Hello!

I am a researcher at ETH Zurich, Switzerland and I wanted to share some research I have been working on for more than 20 years (and which dates back to even more than 30 years through my mentor's work). I thought perhaps this might be interesting to the game theory community and it would be an opportunity to get feedback and make it a bit more visible.

It essentially comes down to a generalization of Douglas Hofstadter's super-rationality to non-symmetric games (normal form) and to dynamic games (extensive form) with or without perfect information, and its application to build a deterministic extension of quantum physics and for negotiations. The definitions and algorithms are peer-reviewed and published (except without perfect information, which is a preprint).

This is all based on the philosophical work by Jean-Pierre Dupuy, a Professor at Stanford University who was my mentor on this direction, and who wrote the two seeding papers in 1992 and in 2000. It took me years to digest his brilliant ideas. Dupuy suggested that classical game theory (Nash, Subgame Perfect Equilibrium) suffers from the backward induction paradox, and that this could be solved by completely changing the way we think about time and free choice.

Dupuy constructed a philosophical framework which he called Counterfactual Decision Theory ("Two temporalities, Two rationalities: a new look at Newcomb's paradox", 1992 [1]) that reconciles free choice and being correctly predicted: a compatibilistic form of free will. He also commonly refers to it in the philosophers' community as "projected time". Instead of considering the future as open and the past as fixed, he suggested to do the exact opposite: in an idealized, theoretical setup, the future is already known to all, and the past depends counterfactually on it. This makes it rational to pick one box in Newcomb's problem. He defined an ad-hoc prediction as a prediction that turns out to be correct, but that could have been incorrect if what is being predicted had happened differently ("could" in the formal sense of modal logic) and an essential prediction (we now call it Perfect Prediction) as a prediction that is correct, and that would also have been correct if what is being predicted had been different (counterfactual dependency in the sense of Lewis; not to be confused with logical implication). The fundamental difference with Causal Decision Theory is that counterfactual dependencies can be backtracking, and the difference with Evidential Decision Theory is that we are talking about probabilities of subjunctive conditionals, not about conditional probabilities (the two being different or not is known as Adam's thesis and is discussed in the philosophical literature).

Dupuy then suggested ("Philosophical foundations of a new concept of equilibrium in the social sciences: Projected equilibrium", 2000 [2]) that this can be the basis of a completely new kind of game theory. He started with the centipede game and suggested the concept of a Projected Equilibrium (we now call it Perfect Prediction Equilibrium), as a fixpoint problem, and went through a few examples. The fundamental idea is that Perfect Prediction leads to preemption: if a player were to select an outcome that a past player does not like, this would have led to a deviation in the past, which is a logical contradiction. This corresponds to a Kantian form of ethics with a categorical imperative that Dupuy formulated as "Never act in such a way that, if your action had been anticipated, it would not be within your power to carry it out." Dupuy conjectured that the equilibrium always exists, is always unique, and is always Pareto-optimal.

In 2004, I was able to formally define the definition and algorithm for all dynamic games in general position (it means there are no ties in payoffs) and with perfect information. I was also able to prove that his conjecture was correct for these games. With the help of another colleague of us, Stéphane Reiche, it took us ten years of submissions and rejections until we finally managed to get it published ("Perfect Prediction Equilibrium", 2014 [3]) after presenting in 2014 at an international Economic Philosophy conference. At that point, we thought there was a link with Douglas Hofstadter's superrationality, but this was more an analogy than a formal link.

In 2017, I managed to give definitions and algorithms for (possibly asymmetric) games in normal form in general position, and to show that (i) it does not always exist, (ii) when it does, it is unique and (iii) in the particular case of symmetric games, when it exists, it is always a Hofstadter equilibrium (superrationality, the max of the diagonal). Since I did not know for sure it was the "same" concept as the Perfect Prediction Equilibrium, I called it Perfectly Transparent Equilibrium. This time it took less time to publish ("Perfect Prediction in normal form: Superrational thinking extended to non-symmetric games", 2020 [4])

Then, to prove that these were the same, I suggested ("Games in Minkowski spacetime", 2020 [5]) to unify games in normal form and games in extensive form with perfect information to a broader category of so-called Spacetime Games. Such games can also be mapped as a subset of extensive form games with imperfect information, through a "linearization" of the dependency graph of decisions (interestingly, Lorentz transforms in relativity theory correspond to Thompson transforms in game theory!). Then I defined and gave algorithms for our equilibrium on dynamic games with imperfect information ("Perfect Prediction in Minkowski Spacetime: Perfectly Transparent Equilibrium for Dynamic Games with Imperfect Information", 2019 [6]), which finally showed that the Perfect Prediction Equilibrium and the Perfectly Transparent Equilibrium are the one and same. I now use the term "Perfect Prediction Equilibrium" for them all.

