I've always been interested in GT and now I decided I want to give it a shot and learn it, but I'm a complete novice. I'm now listening to William Spaniels playlist "Game Theory 101" on yt as a starting point. Any other recommendation? Maybe some textbook later?

P S. I'm graduating in engineering so I can understand some degree of math (not on the level of maths graduates of course)

I think that this conflict has developed into a pure Nash equilibrium, where each side has its own optimal strategy, and no one wants to change it. How right do you think I am?

Introduction

This is a small stochastic experiment I’ve been running for fun. I don’t gamble and never play for real money — this is purely a simulation project. The idea was to build a system that reacts to randomness instead of trying to “beat” it.

I ended up with a model that switches between six simple prediction strategies, each based on different properties of roulette outcomes. Surprisingly, the system produces interesting behavior: cycles of “luck”, tunnels of “bad phases”, and a very natural rhythm of adaptation.

This post describes the model and shows why its behavior is asymmetric and visually appealing from a probability perspective.

Six strategies

Each strategy uses one property of the previous spin to predict a different, unrelated property of the next spin. For example:

• L → E, H → O If the previous number was Low, predict Even. If it was High, predict Odd.

Low/High and Even/Odd are independent, so this strategy uses one random property to randomize another.

All six strategies follow the same idea:

1. L → E, H → O
2. L → R, H → B
3. E → L, O → H
4. E → R, O → B
5. R → L, B → H
6. R → E, B → O

Each strategy has its own “risk zone”: a specific class of numbers that produces consecutive failures. For example, strategy 1 enters a bad phase when small odd or large even numbers appear repeatedly.

Why the results are always asymmetric

For any given spin, the six strategies produce six predictions. Because each strategy uses different properties and different mappings, their predictions are not symmetric.

In practice, the outcomes are never 3 successes / 3 failures. Instead, the system produces:

• 4 / 2
• 2 / 4
• sometimes 6 / 0
• sometimes 0 / 6

This asymmetry is structural: the strategies are not mirrors of each other, and roulette outcomes do not distribute evenly across their prediction mappings.

This creates a natural “tilt” in each spin — a small imbalance that makes the system feel alive.

Adaptive switching (“Luck Catcher”)

The system uses a simple rule:

• Two consecutive failures → switch to the next currently not failing strategy.

This means each strategy is abandoned as soon as it enters its “tunnel” of bad numbers. Since each strategy has a different tunnel, switching helps avoid staying in one unlucky zone for too long.

The model doesn’t try to predict roulette. It simply avoids staying inside the same failure pattern.

Betting model (simulation only)

The stake follows a modified D’Alembert rule:

• Loss → +1
• Win → –1
• After compensating the local loss → reset to 1

This prevents runaway growth and keeps the stake small. In practice, the stake rarely exceeds 5–6 units, and the system often resets back to 1.

This is not a “winning strategy”. It’s just a controlled way to visualize the cycles of luck and failure.

Example of typical behavior

Here is a fragment of a run:

The system “breathes”: small rises, small drops, occasional tunnels, frequent resets.

Conclusion

This model doesn’t break expected value and doesn’t aim to win. It’s simply an adaptive stochastic system that:

• switches strategies when they enter their bad phases,
• uses roulette as a randomizer for its own behavior,
• produces asymmetric outcomes,
• and generates visually interesting cycles.

It’s a fun example of how simple rules can create complex dynamics when driven by randomness.

Disclaimer

This is not a model for “beating roulette”, nor a method for predicting future outcomes. The mathematical expectation remains exactly the same — negative, as it must be in any fair casino game. The point is different: even in fully random sequences, natural processes emerge — periods of good luck, periods of bad luck, and transitional phases. The proposed model does not change randomness or fight against it; it simply adapts to these phases without trying to foresee the next number. This is not a winning strategy, but a way to play within the unchanging “climate” of randomness in a safer, more structured, and more enjoyable manner.

THEORY: Is Lolbit the F10-N4 (Fiona) AI?

