends on the choices made

by the others. This can include games like chess  and poker, but it also includes nearly everything

else. Of course, not literally everything—but  all direct interactions that occur between

individuals or groups that involve competition or  cooperation, where there is a mutually affected

outcome. And this is almost everything. Importantly, however, game theory does

delineate two types of interactions (or games):  cooperative and non-cooperative. Cooperative

game theory includes dynamics like players on  the same sports team, roommates (in theory),

business partnerships, as well as international  alliances and trade agreements. In these cases,

goals are shared, resources and information are  often freely exchanged, and fairness and mutual

benefit is both implied and actively pursued. Non-cooperative game theory, however,

is far more prevalent in the world—and arguably  much more interesting. In non-cooperative games,

there are typically winners and losers, as players  act independently in their own interests, making

choices intentionally to benefit themselves,  potentially at the expense of their opponents.

This sort of non-cooperative dynamic and  tension is often used and simplistically

reproduced in game shows. For example, in the  late-2000s British game show Golden Balls,

two strangers would sit across from each other  and decide whether they wanted to split or steal

a large sum of money with the other person. Each  persons’ choice directly affected whether either

individual got any money and how much, but  neither would know the other’s final choice

until it was revealed and locked in. If both chose  to split, they shared the money equally. If one

chose to split, and the other chose to steal,  the one who chose to steal got all the money,

and the other person got nothing. If both  chose to steal, neither person got anything.

In these sorts of one-off situations, where one  can either split or steal–cooperate or defect—game

theory shows us that there is a clear rational  choice. What is known as the dominant strategy

refers to a choice that provides a player with the  best results no matter what the other player does.

And this is always the most rational choice  to make. The choice is not about what could

lead to the best possible outcome, but about  choosing for the best outcome no matter what

the other person decides to do—since you have  no control over that. And so, in Golden Balls,

the most rational thing to do would be to always  steal. This is because if one person splits,

then the other person does better by stealing.  If one person steals, again, the other person,

in a sense, does better by stealing, because  they get the same amount as splitting (zero),

but are not manipulated or exploited by the  other person. Technically, this is what game

theorists would call a weakly dominant strategy,  since the literal payoff in this later situation

would be equal to splitting, rather than better. Of course, however, life is not a gameshow.

Interactions are almost never one-offs without  lingering, continued effects. Decisions are rarely

as simple as splitting or stealing, and outcomes  are rarely as simple as half, all, or zero. In

real life, there is almost always a much greater  interplay with time, repeated interactions,

uncertainty, leverage, and resources. If  someone does or doesn’t do the dishes once,

that game is not over. The relationship and space  are and can be either benefited or strained,

moving forward. When a business smears or partners  with another business, that game is not over.

Retaliation or a growth in resources can and will  likely follow. When a country attacks, retaliates,

or allies with another, that game is not over.  Wars can begin or end. Nations can begin or end.

With all this in mind, what is the most effective  decision-making strategy (or approach and

temperament) in life in general. Is there one? In 1980, political scientist Robert Axelrod set

out to test and answer this very question.  Using computer programs to model different

decision-making strategies, Axelrod orchestrated  an experiment. He had leading theorists from

various disciplines and places around the  world create and submit programs that would

compete in a tournament of an iterated  version of the prisoner’s dilemma. The

goal was to submit the best strategy and win. The rules of the tournament were simple. Each

player (or program) played a single game against  every other player—as well as a copy of itself.

In each game, each player had the option to either  cooperate with or defect against their opponent.

If both players cooperated, they both received  three points. If one cooperated and the other

defected, the player who defected received  five points, and the player who cooperated

received zero. If both defected, both received  one point. Each individual game contained 200

rounds. The player with the most points by the  end of all the matchups in the tournament won.

In total, fourteen programs were submitted—and  then Axelrod added one that defected or cooperated

at random, with a 50% probability each round.  Most of the submitted strategies began with

cooperation, while others began with early  defections. Some players were complex and

calculating, probing for weakness and then  exploiting it—like a program called Graaskamp.

Some mixed in random moves to utilize confusion  and surprise–like a program called Joss. Others

were far more straightforward. Together, the  programs spanned from what Axelrod referred

to as simple and nice to cunning and nasty. After the tournament concluded, Axelrod, along

with many other game theorists, found the results  profoundly surprising. He ran the whole tournament

again, five times over, to ensure the results were  dependable and repeatable. Each time, the results

were consistent, and the same winner emerged: a  program called tit-for-tat, which was one of the

simplest and most cooperative programs of all. To further elevate the complexity and better

mirror real-world circumstances, Axelrod conducted  a second tournament. This time, there was no

defined number of total rounds per game. With it  now being a random, unknown number, players could

no longer track and calibrate their decisions  against a defined endgame. Just like reality.