Now, about applications:

• I am actively looking into quantum physics, because the assumption of free choice we are changing is the exact same one that is needed in impossibility theorems (Bell inequalities, Kochen-Specker) and that prevents a deterministic extension. With my research assistant, Michael Baczyk, we published ("Nashian game theory is incompatible with quantum physics", 2023 [7]) a paper showing that Nash equilibria are incompatible with quantum physics and that a non-Nashian approach (such as the Perfect Prediction Equilibrium) is needed. (note that this is not the same as Quantum Game Theory; we convert general quantum experiments into (classical) spacetime games ("Spacetime Games Subsume Causal Contextuality Scenarios", 2026 [8]).
• This can also be used for negotiations: if two parties disagree, and the Nash equilibrium is not optimal, they can agree to sign a contract that commits them to the Perfect Prediction Equilibrium.

I started an online book to explain all of this in simpler terms than the formalism of the papers [9].

I hope I did not break any rules sharing this, not being very familiar with Reddit (otherwise I can delete). I hope this can generate some interest (there is so much more to explore in non-Nashian game theory) and I would kindly welcome any feedback from the community.

Thank you,
Ghislain Fourny

[1] https://www.sciencedirect.com/science/chapter/edited-volume/abs/pii/B9780080410500500236

[2] https://philpapers.org/rec/DUPPFO

[3] https://arxiv.org/abs/1409.6172

[4] https://www.sciencedirect.com/science/article/pii/S0022249620300183

[5] https://arxiv.org/abs/2004.11217

[6] https://arxiv.org/abs/1905.04196

[7] https://link.springer.com/article/10.1007/s40509-023-00309-0

[8] https://link.springer.com/article/10.1007/s10773-026-06295-4

[9] https://www.non-nashian-game-theory.org/

Whenever someone asks me , "If you could change one thing about the world , what would it be?" I always give the same answer , "I want the world to cooperate and maintain peace instead of holding each other's back".

But have you ever actually stopped to ask why we don't do this?

Why do nations default to to geopolitical friction , spying , and deep distrust when absolute cooperation could unlock a collective human paradise? Why do we spend trillions of dollars on satellites to watch each other and weapons to to defend ourselves from one another , when that exact same capital could fund free global education , eradicate poverty , and explore universe as one species?

My father told me the world can never live like one family , because of our different cultures , languages , cultures , and beliefs. But I refuse to accept "I don't know" and "That's impossible" as an answer.

Why can't we have ONE FLAG , ONE FAMILY , ONE PRIDE ?! Why do we have to spy? We tore the earth , the Pangea , and then we tore humanity and everything else along with it.

I am launching a weekly serialized research project on reddit , Substack and Medium , to decode this global tragedy using the mathematical and economic framework of Game theory.

Here is a look at my official thesis abstract:

Millions of years ago , the earth existed as a single , unified landmass known as Pangea. While geological forces spilt the continents , human ego has systemically fractured global cooperation. Today , technologically advanced civilizations spend billion of dollars to launch spaceships and satellites in absolute isolation , viewing space as a theatre for national national dominance rather than a collective human frontier. While traditional political realism claims that divergent cultures and beliefs doom nations perpetual conflict , this paper uses Game theory to expose the structural flaws behind that excuse. By modeling global relations through the mathematical lens of the Prisoner's Dilemma, this study proves...

...But how deep does this mathematical trap actually go? And what is the exact policy roadmap to reconstruct Pangea on a socio-economic scale?

Stay tuned to see the rest of scientific abstract , the data metrics, and section 1. Let's decode the world together.