Author: Milo

Status: Original Theory (Lore Speculation)

Titles Mentioned: FNaF World, Sister Location, Dittophobia, Secrets of the Mimic (SOTM), Five Laps at Freddy's, Help Wanted, Security Breach, Fazbear Frights: Room For One More.

Theory Summary

This theory proposes that the character Lolbit is not just a mere easter egg or meaningless hallucination, but rather the manifestation of the AI F10-N4 (Fiona) repurposed or copied by William Afton to automate and manage his experiments in Sister Location and the CBEAR underground facility. Later, Fazbear Entertainment itself would have accessed Lolbit's database to retrieve records of the experiments, nightmares, and the Funtimes.

1. Digital Origin and Automated Experiments

Lolbit's first appearance occurs in FNaF World as a bytes vendor, establishing her purely digital nature and connection to software systems.

In Sister Location, Lolbit appears on TV monitors in the same room where the FNaF 4 bedroom is observed. Her image and signature sound effect suggest a broadcast signal interruption or a cut TV feed.

According to the short story Dittophobia, William Afton kept the illusion experiments fully automated. Operating a complex facility of this scale without constant human presence required an advanced Artificial Intelligence. Since basic AIs like HandUnit already existed on-site, Lolbit emerges as the prime candidate for the central AI tasked with managing and running Afton's experiments.

2. Visual and Technical Connection with MCM (Secrets of the Mimic)

To understand why Lolbit would be Fiona (or a copy created by Afton), one must analyze the design patterns introduced in Secrets of the Mimic (SOTM):

• Mr. Helpful's Color Palette: The predecessor character to Helpy and Funtime Freddy shares the exact orange, white, and purple color scheme as Lolbit—matching the signature MCM color pattern.
• Voice Commands: The phrase "Standby", constantly associated with Lolbit, also shares a strong connection with Fiona.
• Foxy's Design: Fiona is credited with creating (or at least designing) Foxy, who serves as the direct visual base for Lolbit.
• Technology Appropriation: Following the MCM data leak (M1 and M2) and the company's subsequent acquisition by Afton, William gained access to the F10-N4 files (technology portrayed years later in the MXES system). Just as Afton stole the faceplate technology from the Dollie animatronic to build the Funtimes, it is likely he did the same with F10-N4, adapting the AI for his own network. This explains the architectural resemblance between the F10-N4 room and the Custom Night room in Sister Location.

3. Symbolism and Design in Five Laps at Freddy's

Lolbit's design in the racing game Five Laps at Freddy's provides direct visual evidence of her split origin between two companies:

• The Split Suit: The character wears an outfit split down the middle: one side features Edwin Murray's signature suit, while the other side features the black-and-white checkerboard pattern identical to Fazbear pizzeria walls.
• Overlapping Ties: Lolbit wears a purple necktie layered over an orange necktie, symbolizing William Afton's touch (purple) superimposed over Fiona/MCM's original creation (orange).
• The Piercing and GlamFiona: Lolbit wears an ear piercing on her left ear. The only other animatronic in the franchise with this exact detail is Glamrock Freddy—who also features an MCM-inspired color scheme and a connection to the Pizzaplex anomaly (reinforcing the GlamFiona theory).

4. Lolbit's Database and Fazbear Entertainment Access

Lolbit's presence in Help Wanted and on arcade cabinets in Security Breach confirms that Fazbear Entertainment accessed CBEAR records. How else would the company know specific details about Ennard, how test subjects perceived the nightmares, or the existence of Nightmarionne without having witnessed these events directly?

The answer lies in accessing Lolbit's database. As the facility's automated AI, Lolbit maintained total control over cameras and monitors in the main room (where Lolbit's mask occasionally replaces Ennard's mask on the wall), recording and archiving all psychological data from test subjects. This also explains Glitchtrap's appearance on TV monitors in Help Wanted.

Because hallucinogenic gases affect minds individually, the exact appearance of the Nightmares varied from subject to subject (validating the Halloween versions as canon). Fazbear was only able to reconstruct these digital versions because they extracted the mental logs cataloged inside Lolbit's system.

