Game Theory 102 - Blockchain and Cooperative Games

in blockchain •  10 months ago 

This post looks at how blockchain systems can improve our societies through an analysis based on "game theory".

"Games" and theory

A few months ago I wrote Game Theory 101 - Schelling point or "Why is important".

For those who are not familiar with "game theory", it is a branch of mathematics, more precisely the “mathematical models of strategic interactions between rational decision-makers”. Most if not all human interactions can be seen as "games" through the lens of this branch of mathematics.

One of the best books I've read on this topic is "The evolution of cooperation" by Robert Axelrod (pretty old book, I recommend you buy it if you can afford, but you can probably also find it as downloadable PDF).

Table on the right - payout matrix in "Prisonner's dilemma" - from the "Lime 'n' Lemony" blog of Ashima, a lady I can easily picture blogging on Steemit

I do not intend to make this article into an introduction to game theory, enough saying that this is an absolutely fascinating and highly relevant field of study. If you are more of a "video" person than a "book" person, I recommend watching the YouTube videos on this topic from Systems Academy


Simplifying a bit, let's say there are two types of games, "competitive games" and "cooperative" games.

Competitive games involve interactions where the sum of pay-offs is constant and one player's win is another player's loss. Imagine dividing a pie in two or more parts: increasing the size of one player's part necessarily reduces the size of some other player's part.

In contrast, cooperative games arise where the total sum of pay-offs is not fixed but instead depends on the strategies chosen by the different players. To use the same analogy, depending on the choices of the playrs to total size of the pie can increase.

The majority of our real life interactions can be framed as "cooperative games", whereas "competitive games" are mostly to be found in sports and competitions.

As illustrated in the schematic below, when people cooperate, there's often an "added value", which is the difference between the actual result of their cooperation and the simple arithmetic sum of their separated efforts.


In this example, the output of the effort is measured in little blue squares. Person A working alone produces 1 unit, while during the same period person B working alone produces 2 units and person C produces 3 units.

You can notice that B and C working together produces no added value: the combined output is 2+3 = 5 units.

On the contrary, A and B working together produce 6 units rather than the sum of their individual outputs (1+2 = 3). A also displays synergy with C, as their combined efforts produce 6,5 units, or 2,5 more than the sum of their separate efforts.

Now look at the result of all three (A, B, and C) cooperating: their combined output is 10, or an added value of 4. Clearly, they should work together, right?

Well, not so fast ... The real question that all three are asking is: "how are we going to split the proceeds of our cooperation?" Imagine each one starts by getting what she would have produced on her own; how then to equitably split the added value of 4 units?

The importance of having a commonly accepted answer to this question from the outset cannot be underestimated. If any of A, B, or C fears that they might end up shortchanged, cooperation will be less effective or won't happen at all!

Found on the blog of Marcella Purnama, another blogger that we could have here on Steemit

The Aumann-Shapley value

It turns out the problem of fairly distributing the added value produced by cooperation is a mathematical problem which has been solved more than half a century ago by Lloyd Shapley. The solution concept he introduced has been called "the Shapley value".

The concept has been extended later to repeated games by Shapley with Robert Aumann in a book published in 1974: Values of non-atomic games

Blockchain as an Aumann-Shapley machine

Blockchain has been dubbed "the trust machine" since at least 2015. Yet more than 3 years after, I seldom meet people who truly understand what its implications are.

Most people still think of it as yet another fancy technology, like Cloud, IoT, AI and what have you, “so let's sell consulting gigs and brand new IT projects and systems under this new blockchain label".

Blockchain systems have several important capabilities:

  1. Transparency, which breaks information asymmetry.
  2. The ability to record pledges, facilitating coordination
  3. The built-in value-tracking token and associated transaction ledger, which facilitate calculation of the Shapley value.

Most (or almost all) businesses are built with "a moat" to help them protect their competitive advantage, and secretly dream of becoming monopolists and extracting the ensuing rent. Against this background, blockchains appear horribly disruptive, as they expose rents being extracted by incumbents.

