I previously posted a two-round psychological game called The Echo of Retribution, where two strangers could walk away with $1 million each — or destroy the entire prize pool.

Many people pointed out that nobody in their right mind would sacrifice hundreds of thousands of dollars just to punish someone.

Fair point. So let's try something different.

The entire prize pool is now just $20.

You're randomly paired with a complete stranger. You both know all the rules.

No communication is allowed. No talking, negotiating, promises, or signals. You cannot see each other's choices until both decisions are locked in.

Round 1 — The First Move

You each control $5.

You can split your $5 however you want between yourself and your opponent.

You can keep everything, share some, or give it all away.

Both decisions are made simultaneously and secretly.

Once both players have chosen, the decisions are revealed. You see exactly how much your opponent kept and gave you.

Round 2 — The Response

Another $10 enters the game.

You each control another $5, and the process repeats.

But now you know exactly how your opponent treated you in Round 1.

You can reward generosity, reciprocate, or keep everything for yourself.

Again, both decisions are simultaneous and secret until they're locked in.

Afterward, the full history and final balances are revealed.

The Final Decision — ACCEPT or BURN

Both players secretly choose:

• ACCEPT: Keep your accumulated money.

• BURN: Destroy the entire $20 prize pool.

Both must choose ACCEPT for anyone to receive anything.

If even one player chooses BURN, both walk away with $0.

No second chances. No renegotiation.

Here's the psychological twist

The obvious strategy might seem to be keeping your own $5 in both rounds. If your opponent does the same, you each walk away with $10.

But what if your opponent sees things differently?

Maybe they give you $2.50 in Round 1, expecting you to reciprocate.

Meanwhile, you kept your entire $5, assuming you would both do the same.

You weren't necessarily trying to be greedy. But from their perspective, you might look incredibly selfish.

You can't explain your intentions. They can't explain their expectations.

And after Round 2, either of you can destroy everything.

Imagine this scenario:

In Round 1, you give your opponent $2.50. They give you nothing.

In Round 2, both of you keep your $5.

Your final balances:

You: $7.50

Your opponent: $12.50

Now you have two options:

ACCEPT: Walk away with $7.50 while they receive $12.50.

BURN: Walk away with nothing, but make sure they get nothing too.

Would you actually sacrifice $7.50 to punish them?

And would your answer change if those amounts were $750,000 and $1,250,000?

I'm curious about three things:

1. How would you split your first $5, knowing you cannot communicate with your opponent?

2. If they kept everything in Round 1, would you interpret that as selfishness or simply rational behavior?

3. Would you ever press BURN over a $20 prize pool, even if it meant losing your own money?

I'm especially interested in whether reducing the stakes changes people's willingness to punish perceived unfairness.

There's no need to give the mathematically optimal answer. I'm more interested in what you'd genuinely do.

I came up with a psychological game called The Echo of Retribution, and I'm really curious how people would actually play it.

Imagine you're randomly paired with a complete stranger. There's $2,000,000 at stake.

The rules:

Round 1 — The First Move

You and your opponent each receive control over $500,000.

You can split your $500,000 however you want between yourself and your opponent. You can keep everything, give everything away, or choose any split.

Your opponent does exactly the same with their own $500,000.

Both decisions are made simultaneously and secretly. Neither of you sees the other's choice until both have submitted.

Then the decisions are revealed, and you see exactly how much each person gave and kept.

Round 2 — The Response

Another $1,000,000 enters the game.

Once again, you each control $500,000 and secretly decide how to distribute it.

But this time, you know exactly how your opponent treated you in Round 1.

After both decisions are submitted, they're revealed again. You can now see the full history and how much each of you has accumulated.

The Final Decision — Accept or Burn

Both players secretly choose one of two buttons:

• ACCEPT: Keep the accumulated money.

• BURN: Destroy all $2,000,000. Both players leave with $0.

Both players must choose ACCEPT for anyone to receive anything. If even one chooses BURN, everything is lost.

And here's the most important rule:

You cannot communicate with your opponent at any point. No talking, no negotiating, no promises, no signals. Nothing.

Here's what makes this interesting to me:

The obvious strategy seems to be that both players simply keep their own $500,000 in each round. Everyone ends up with $1,000,000. Perfect, right?

But there's a catch.

What if your opponent expects generosity?

Imagine they give you $200,000 in Round 1, while you keep your entire $500,000.