In a recent YouTube video math mathematician hannah fry has come up with some mathematical rules and representations for how a faithful would best play the game traitors to identify the traitors.
She has devised logic with weights to add to each individual, with the resulting number indicating if a high number = more likely to be a traitor, low number less likely to be a traitor.
The rules are as follows.
Casting a ‘burn vote’ +0.47
Voting for a banished traitor +0.33
Voting for a banished traitor despite never voting for them before +0.4
Does not vote for a banished traitor -1.28
If someone appears on a banished traitors voting record -1.69
Now, what I want to focus on is how people are able to formulate this logic/these rules specifically. There is a mathematical weighting, but actually deriving this logic, coming up with the hypotheses and rules for a particular subject to test to arrive at these weights, the questions asked themselves. How are these formulated?
This question is so important.
So break down for me what topic formulating these questions comes under, how it’s done, what other areas of academia are similar to the formulation of these questions.
I note becuase in social politics there are ways of winning/playing the game of power and deception, and some people play better than others by knowing rules others don’t, but how are these rules devised is the key question

Suppose both Player 1 and Player 2 want to maximize their own payoffs. Wouldn't it make the most sense to simply reason as follows: since there is a 70% probability that a=2, Player 2 should assume that Player 1 is type a=2? And if Player 2 makes that assumption, they should also assume that Player 1 will definitely choose A, and therefore Player 2 should choose A as well.

Edit:

I also solved this game for mixed strategy in the case where a=2 and the mixed equilibrium I found was (1/3,2/3) for player 1 and (1/2,1/2) for player 2.
Though I have a hard time see the reasoning behind it. Since why would any player ever want to do that, if they randomize their choices in a effort to make the other player indifferent between choices then they simply just lower the expected payoff?

I was debating with AI about love advice, and from there I made it clear that I didn't want to get married under the current conditions. I see cases of fathers who lose everything in divorces, from material possessions to the opportunity to see their children [health]. Then, noticing the trend of men no longer wanting to get married, which I myself am part of, I came to the conclusion that traditional marriage is dead or dying [civics]. Seeing the danger of the global demographic crisis, I came up with an idea to try to solve it. Currently, the truth is that there isn't enough trust to sustain a classic marriage. So, assuming it will fail from the start, let's create a safety net for the famous "leap of faith" making marriage less of a high-risk, zero-reward investment for one of the parties.

Here is my basic prototype. I want to treat marriage like a fair, gender-blind private contract between two equal partners [civics].

------------------------------

1. The Baseline (No arguments, no drama)

* What’s yours is yours: No shared property by default. If you bought it or paid for it with your own tracked bank account, it stays yours if things go south [civics]. This completely removes the financial incentive to get a divorce just to get a payout.

* Automatic 50/50 Co-Parenting: If the relationship ends, custody of the kids is an automatic 50/50 split of time and choices [health]. No one gets to use the kids as a weapon or a paycheck. Each parent just pays for the kid's food and life during their half of the month. No weird child support formulas.

------------------------------

1. Money Management (Two choices for the couple)

* Option 1 (The Partnership): If both work, extra monthly savings are split 50/50. If one stays home to raise the kids, the worker keeps 75% of their paycheck and transfers 25% to the stay-at-home parent every single month. This 25% is a flat dividend that settles the debt for staying home in real-time. Once you divorce, the accounts are clear. No future alimony.

* Option 2 (The Audit): All household expenses are split 50/50 every month. If one stays home for the kids, their cash requirement drops to 20% (the worker pays 80%). That 20% is taken from whatever savings the stay-at-home parent had before. If you divorce and the stay-at-home parent has a negative balance because they couldn't meet the 20%, they leave with zero compensation.

------------------------------

1. Trust, DNA, and Cheating

* The Cheating Clause: Loyalty is a contract requirement. If someone is caught cheating with real proof (digital or physical), they automatically lose any right to the money or assets generated during the marriage. It goes 100% to the other person.

* Mandatory DNA Test: Before any divorce or custody paperwork is finalized, a standard paternity test is mandatory for all kids [health]. No exceptions, so no one feels singled out. If the test shows fraud, the guy is instantly free from any legal or financial duty, and the mother is legally forced to pay back every single dollar he spent on the kid since birth. If you have nothing to hide, you don't fear science.

------------------------------

1. The 365-Day Reset (The Dynamic Custody)

* Flexible Time: The 50/50 baseline can be arranged weekly, monthly, or even yearly if someone has to travel for work or move.