This time, sixty-two program strategies were  submitted—and again, Axelrod added one that

was random. The results were very consistent to  the first tournament. Again, tit-for-tat won.

Axelrod and many other game theorists found this  extremely surprising because the expectation was

that the winning strategy would be either  highly complex, highly competitive, or both

(i.e. cunning and nasty). And yet, tit-for-tat  was generally simple, nice, and forgiving.

In terms of specific gameplay, tit-for-tat  always starts with cooperation. From there,

it always copies its opponent’s last move. And  so, it continues to cooperate unless or until

its opponent defects. At that point, tit-for-tat  immediately defects back and continues to do so

unless or until its opponent cooperates again. As  soon as its opponent cooperates again, tit-for-tat

then forgives (or no longer accounts for previous  moves) and returns to cooperating unless or until

its opponent defects. So on and so forth. Interestingly, the results of this strategy

equated to tit-for-tat never winning  any individual games, since one-on-one,

it can only lose or draw. But across all  match ups and games, it cooperated with

enough other players to consistently end up with  the highest score overall and win the tournament.

Axelrod writes in The Evolution of Cooperation: What accounts for TIT FOR TAT’s robust success

is its combination of being nice, retaliatory,  forgiving, and clear. Its niceness prevents it

from getting into unnecessary trouble. Its  retaliation discourages the other side from

persisting whenever defection is tried. Its  forgiveness helps restore mutual cooperation.

And its clarity makes it intelligible to the other  player, thereby eliciting long-term cooperation.

Moreover, almost all top performing players  in the tournaments shared in these similar

qualities. And in later simulations with  even more realistic, chaotic conditions,

a more generous version of tit-for-tat, that  occasionally forgave defections instead of

reciprocating them, proved to be even more  effective. Nasty players, on the other hand,

seemed to often find themselves in defecting wars  that lead to mutual destruction. Axelrod says:

“What makes it possible for cooperation to emerge  is the fact that the players might meet again.”

The takeaway from this is reasonable clear.  In continued non-cooperative, competitive

interactions—like these tournaments—it is often  beneficial to, at the very least, try to be nice.

To lead with niceness and cooperation. This  is not a weakness, but a strength. Conversely,

an individual who often leads with or insights  defection is more likely to weaken itself

and lose over time—even if it initially  appears as if they are winning. Moreover,

holding grudges is a weakness; forgiveness is a  strength. Of course, however, weakness itself is

a weakness. That is, letting someone do you  wrong without consequence will lead to being

taken advantage of and losing. One’s approach to  exacting consequence, however, is also important:

it must be relatively equal, consistent,  and clear, not opaque and manipulative.

From a moral and historical perspective, the  winning tit-for-tat strategy essentially mirrors

an eye-for-an-eye ethos. That is, justice and  punishment should be proportional to the harm

caused by an offense, but after proportional  consequence, balance and cooperation can and

should be restored. On a more individual level,  it essentially equates to being kind, forthright,

and understanding, but never a push-over. Of course, there are problems and limitations

both with Axelrod’s experiment as well as  game theory in general. Programs, simulations,

and theories can arguably never truly reproduce,  model, or assess the true scale and complexity of

real-world interactions. Real interactions  often involve many people and many issues;

many perspectives, many goals; shifting ideas and  opportunities; asymmetric leverage and resources;

known and unknown information; vast errors and  chaos; and, perhaps most importantly, they involve

the very emotional, sentimental, spiteful, and  irrational nature of the human mind. As humans, we

feel and hope and believe at least as much as if  not more than we assess, calculate, and execute.

Ultimately, however, game theory teaches us  many important things. Perhaps one of the most

important being is that every interaction  and game is not always about winning.

A strategy always focused on winning can actually  be the least effective at winning overall—whereas

one less focused on always winning can, over  the long term, win. If we want to truly be

successful across various areas of life, there  are going to be—need to be—many instances of draws

and losses. But so long as we continue forward  with each new moment and each new interaction,

open and willing to try again, ensuring we stand  up for ourselves and hold true to our values,

while striving to meet and unite with the  world around us, we can steadily and surely

move toward bigger, more important wins—wins  of cooperation, kindness, and mutual benefit.

We can never truly know or control if people will  cooperate or defect with us, but we can know and

control if we will and why. And we can know that  each decision we make will likely influence the

nature and outcome of all the games in which we  participate—present and future—potentially making

or breaking relationships, goals, systems,  or even society and the planet. And so,

at least for starters, for own sake, when our  day comes, let’s be sure we do the dishes.

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