# thoughts on and conjectures about finite and infinite games

### where I let this idea die in my mind and move on

I've been thinking about an idea that can be called finite and infinite games for several months now and I've yet to write anything about it, so here that goes. I feel like I only understand a small fraction of the topic, however, and some of this is probably wrong, or at least incoherent to others.

Four years ago I loathed a book I read called *Finite and Infinite Games* by James P. Carse. However, due to a series of interactions I had late last year I found myself thinking about the concept again, and it helped me understand what I was feeling at the time. Here are my thoughts.

*Note that I currently only comprehend the first of five chapters in this book. If you understand chapter two, I'd like to talk to you! chris@chrislakin.com*

## Definitions

Carse summarized his distinction (via *NYT)*:

There are at least two kinds of games: finite and infinite. Finite games are those instrumental activities - from sports to politics to wars - in which the participants obey rules, recognize boundaries and announce winners and losers. The infinite game - there is only one - includes any authentic interaction, from touching to culture, that changes rules, plays with boundaries and exists solely for the purpose of continuing the game. A finite player seeks power; the infinite one displays self-sufficient strength. Finite games are theatrical, necessitating an audience; infinite ones are dramatic, involving participants…

And here is how I define them—

def. **Finite game**: a game with bounds in space and time (i.e. it starts and ends at a specific point in time), for which there also exist agreed win conditions and therefore also exist clear metric(s) of success. The purpose is to win.

E.g.

chess

tennis, baseball, sports

monopoly

pickup artistry

def. **Infinite game**: a game with no bounds in space or time, no fixed rules, and no win conditions— or, everything else with players but without boundaries and win conditions. Therefore, there is no purpose (except, possibly, to continue the game).

E.g.

biological life

non-transactional relationships like marriage, parenting, friendship, and dating

writing

(when not a competition with others)

tag

(when played without a time-limit)

improving the world

*pursuit of beauty, goodness, and truth*

There is no winning marriage, for example. The game doesn't end, and a victor can never and will never be declared. You can do "well", but only on arbitrary metrics of success that others might not even agree to respect. Instead, the closest definition of "winning" might just be

*to keep playing and enjoy doing so*.(Note that individual players have finite lives and they do die, but the game lives on.)

Note that all finite games exist *within* either the infinite game, or another finite game. (The one infinite game is the single ‘source’.)

## Implications

### Newcomb's Problem

The relationship between Newcomb's Problem (described below) and finite and infinite games is interesting to me.

The best description I’ve seen of Newcomb’s Problem follows:

An agent finds herself standing in front of a transparent box labeled “A” that contains $1,000, and an opaque box labeled “B” that contains either $1,000,000 or $0. A reliable predictor, who has made similar predictions in the past and been correct 99% of the time, claims to have placed $1,000,000 in box B iff she predicted that the agent would leave box A behind. The predictor has already made her prediction and left. Box B is now empty or full. Should the agent take both boxes (“two-boxing”), or only box B, leaving the transparent box containing $1,000 behind (“one-boxing”)?

*(Source: Functional Decision Theory, by Eliezer Yudkowsky and Nate Soares)*

I claim that if someone perceives this situation as a finite game with a fixed time horizon and value to be maximized until then, then they will have the inclination to two-box; meanwhile if they perceive this as within the infinite game, then they will one-box.

There’s more I could explain here but the gist is that I claim “one-boxing is like infinite play; and two-boxing is like finite play”.

### Truth vs Value

One cannot 'gradient descent' from finite play to infinite play, or similarly from two-boxing to one-boxing. If you are motivated purely by gain, there is no incentive that will cause you to become, for example, a trustworthy person. (I claim that trustworthiness/integrity is most like one-boxing. It’s not something that you *do*, it’s something that you *are*.) And there will always be an incentive— e.g. a metaphorical $1,000 bonus— for defecting on integrity. Therefore he who is only receptive to extrinsic motivations— be it for money, prestige, sex, romantic attention, utilitarian impact

(Note that it may still be locally advantageous for you to deceive others into thinking that you are trustworthy, however.)

For proof of this untrustworthiness, consider whether you would unconditionally cooperate with such a person.

So here I observe that there is a game that is 'optimizing for value/a goal', and a game that is 'striving towards truth (e.g. integrity)'. And these map onto two-boxing and one-boxing, respectively.

If you have a goal that can be stated and optimized, then it seems to be that you're playing a finite game.

But there is another thing, there is a thing that is more ~ the pursuit of beauty, goodness, and truth. But it is difficult to describe, measure, and explicitly optimize for.

The Tao that can be told is not the eternal Tao.

The name that can be named is not the eternal name.