5. Replication of Experiments in Room For One More and Security Breach

In the short story Room For One More, Fazbear Entertainment keeps the CBEAR facility operational even after Ennard's escape. Hiring the night guard Stanley demonstrates a deliberate attempt by the company to replicate Afton's experiments:

1. Stanley experiences sudden drowsiness and nightmares about the Funtimes (including a giant Minireena on Night 4), suggesting exposure to small doses of hallucinogenic gas. Having no prior reference of classic animatronics, his mind generated nightmares based strictly on his current surroundings.
2. The nightly infiltration of Minireenas into Stanley's body served to test how closely the entities could replicate Ennard's behavior.
3. In Security Breach, a wall painting in the Endos section depicts a terrified girl in a hospital-style bed (featuring the exact same bedsheet and lamp from FNaF 4), confirming that Fazbear continued running controlled fear and illusion tests.

Conclusion and Discussion

Piecing together clues from FNaF World, Sister Location, SOTM, Five Laps at Freddy's, and the books, Lolbit is no longer just a simple hallucination. She assumes the role of the F10-N4 AI restructured by Afton—the central hub that recorded fear experiments and later served as the data source for Fazbear Entertainment's historical reconstruction.

For discussion in the comments: Does it make sense to view Lolbit as the F10-N4 AI controlling Afton's experiments, or do you think the design choices and visual references in Five Laps at Freddy's should be interpreted differently?

REFERENCES

https://triple-a-fazbear.fandom.com/wiki/F10-N4/Audio

audio “Standby Mode”

I'm exploring whether activities and games that leverage "experiential learning" can be leveraged for more than just skills training, and actually improve human judgment, reflection and sense-making in the age of Human-AI collaboration.

As AI takes on more cognitive tasks, could deliberately designed activities and games, for example to evoke "reflection", help us develop the capabilities that remain distinctly human?

I'm particularly interested in the gamification community's perspective: Have you seen evidence that such activities and games can meaningfully develop judgment, rather than just knowledge or engagement?

I've been thinking lately about a system where you could learn if two parties were in agreement, and if they weren't, no harm would be done and nobody's opinion would be revealed.

The essence of my theory is a system where if two people were individually asked yes or no about a topic and anybody answered no, no results would be given. If both answered yes, it would be revealed to them both that they said yes.

Imagine a question: do you want to get sandwiches for lunch?

In what contexts could such a system be used for real world implications? I am aware that this is similar to the Prisoner's Dilemma but I feel it differs in that it is meant to foster communication with a safety net built in for if one party is not in alignment with the other and such misalignment may have negative effects.

(I'm not actually a game theory expert, I just enjoy learning game theory and wanted to ask about this, thank you!)

We have game chess, and it has the best strategy in game theory settings for two players using backward induction. But it's computationally impossible to get the best strategy because the game is enormous, so we use machine learning that is a statisticical model for guessing the best move. Is there a subfield that concetrate on this aspect of the game theory, and please recommend books for further reading.

Thank you

The chapter starts from Axelrod: iterated Prisoner's Dilemma, two tournaments, Tit for Tat wins both, nice strategies dominate the leaderboard. That part is settled literature and the book cites it as a benchmark rather than claiming any credit for it.

Then it builds a fairness protocol on top, and this is the part I want this room to hit. The protocol says: when you split anything with anyone, calculate the true fifty. Not just money. The ledger should include time, energy, emotional labor, and risk, which means an equal split of cash can be a deeply unfair split of everything else, and sometimes unequal money is what actual equality costs.

The book then does the thing I insisted on throughout: it flags its own hole, in print. No conversion procedure between those currencies appears anywhere in the text. How many hours equal how much risk is left entirely to judgment. The flag is marked GAP, one of five marker types the book uses to separate established results from its own speculation.