Blockchains can support "open enterprises" or "cooperatives" where participants can pledge a contribution, their fellows can track that contribution and the blockchain can reward the contribution made in a fair manner. In "game theory" terms, "prisoner dilemmas" games become "stag hunt" games. In other terms, blockchain systems can support more and better coordination in "cooperative games".

Steem is the first example I know of such a blockchain eco-system, and Utopian is one of the most remarkable examples of such "open enterprises", governed not by a de jure contract but by social contract.

If you know what witnesses are and agree that people commited to keeping this blockchain ticking play an important role ...

(by simply clicking on the picture - thanks to SteemConnect)

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Game Theory was designed as one of the main pillars in the Proof-of-Work consensus algorithm that made Bitcoin Possible.

Seeing as Blockchain is the by-product to give Bitcoin its immutability, it's only fitting that the application of Blockchain technologies can improve society via the application of Game Theory.

Good Read!


@sorin.cristescu Don’t you think this must be like;

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If I understand well you'd split the added value evenly. A+B gives indeed an added value of 3 (total is 6). But B+C has an added value of 0: B produces 2 alone and C produces 3 alone and B+C produces exactly 5.
Anyway, splitting the added value half-half seems fair when there are only two participants but becomes problematic at A+B+C. The added value is 4 (1 of A + 2 of B + 3 of C + 4 of added value from cooperation= 10). A receives 4/3 = 1.33 on top of his 1, for a total of 2.33. But if A only works with B then it gets 1+1.5 = 2.5. So for A, it makes more sense to work only with B than with B and C, although the A+B+C combination produces more (10) than the (A+B) combination and C taken separately (6+3 = 9)

The Shapley calculation (which you find on Wikipedia) takes this into account in order to compensate A such as it's in his own interest to enter into the A+B+C combination

yes A+B+C produce bigger value at the total but C always gets lower value because of A in return

"Lower" with respect to ?... Each of them starts by receiving what they would have gotten working alone, so C will anyway always get at least 3. Whether he receives more than that and how much more depends on how successful he is at cooperating. For instance, with B, the team is not great as it produces 0 added value. With A, the total added value is 2.5 so C receives 1.25. For A+B+C, as long as C gets at least 1.26 (instead of 4/3=1.33) it will be in his own interest to work in the trio. That 0.07 allow A and B to go from 1.33 to 1.36-1.37 for instance. Still not 1.5 though, but a bit better

Thaks for the witness vote!

Game theory is incredibly interesting. Prisoner's dilemma is one of the most discussed games. Prisoner's dilemma is a bigger problem for one-off games. Repeated games are mostly to reach some form of cooperation to avoid perpetual defecting.

Steem bid bots are a perfect example of prisoner's dilemma for both buyers and sellers. Lucky for us it is a repeated game with infinite rounds.

In reality there are games within games which involve competition and cooperation. I think many focus on competition but cooperation has great potential especially for smaller participants.

This is a good theory, however, when I see "the rational" decision makers then I think that it would be possible to discuss it as well... for me, this statement about rationality is similar to communism where they foresee that all people are good...

You don't need to - blockchain enables transparency, you enter in a cooperation with who you trust

Nowadays the situation that we are going through in Venezuela is critical economically, politically, and even socially and you all know it, the government is a huge brazenness, people no longer have hope, and only take a decision that is to emigrate to another country. . These months have been getting worse, with your vote you will help a group of people you will be very grateful AYUDAME CON TU VOTO EN ESTE COMENTARIO se te agradecera mucho


Most (or almost all) businesses are built with "a moat" to help them protect their competitive advantage, and secretly dream of becoming monopolists and extracting the ensuing rent. Against this background, blockchains appear horribly disruptive, as they expose rents being extracted by incumbents.

How about investing unlimited amount on Steem, is this not a monopoly?
Maybe we could minimize or say put some tolerance on investments, a limit on amount to invest on Steem in order in some way to reduce the gap or make some a little bit of balance on the investments between the few huge amount investors and the many little investors.
My words are quite rambling, I hope you understand what I mean.