*(A translation of the first two sentences of The Tao Te Ching)*

### Optimizing for value almost always encourages defection against others

Here's a proof that the best strategy in many finite

games includes defection:I'll use friendship to represent the infinite game. Note that actions in friendship are of course also positive-sum. (By cooperating, both friends can ‘win’ and increase the total wealth of everyone involved.) And so when we enter a friendship, we go into it with the intention to cooperate, and to always cooperate. At any given point it might locally advantageous to engage in zero-sum actions against your friend (e.g. to "borrow"-but-soon-steal money, attention, or secrets), but it wouldn't make sense to do so because this would also destroy the relationship and the potential for all future positive-sum collaborations. The relationship could just go on forever to the benefit of you both.

Now instead let's say that you're playing iterated rounds of Prisoner's Dilemma with someone. We will take this as a metaphor for friendship. If you knew that you would be playing the game forever (or even just for a very long time into the future), you would keep cooperating with your partner and would not defect. Again: At any given point it might locally advantageous to engage in zero-sum actions against (i.e., to defect against) your partner, but it wouldn't make sense to because this would also destroy the relationship and all future positive-sum collaborations: You know that if you started defecting, so would they, so you don't defect.

You could just keep cooperating forever.I claim that *the best strategy in any finite game that locally rewards defection (zero-sum behavior) more than it rewards cooperation is a strategy that includes defection*. For example, if you're playing something like an iterated Prisoner's Dilemma with a partner and you know the game is certainly ending soon, what do you do? Well, you will probably start defecting near the end because you can squeeze out a couple extra drops of value from your opponent if they're naive.

A real life example of the above: A friend of mine had a landlord who was very amicable all throughout his lease until the last few months when landlord transformed into an abominable, grifty monster. Once cooperation (i.e.: amicableness) was no longer favorable for the landlord’s narrow definition of gain, he started to defect. This is, of course, not the way of integrity.

So while the best strategy in a positive-sum

infinite game is obviously one of infinite cooperation. The best strategy in any finite portion of an infinite game, however, will involve defection, e.g. a defection in the last round.**Thus the best strategy in a finite game that (locally) rewards zero-sum behavior (more than it rewards positive-sum behavior) will always be one that includes defection.**

So then if you accept the premise that defection is deceit— and, after all, you can only steal from people who are cooperating with and therefore trusting of you— then the best strategy in such finite games is to not be totally honest. **Finite games encourage achieving their goals over e.g. acting out the truth.**

(“But what about the finite game of telling the truth!” a reader says. Except that truth cannot be objectively measured, and so it cannot form the basis of a competition, and so it cannot be the objective of a finite game.)

### A definition of creepiness

Sometimes we enter relationships, relationships that we expect to be infinite games, and then we discover that the other party treats it as a finite game. This I define as **creepiness: when you see other players playing strategies of finite games inside of what you thought was an infinite game**.

For example, say you've just begun dating Dexter. Then you notice that seems like he's trying to rush the relationship along and, for example, try to get you to have sex with him as quickly as possible. You might wonder, *What's the rush? If this were really an infinite game then we would get together eventually anyway, so what's the matter? Do you think my opinion of you is going to change in the near future?* … — And wouldn't this feel quite weird?

It's like playing Prisoner's Dilemma with someone and you think that the game is not going to end for a long time, if ever, but you can see that your partner is starting to act in a way that seems a little off, and it seems to you like they're preparing to start defecting, like they're concealing something from you. *This* is creepiness.

(I think this is also the core of what is off-putting about pickup artistry, and also cult-indoctrination and similar frameworks that **instrumentalize** individuals.)

**I claim that creepiness can only exist if finite games are being played.** After all, deception is an ineffective strategy in an infinitely-long game: others will always figure out your true intentions.

In finite games, others are tools, if not enemies; in the infinite game, others are comrades.

### Intrinsic and extrinsic motivations

It also seems clear to me that intrinsic motivations and extrinsic motivations map onto the infinite game and finite games, respectively.

Extrinsic motivations have a tendency to turn everything that is not the goal into something that is instrumental for the goal. For example if you're maximizing for the extrinsic goal of making money, then you may be inclined to lie in order to move towards making money, and therefore instrumentalizing truth in the process.

Moreover, remember that finite games can only exist within larger finite games or within the infinite game. And there is only one infinite game.

Finite games cannot exist on their own.

Similarly, extrinsic motivations cannot exist on their own: they must have a justification of a higher extrinsic motivation or an intrinsic motivation.

An infinite game cannot exist within a finite game.

Similarly, intrinsic motivations cannot be sustained by extrinsic motivations.

E.g. You can't decide "I am going to enjoy programming now" (intrinsic motivation) because "this would make me a lot of money" (extrinsic motivation).

E.g. You can't decide "I am going to love you" (intrinsic motivation) because "this would get me a lot of sex" (extrinsic motivation)

(I do, however, believe that intrinsic motivations can be

*rediscovered*due to extrinsically motivated nudges, but I do not believe that they can be*sustained*by extrinsic sources of motivation.)