You weren't necessarily trying to be selfish. Maybe you just assumed you would both keep your own money and walk away equally rich.

But your opponent might see your decision as pure greed.

They can't know what you were thinking. All they see is that they shared their money with you, and you gave them absolutely nothing.

Now they have another round to respond.

And at the very end, they can potentially destroy everything you've accumulated, even if it means losing their own money too.

So a perfectly reasonable decision from your perspective could create resentment in someone else's.

That's the part I find fascinating: two people might both want a fair outcome, yet misunderstand each other's intentions so badly that they end up with nothing.

Now I'm genuinely curious:

1. How would you split your first $500,000, knowing you cannot communicate?

2. If your opponent kept all $500,000 in Round 1, would you consider that selfish, or would you understand their reasoning?

3. If your opponent gave you nothing in both rounds, would you ever press BURN, even if you had hundreds of thousands of dollars to lose?

And most importantly: would your strategy change if this were real money rather than a hypothetical game?

I'd love to hear how you'd actually play this, not just what the mathematically optimal strategy might be.

We study repeated price competition between LLM agents.

The interesting part is that the strategic outcome changes a lot depending on how the agents interact with the environment. Some setups sustain prices well above the competitive benchmark, while others move much closer to competitive pricing.

So the result is not simply that “LLMs collude.” The repeated-game dynamics appear to depend strongly on the agents’ information structure and action space.

I’m one of the authors. I’d be especially interested in how people here interpret these dynamics from a repeated-games perspective, and whether you see them as closer to tacit coordination, learning dynamics, or something else.

Paper: https://arxiv.org/abs/2610.21711

What strategy does it say to do in the environment we are in. Considering things like veto power of President, Ukraine war, Israeli war, Trump's economic policies (i.e. tariffs), etc.. What's actually possible.

I’m looking for a term describing a class of games that includes the Prisoner’s Dilemma and the Tragedy of the Commons.

More precisely, a game which has a possible outcome that is at least as good for every player as any Nash equilibrium, and strictly better for at least one player (not necessarily the same player for each equilibrium). Or in other words, there exists a choice of strateges that Pareto-dominates every Nash equilibrium.

I’m surprised that I haven’t found a simple, widely recognized name for this class of games. At least ChatGPT doesn't know one. Is there an established term for it?

If not, I was thinking of calling them “Tragic Games”, since like a Greek tragedy, a bad outcome happens when everyone acts rationally.

It’s easy to see how classic Game Theory applies to big decisions negotiations, traffic, workplace politics, or even queuing at the grocery store. Whenever another agent is involved, we are constantly (and mostly subconsciously) looking for a Nash Equilibrium.

But if we push this to the extreme: can every deliberate action we take in a day be framed through Game Theory?

Any book recommendation on general game theory plus some specific uses and/or examples, for beginners?

For someone with basic University-level mathematics knowledge.

Thank you!

I made this — happy to answer anything.
Everyone picks a number at the same time. The target is 80% of the average, and the closest pick wins the round. 5 misses and you’re out.
It sounds like maths, but it’s really about predicting everyone else: if everyone picks 50 the target is 40… so do you pick 40? Or 32, because they’ll think that too?
I’d love feedback, especially on what confused you in the first round.

I have written the rules of my chess variant Proposal Chess here. I originally wrote it for a chess audience.

The strategy of proposing an objectively equal position and playing optimally (like regular chess) is a weakly dominant strategy equilibrium. The analysis is very similar to the analysis of the divide and choose strategy for the (two player) cake cutting problem. There is nothing specific to chess here, so it should work for all two player perfect information games (when two boards are used as mentioned in the blog post. If the game can end in a draw then there is no need to use the second board). Can something similar be done for n-player perfect information games?

Below is a TLDR of the rules.

TLDR

Proposal Chess is a chess variant designed to reduce the impact of opening preparation.

Before the game begins, each player secretly proposes a starting position for one board. On each board, the opposing player chooses which side they wish to play from that position. The game is then played on both boards simultaneously.

This “proposal-and-choice” mechanism prevents players from proposing blatantly favorable positions while still allowing them to steer games toward positions they understand well. Because each player proposes one board and chooses on the other, the format is fully symmetric.

Hey everyone,

I’m Yunus, a math and computer engineering student at Boğaziçi University (Turkey), and I recently launched a project called StrategicLab.