Yes, I think I understand. Steem is a "plutocracy". Far from perfect when compared to our current democratic society but the human society has evolved 7000 to reach this state. Blockchain community have evolved from "absolute monarchies" to include some degree of power dispersion over only 3 years, a pretty good result.

I recommend you read this post: Why Blockchain is a Revolution

Spotting this post made me join steemit. I lived that book and your post is really informative. More of this!

Thanks, enjoy the freedom :)

Still trying to understand the concept being of steemit .
In past 4 days i concluded that 70% are bots rest 30% are giants who just eats up new commers ;D

Nobody eats up anybody. If you like to create content, whether prose, poetry, photography, art, you are free to do so and post here.

The worst that can happen is that you get less engagement than you hoped for.

If you came for the money you'll notice that you make a lot less than "the giants". Just like in the real world, no reason to expect steemit to be somehow "magic"

  ·  10 months ago Reveal Comment

I guess Steemit has yet to perfect their security algorithms.

the bots are a kind of advertising mechanism - you pay for visibility. Please read this article
Help Yourself! (steemit for dummies)

Hey there !
Very well made posts (replying here for your whole blog), very inspiring for me as I try myself to write articles. I recently made an article about an idea of dApps on the steem blockchain and I'm satisfied but I can't see by myself how I could have done better..
I let you the link if you have the time ;-) / url

Continue your very well written blog, it's a pleasure to read it !

I m still worrying about the bots and power of the decision makers @sorin.cristescu

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I came to a pragmatic conclusion: "if you can't beat them, join them!"

Fair enough

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Thanks for the knowledge- I am trying to learn all I can I aside from the fact I am going to re-read it a few more times, I like that you made it understandable. I upvoted and all that ... have a fabulous night!

i love your all posts... very nice


nie wiele z tego zrozumiałem co napisałeś ale cieszę się że mogłem zapoznać się z tą tematyką jest to ciekawe.

Jeśli potrafisz czytać po angielsku, radzę śledzić filmy z YouTube na temat teorii gier, które zamieszczam w poście, są bardzo łatwe do naśladowania

Very interesting i studied game theory in my poker player times


Nice Post bro, u are a Monster. Respect from Venezuela

New knowledge for me

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I'll be here, waiting for my curation rewards, then.

Look at these nice curation rewards (proportionally speaking)

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Deleted comment

Your comment is a bit intrusive and closely resembles spam. Please decrease the size of the picture and of the text if possible. Thanks

Hello, sorry about this. I have removed that comment from your post, someone thought a bad idea was a good idea but that's how we learn.

I assure you it is not a scam, @mazzle would be correct most of the time but not this time. Sorry for inconvenience.

No worries, thank you!

It is spam and more than likely a scam. The best thing that you can do is flag the comment so that it is hidden.

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give me a vote

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Thanks for using @edensgarden!

It is a good theory, seeing that there is something to discuss in my mind, I want to discuss it in this matter.

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Good post
I like your post

Congratulations @sorin.cristescu!
Your post was mentioned in the Steem Hit Parade in the following category:

  • Pending payout - Ranked 2 with $ 328,58

It looks like it looks interesting but complicated.

make a friendship with each other by giving vote and commenting post.

You got a 51.36% upvote from @brupvoter courtesy of @steemium!

Woah. I really love this bro

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Union OF ANY TWO OR ALL THREE have more strength to produce output (union is strength)

Compound interest nicely divided

I find this very interesting and I would love to know more about it.

good post, Blockchain is the by-product to give Bitcoin its immutability, it's only fitting that the application of Blockchain technologies can improve society via the application of Game Theory.You can earn money by making comments and can not earn without comment and due to the comments, you can correct their mistakes.

As Seeing as Blockchain is the by-product to give Bitcoin its immutability, it's only fitting that the application of Blockchain technologies can improve society via the application of Game Theory.

When everything are publicly recorded people are less likely to try to defect.

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nice sharing sir.

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  ·  10 months ago Reveal Comment