It seems that we also sometimes get stuck in finite games, and I'm not sure why. Surely lying for profit is a bad tradeoff to make with regards to the infinite game, so why would we choose this in a finite game?

## list: contrasts between playing the infinite game and playing finite games

I've split this into multiple parts for viewing (Substack doesn’t have tables). The ordering corresponds between the two. Here are the intuitions that seem salient here:

### infinite play is like (pt. 1)

1. playful and exploratory

2. beyond utilitarianism— recognizing that there exists no ideal utility function.

3. maintains curiosity

4. maintains fundamental uncertainty

5. follows beauty

### finite play is like (pt. 1)

1. optimizing.

2. utilitarianism (for a defined utility function).

3. has lost curiosity

4. no time for uncertainty

5. chases gain

### infinite play ~ (pt. 2)

6. one-boxing in Newcomb's Problem

7. expanded awareness, ~Alexander technique, “non-doing”

8. prioritizing integrity over defection

9. others are comrades. holism.

10. wins by playing

### finite play ~ (pt. 2)

6. two-boxing in Newcomb's Problem

7. narrow awareness like a predator; “trying”

8. prioritizing pursuit of the goal over all else (defection occurs and integrity is lost in the process)

9. others are either tools, or competitors. separateness.

10. plays to win.

### infinite play ~ (pt. 3)

11. has no formal goal but except wanting to be its truest and purest self.

12. pursues 'freedoms from'. detached from outcomes.

13. not self-coercive

14. surrendering

15. unconditional love

### finite play ~ (pt. 3)

11. has a goal and is heavily optimizing for it. sacrifices other goals for The One Goal. Wants gain.

12. pursues 'freedoms to'. attached to outcomes.

13. self-coercive in pursuit of the goal

14. clenching

15. conditional love, transactional relationships.

### infinite play ~ (pt. 4)

16. can be satisfied with *what is*, and yet still strive for more

17. transforms zero-sum games into positive-sum games

18. intrinsically motivated

### finite play ~ (pt. 4)

16. unsatisfiable desire for more.

17. transforms positive-sum games into zero-sum games

18. extrinsically motivated

## Other miscellaneous claims

Claim:

**"Finite play" is not better than "infinite play", they're just fundamentally****different****.**I cannot stress this enough.I admit to having a sense that one is "better" than the other, but I strongly suspect that this is misconceived and I expect that this sense will dissolve with time.

Claim: There is the capacity for infinite play within all of us. We all have intrinsic motivations, unconditional love, etc., but we choose to suppress it. We play our finite games not because we have to but because we choose to. And we can equally choose not to. We decide to neglect our intuitions and greater senses.

There is supposedly a phenomena with Kegan Levels where those who are on earlier stages do not understand those who are on later stages. Claim: it might be the case that finite players don't understand infinite players.

Claim: "Finite and infinite games" is just a particularly modern way of factoring a timeless distinction. (E.g. I quoted Tao Te Ching earlier in this post.) For example, this excerpt from 1 Corinthians 13 appeals to my sense of what infinite play is:

4 Love is patient, love is kind. It does not envy, it does not boast, it is not proud. 5 It does not dishonor others, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. 6 Love does not delight in evil but rejoices with the truth. 7 It always protects, always trusts, always hopes, always perseveres.

## Open questions

When and why do we step into finite games?

And why do we seem to sometimes get stuck in them?

## Why am I so interested in finite and infinite games?

This idea has absorbed a lot of my interest in the past several months, and, oddly, I’m unsure of exactly why. I’m also unsure if finite and infinite games have explanatory and predictive power… And, even if they do, then surely the insights here can be explained more parsimoniously through statements like “Don’t treat others as a means to an end.” and (roughly) “Follow your intrinsic motivations, and don’t get too caught up in games of extrinsic motivation.”?

This idea, however, has become less interesting to me as of late and I suspect that writing this post is where I let the idea die in my mind. Perhaps all along I was trying to ‘get out’ of finite play, in my case maybe I sensed that I had a mindset of “goals are the only objects— and everything has to be useful towards some goal, *and everything has to be efficient*”. Anyways, I think I’m out now and am moving on.

In practice, sometimes… so I’m unsure how to factor it. I guess it might be more fitting to say “naive utilitarian impact”

I have made a subtle jump here, and assumed that "optimizing for value" must necessarily imply that a finite game is afoot. I'm not entirely certain of this assumption, but I find it difficult to imagine that 'optimizing' could exist outside of a finite game. (Although this still might not even be necessary for the overarching claim to hold.)

"tit for tat" strategies, cf. Robert Axelrod.

A friend accentuated that it would be more accurate to say that this applies for *diverging* positive-sum infinite games: If a game is positive-sum game but each successive round of cooperation is, for example, half as rewarding as the last but each successive round of defection is of constant reward, then the conclusion. So the conclusion only applies for games in which the integral of value(cooperation) - value(defection) dTime diverges.