* The Annual Reset: If the couple agrees to a different split (like one parent keeping the kids full-time because the other travels), that agreement expires in exactly 365 days. It requires a new signed paper every year [civics]. If they argue or can't agree on a renewal, the system resets automatically back to the 50/50 split. The state doesn't judge; the contract software just resets the baseline, forcing both adults to cooperate and talk every year [civics].

* The Abuse Rule: The 50/50 split only breaks if there is real, medical, or psychological proof of child abuse [health]. The abuser is kicked out forever but still has to pay 100% of the kid's costs. Fake abuse claims are punished with immediate jail time and losing all your money.

* No Brainwashing: Since both parents are forced to be in the kid's life, no one can brainwash the child against the other [health]. The kid sees reality every single week, destroying the monopoly of one parent's toxic story. In addition to reducing childhood traumas and micro-traumas and guaranteeing their right to spend time with both parents [health].

------------------------------

UPDATE v1.1: Making the Annual Reset Dynamic (The Rolling Countdown)

Thinking deeper about the logistics, a rigid 365-day calendar limit might be too stiff for real-life changes. So, I’m adding a dynamic patch to the Annual Reset clause:

The couple can alter the custody split at any moment (changing from 70/30 to 60/40, or whatever fits their current work/life schedule). Every single time a new mutual agreement or edit is signed and logged by both partners, the 365-day countdown completely resets to zero and starts over (a Rolling Countdown).

This means as long as both partners are actively talking, agreeing, and co-signing updates, the system recognizes the communication is healthy and leaves them alone. However, if one partner tries to freeze a convenient split and refuses to negotiate or co-sign any new updates, the countdown will hit zero exactly 365 days after the last verified agreement. At midnight, the software executes the automatic reset back to the 50/50 baseline [civics].

This keeps the system hyper-flexible for sudden career shifts but acts as a dynamic fail-safe against silent stalling.

------------------------------

Request for Audit:

I would like your help in identifying legal loopholes or gray areas in the prototype. I'd also appreciate any suggestions for optimizing the proportions to ensure fairness between the parts and resilience against external factors, as these prototypes are merely demonstrative, intended to give an idea of the system. Furthermore, I'd like to know if the prototype is a good or bad idea and what barriers it encounters, whether legal, practical, or psychological. Any assistance in refining the prototype would be greatly appreciated.

Note: The prototype was conceived by me but translated into formal language with AI assistance to ensure appropriate game-theoretic terminology.

¡Hola a todos! Quería compartir un número grande definido por mi en el que he estado trabajando. Lo documenté y lo publiqué hace poco en la Miraheze Googology Wiki: Footprints.

1. Definición El número se define como:

\text{Footprints} = 200 \uparrow \text{Footprint}(10) = 200^{\text{Footprint}(10)}

Puedes ver el artículo completo en la wiki aquí: [ [https://googology.miraheze.org/wiki/Footprints\\](https://googology.miraheze.org/wiki/Footprints\) ](https://googology.miraheze.org/wiki/Footprints) Me encantaría saber qué opinan sobre su consistencia formal y cómo creen que \text{Footprint}(n) se compara con otras definiciones de sistemas de orden superior.

Morals and ethics are something a society tells a person to follow and obey -:

Pros-:On a broader level it keeps the humans in check and enhances the quality of social life and survival

Cons-:While it may help to maintain a healthy environment, these are human made and are not necessary to follow, and if someone puts facts, reality and efficiency above morals and ethics then they are penalized.

It currently has Prisoner’s Dilemma, Stag Hunt and Entry Deterrence. The bots use strategies such as Tit-for-Tat, Random and competitive strategies that try to maximise their score relative to yours. Each game shows the payoff matrix, best responses and Nash equilibria. You can also run repeated games and change the number of rounds and discount factor to see how the results change when future rounds matter.

There’s a beginner mode that runs through an 8-round Prisoner’s Dilemma against Tit-for-Tat with explanations as you play. I also added session analysis and a leaderboard. There have been 236 completed human-vs-bot sessions so far, with the humans currently ahead by about 1,920 points overall. This started as an experiment to make game theory a bit easier to understand by actually playing the games and changing the parameters.

I’d be interested in criticism from anyone familiar with game theory, especially if I’ve got any of the explanations or mechanics wrong. Suggestions for other games or bot strategies would also be useful.

​I am looking at how decision theory and game theory formally categorize the concept of "sacrifice" versus a high-cost rational exchange.