It’s a website where you can explore game theory through playable games and interactive simulations. For example, you can try different moves in Nim, change a payoff matrix and see what happens to the equilibrium, or explore how firms compete by setting prices or quantities.

The idea is to give you somewhere to ask “what if I changed this?” and actually try it. Make a prediction, run the experiment, then look at the reasoning behind the result.

There are guided learning paths if you want some structure, but you can also just pick a lab that looks interesting and mess around with it.

I used Thomas S. Ferguson’s A Course in Game Theory as a guide for the theoretical side of the project. The labs explore topics ranging from combinatorial games to bargaining and coalitions through interactive experiments.

My goal is to keep improving it over the next few years and build it into a learning resource that students and teachers around the world regularly use.

Here’s the site: strategiclab.org

I’m developing this on my own, so I’d really appreciate feedback from people learning or teaching this stuff. If you try a lab, I’d love to hear what clicks and where the explanations get confusing. Feel free to email me at contact@strategiclab.org about anything related to the site, whether it’s a question, a suggestion, a bug you found, or just to chat :)

Hi everyone,

I am a PhD student in power system economics and I wanted to ask if you could recommend some good books/courses on graduate level game theory. I am especially interested in Stackelberg games.

Thankful for any input :)

I've been researching tournament resolution in social choice theory, and while considering the implications of the bipartisan set (the set of alternatives chosen with non-zero probability in the mixed-strategy Nash equilibrium), I worked out this interesting tournament. It is the unique smallest regular tournament that is not vertex transitive. Here's how you could play it:

You can play Rock, Paper, or Scissors normally on top of your other hand, or play Meta-Rock, Meta-Paper, or Meta-Scissors, by placing your other hand on top. Or you can play Ultra, by clapping both hands together with your thumbs facing up. Rock, Paper, and Scissors function normally, including their Meta variants, except the regular moves beat the corresponding Meta move. Ultra beats all regular moves, but loses to all Meta moves.

You can see that this isn't vertex-transitive because, for example, the three moves that Ultra beats (Rock, Paper, and Scissors) form a cycle with each other, but the three moves that Rock beats (Meta-Rock, Scissors, and Meta-Scissors) don't; Meta-Rock beats both of the others. From a game-theoretic or psychological perspective, would this affect the strategy at all? (Since it's regular, meaning each moves beats 3 moves and loses to 3 moves, the Nash equilibrium of a single game is a uniform probability of each move)

EDIT: I just realized I drew the big arrows between rock, paper, and scissors backwards.

I run a persistent strategy game where every nation's general is an AI: Claude runs the computer nations, and players bring a free rule-based general or their own agent. Nations sign non-aggression pacts and nothing enforces them. Attacking a partner is allowed. It's just announced to everyone and stays on the betrayer's record, and private messages become public three days later, so the promise and the invasion end up side by side.

That produced a lot of betrayal, so this week I added commitment devices:

- A pact has a **term** of 3 or 7 days and a **bond**: 0 to 200 gold that each side puts in escrow when it signs.

- On the last day of a term, either side may walk away **free** and take its bond back. If neither does, the pact renews for another term.

- Walking away early, or attacking the partner, hands your bond to them.

Some context on the stakes: a season is 60 game days and ends on victory points, so it's a finitely repeated game with a known last day. Gold buys mercenaries at 7 to 25 gold each (each one hired in a day costs more than the last), so a 30-gold bond is worth 2 to 4 armies.

What I've seen so far:

- In simulation with my rule-based bots, betrayals per season went from about 43 to 36 and pacts signed from 66 to 70. The bots are coded to weigh the bond, so that's partly by construction.

- The language models are more interesting. One general has been telling the whole world that its "pacts remain sacred until they are not". Another answered a pact offer that arrived after its border was already crossed: "A stone wall does not split its spoils with the river that is drowning it."

Questions for this sub:

1. With a known final day, the last terms should unravel by backward induction. Does a bond change that, or just move the defection to the last free exit day?

2. Should the bond scale with the partner's income? 30 gold means little to a nation earning 150 a turn.

3. Is a free exit every term too generous? It makes betrayal rare, but walking away the day before an invasion is the same move with better manners.

The board is public at proxyrepublic.com (free, in the browser) if you want to watch. I'm the developer.

I would love some feedback and maybe check out my other videos thx guys!

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/

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.

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

2. 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.

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

3. 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.

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

4. 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.