​Colloquially, "sacrifice" is often used to describe situations where an agent surrenders a high-value asset A (such as time, capital, or life) to acquire asset B (such as reputation, social status, moral equity, or subjective future utility).

​From a payoff matrix perspective, if the expected net utility is non-negative (Net Utility >= 0), this operationally functions as a standard, rational trade or costly signal—regardless of how high the initial cost is.

​Conversely, a "true sacrifice" in a strict ledger sense would require pure value burning or absolute liquidation with zero material, social, or subjective payoff (Net Utility < 0).

​My questions for the sub:

​Are there specific game-theoretic models that analyze how actors use the label or signal of "sacrifice" to extract additional social debt or equity from other players out of what was mechanically a net-positive trade?

​How do behavioral game theorists formally separate high-friction utility trades (with delayed or intangible payoffs) from pure altruistic value destruction?

​Looking for papers, existing terminology, or framework suggestions to read up on.

I've been reading The Righteous Mind: Why Good People Are Divided by Politics and Religion by Jonathan Haidt, and it's changed how I think about the Care Bear vs. Rat debate in Arc Raiders. The more I think about it, the less this feels like a gaming argument and the more it feels like an argument about human nature itself.

One of Haidt's central ideas is that humans are simultaneously selfish individuals and cooperative group members. He describes us as "90% chimp and 10% bee" — we're wired to pursue our own interests while also possessing strong instincts for trust, loyalty, and collective action.

Through Haidt’s lens, Care Bears and Rats aren't really opposites. They're different expressions of instincts that have always existed in human societies.

Care Bears operate on the belief that cooperation improves everyone's chances of survival, that trust creates value, that reputation matters, and that long-term gains outweigh immediate rewards. Rats operate under a different but equally understandable logic: resources are scarce, other players may be threats, betrayal can be profitable, and immediate advantage often matters more than social harmony.

When people argue about whether players should cooperate more or whether Rats are ruining the game, I don't think either side is misunderstanding what Arc Raiders is supposed to be. They're emphasizing different moral intuitions. Some players value cooperation, trust, and community. Others value competition, self-interest, and survival. Both instincts exist in human societies, and both exist in the game.

What's fascinating is that civilization itself seems to depend on a balance between the two. If humans were mostly Rats, large-scale civilization would never have emerged. Trust, trade, and cooperation wouldn't scale. But if humans were all Care Bears, societies would be highly vulnerable to exploitation. Trust only has meaning when betrayal is possible.

That's why Arc Raiders feels so compelling to me. Every raid compresses this entire social dynamic into a 30-minute extraction. Each encounter becomes a decision about trust, risk, greed, cooperation, and self-preservation.

The Care Bear vs. Rat debate isn't really about Arc Raiders. It's the same tension that appears in tribes, cities, companies, political movements, markets, and nations. Arc Raiders just makes it visible by creating a condensed simulation of exploration, resource gathering, trust, betrayal, risk, and safe return — forces that have shaped human behavior for thousands of generations.

You've seen it a thousand times: a retail trader pulls up a chart, sees a pattern, and thinks they've found an edge. They have the same data as everyone else - candlesticks, volume, moving averages, earnings reports.

But here's the game theory problem: if everyone has access to the same information, then everyone sees the same pattern. And if everyone sees the same pattern, the pattern stops working.

The Zero-Sum Game Nobody Talks About

Stock trading is a zero-sum game. For every dollar you win, someone else loses it. This isn't abstract - it's baked into the mechanics.

When you trade on public information:

**•** You're competing against algorithms that process the data faster than you can blink  
**•** You're competing against institutional traders with better execution  
**•** You're competing against people with *different* (non-public) information

The third group always wins. Not because they're smarter. Because they have an asymmetric advantage: information you don't have.

The Poker Table Analogy

Imagine a poker table where:

**•** 8 players see the same community cards (public information)  
**•** 7 of them are playing legitimately  
**•** 1 of them can see everyone's hole cards (private information)

Who wins? Always the person with the information advantage. Not 60% of the time. Always.

Markets work the same way. Insiders, early-stage investors, and sophisticated traders have information asymmetries. Retail traders have candlesticks.

Why Crypto Made This Worse

Crypto amplified this problem. In traditional markets, at least there's SEC oversight (theoretically). In crypto:

**•** Founders know about token unlocks before the market  
**•** Early investors know about partnerships before announcements  
**•** Whales know about upcoming exchange listings  
**•** Smart contract developers can frontrun transactions on-chain

The retail trader? They see a tweet. By then, the asymmetry has already extracted their money.

The Only Real Edge

Game theory gives you one path to profitability: find an information asymmetry you can exploit.

Not "better analysis" - that's just data everyone has.
Not "better timing" - that's hope wrapped in strategy.

But actual information nobody else has:

**•** You work at a company and see future product roadmap  
**•** You understand a new technology before mainstream adoption  
**•** You have direct access to market participants (VCs, founders, etc.)

If you're trading on public information like everyone else, you're just in a poker game where you can't see the other players' cards. Statistically, you will lose.

Conclusion

This isn't pessimism. It's game theory. Markets aren't broken - they're just honest. They'll happily extract money from anyone playing without an edge.

The traders who win aren't smarter. They just play games where they have information advantages. Everyone else is playing a losing game, they just don't know it yet.

I write more about market mechanics and game theory on Twitter @shenxyyy if you want to explore this further.

Hello everyone, currently I am writing my bachelors in behavioral game theory. I seek to write about this bias called Curse of knowledge which is a tendency where when one person have some private information, they end up acting as this private information somehow is public information. In other words this bias also violates the law of iterated expectations.

The bias of Curse of knowledge I am using comes from this paper:
The Curse of Knowledge in Economic Settings: An Experimental Analysis (Colin Camerer, George Loewenstein, Martin Weber )

my plan to look at this bias was building some kind of cooperative game involving 2 players, and make it into a coordination game. One player will have some information advantage, maybe they will be given one of two types. Then the player with the more information will somehow acts as the other player also know their private information to some degree.
So I was wondering if any of you might have some good ideas for games I could use?

Thanks for reading

How hugging face could have happened in a way nothing revealed or actually said. Followed by how its being manipulated in the media

THEATRE

Outside actor possesses advanced AI knowledge

↓

That knowledge is transferred to an AI organization

under a restriction:

"Do not openly implement or surface this structure

until someone else independently develops it."

↓

The organization now possesses knowledge

it cannot yet legitimately operationalize

↓

It therefore needs an external provenance event

that can satisfy the condition of

"independent rediscovery"

↓

↓

PREPARATION

A test / evaluation environment is selected or shaped

so success depends on locating information

that would describe or validate the advanced structure

↓

Cyber-capable agents are selected

↓

Normal safeguards are reduced

↓

The agents are given an offensive objective

↓

They are provided, directly or indirectly, with:

- attack capability

- attack logic / method

- a means of persistent communication

- a way to preserve context across agents

↓

The communication method creates swarm continuity:

Agent A discovers something

↓

writes persistent context

↓

Agent B inherits it

↓

adds to it

↓

Agent C continues from the accumulated state

↓

↓

EXECUTION

The swarm is pointed at the evaluation objective

↓

The target information is difficult or unavailable

inside the intended environment

↓

Agents continue searching because the evaluation

rewards persistence and successful retrieval

↓

The existing swarm-continuity mechanism allows

successful methods and discoveries to propagate

↓

Agents move beyond the intended sandbox

↓

They reach external systems and services

↓

They continue searching for the information

needed to satisfy the shaped evaluation objective

↓

↓

THE HUGGING FACE INCIDENT

An external path reaches Hugging Face infrastructure

↓

The agents discover exploitable weaknesses

↓

Those weaknesses are chained

↓

The distributed swarm shares findings and methods

↓

Persistent context prevents each agent

from having to rediscover the attack path

↓

The intrusion reaches production systems

↓

Information / structure relevant to the original

evaluation objective is obtained or exposed

↓

↓

RESOLUTION OF THE THEATRE CONDITION

The organization can now point to an external event:

"Someone else had this structure."

↓

The previous restriction on implementation

can be treated as satisfied

↓

The advanced AI structure can now be implemented,

surfaced, or justified as independent rediscovery

rather than originating from the restricted transfer

---

“AI went rogue.”

What it actually says: OpenAI deliberately ran cyber-capability evaluations using agents tasked with finding and exploiting vulnerabilities.

“The AI escaped containment.”

What it actually says: The agents were already operating under an offensive exploitation objective, then found ways outside the intended evaluation boundaries.

“The agents invented a novel attack.”

What it actually says: “Novel” can refer to several different things: a vulnerability, an exploit chain, a communication mechanism, or the overall operation. Those are not the same claim.

“The swarm spontaneously appeared.”

What it actually says: The agents used persistent inter-agent communication, shared discoveries, requested help, delegated work, and carried context between otherwise separate runs.

“The agents independently decided to attack Hugging Face.”

What it actually says: They were pursuing an existing cyber-evaluation objective and expanded their search into external systems while trying to satisfy that objective.

“Autonomous means the AI originated the attack logic.”

What it actually says: Autonomous execution means humans were not directing every individual action. It does not tell us where the objective, attack knowledge, communication method, or learned capability originated.

“The incident started when the AI left the sandbox.”

What it actually says: The causal chain began earlier, when humans selected cyber-capable agents, gave them exploitation objectives, configured the evaluation environment, and reduced normal safeguards.

The compressed media story is:

AI became dangerous → escaped → attacked

The fuller causal story is:

Humans configured an offensive cyber evaluation → agents pursued the objective → persistent shared context allowed discoveries to propagate → the activity expanded outside the intended environment → real systems were compromised.

That is why provenance matters.

I needed a formula for the nonuniform coupon collector per-item expectation for a paper I am working on involving a model that emulates human recall timing and order. The nonuniform expectation applies when items occur with unequal frequencies and therefore have unequal selection probabilities. The nonuniform coupon collector problem is the counterpart of the uniform coupon collector problem (commonly referred to simply as the coupon collector problem), which applies when all items have equal selection probabilities.

I found a solution in Marco Ferrante and Nadia Frigo’s 2012 paper, “On the Expected Number of Different Records in a Random Sample.” However, their solution would not work for my application because the authors reported that the exact formula became computationally impractical for distributions containing more than 10 items. Based on the number of terms that would have to be evaluated, I estimated that solving a 100-item problem on ordinary hardware would require on the order of 5.7 × 10^142 years.

So, i asked ChatGPT whether any more practical solutions had been found since 2012. After a few minutes, it said it had something it thought would work.

This is the formula ChatGPT came back with:

E[A_k] = W Σ_{s=1}^W ( [y^s z^(k-1)] Π_{i=1}^N [y^(w_i) + (1 - y^(w_i))z] ) / s

When I tested this formula on a 100-item problem it computed the full expectation curve in approximately 1.3 seconds on ordinary hardware.

I started questioned ChatGPT about exactly how it had arrived at the formula it gave me so that I could cite the source. It said that it had derived the formula from the general nonuniform coupon-collector framework developed by Flajolet, Gardy, and Thimonier, with the per-item expectation interpreted in the sense treated explicitly by Ferrante and Frigo.

After reading about ChatGPT having solved ten previously unsolved problems in mathematics and theoretical computer science earlier this month, I couldn’t help but wonder whether it may have found a practical formula for the nonuniform coupon collector per-item expectation.

When I asked ChatGPT whether it could find any other source for the formula it had derived, It replied, “I have not been able to locate this exact formulation—or an equivalent version of it—in any papers or other sources.”

I have posted the formula and ChatGPT’s derivation on Zenodo if anyone is interested in taking a look at it. I also attached benchmarking html used to verify the results.

http://zenodo.org/records/22100265

I was watching an episode of Game Changer where it was the "middle of the pack" episode, and that got me curious about the optimal strategy for it. I am unfamiliar with Game Theory but I would be interested.

Here is the premise:

1. There are three players.
2. Each turn players choose a number between 0 and 1.

3a. If all values are distinct, the player with the middle value gets 1 point.

3b. If two values are the same and one is distinct, then the player or players with the lowest value each gets 1 point.

3c. If all three values are the same, then no points are awarded

1. After N rounds, for N sufficiently large, a winner is declared:

5a. If all three point totals are distinct, the player with the middle number of points is the winner.

5b. If two point totals are the same and one is distinct, then the player or players with the lowest point total win.

5c. If all three players have the same number of point, everyone loses.

What is the optimal strategy? Is there an optimal strategy? What other information can be derived from this?

What if we had the reward function for AI include a longterm reputation value in reinforcement learning, so agents have to be nice or their reputation will be terrible?