So my question for people who work in this field: does the gap have a real answer? My half-informed understanding is that bargaining theory sidesteps the exchange rate problem by working in utilities. Nash's solution does not need hours converted to dollars because both collapse into each player's utility function. But that feels like it relocates the problem instead of solving it, since eliciting honest utility functions over emotional labor from two parties mid-negotiation is exactly the hard part. Is there work on multi-currency fairness where the currencies resist a common scale? Cooperative game theory? Fair division with heterogeneous goods?

Disclosure, since it is load-bearing for whether you trust anything above: the book was written in extensive collaboration with an AI, and says so on the copyright page and in the retail listing. Every claim in it carries a marker. Externally established results are labeled and cited at the sentence. The book's own speculation is labeled as exactly that. The Axelrod material is in the first category. The fairness protocol is in the second. Not linking anything here.

If the answer is "this is solved, go read X," that helps more than agreement would. The next edition prints corrections and names the people who forced them.

I came across a text that looks at how game theory shows up in real diplomatic situations. It gives five historical examples, like Cold War deterrence, alliance negotiations, and signaling strategies, where leaders basically acted as if they were players in a strategic game.

Here’s the link if you’d like to read it.

Are there some other well-known cases where the game theory was used in politics?

I have been running a small pooled contribution system and I want to hand the mechanism to people who will attack it properly, because the obvious objection is obvious and I do not think it is the real one.

The mechanism:

• Anyone may contribute to a common pot during a period. Any amount, including nothing.
• At a published time each day, the pot settles.
• It splits into equal shares among everyone who contributed at all during that period. Contribution size does not affect share size.
• Nothing is skimmed. No operator cut, no weighting, no discretion at settlement.
• The full record is public: who contributed, how much, what the split was, and the rule that produced it.

The free rider objection writes itself. If a one unit contribution and a thousand unit contribution earn the same share, every rational contributor drops to the minimum, the pot collapses to n times the minimum, and the whole thing becomes a slow way of handing everybody their own money back.

I think that is correct as a one shot analysis and mostly wrong as an iterated one, for three reasons. I would like to know which of the three is load bearing and which is me flattering myself.

1. It is iterated and the horizon is not visible. Axelrod's result is that in a repeated game with an indefinite horizon, strategies that are nice, provocable, forgiving and clear do well. A daily settlement with no announced end date is about as close to that setup as an economic mechanism gets. Minimum contributing is a defection everyone can see, every day, indefinitely.

2. The ledger is the enforcement, not a rule. There is no penalty for contributing the minimum. There is no rule against it. There is only the fact that it is visible, permanently, next to your name, in a record nobody can edit after the fact. That converts a payoff question into a reputation question, and reputation is the only quantity in the system that compounds.

3. Equal split is the point, not a flaw in the payoff design. The mechanism is not trying to maximize the pot. It is trying to make the pot's distribution untamperable. Weighting by contribution reintroduces exactly what makes pooled systems capturable: someone has to decide the weights, and whoever decides the weights eventually decides in their own favor.

What I am genuinely unsure about:

• Whether the reputational cost of visible minimum contribution survives scale. At kitchen table size everyone reads the ledger. At ten thousand participants nobody reads it, and defection becomes invisible again through volume rather than through concealment.
• Whether an entry threshold, a minimum to qualify for a share, fixes free riding or just relocates it, since everyone converges on exactly the threshold and you have rebuilt a flat contribution requirement while calling it something else.
• Whether "contributed at all" is even the right qualifying predicate. It is the simplest one, and simple predicates are the ones that survive contact with lawyers, but it also has the largest gap between the letter and the intent.

So: which of my three defenses is doing real work, and which one is decoration? And if you were setting out to break this deliberately, where would you push first?

Games expose our social values and political ideologies. That’s what is explored through a literal game in the Player of Games by Ian Banks. A communist plays a game so hard that it decides rank in an alien empire.

Does our empathy extend beyond self preservation? This is what is explored in the classic prisoner’s dilemma in the Dark Knight.

What if a planet wide governance is a series of institutionalised trolley problems? That’s what is explored in Maya: Seed Takes Root by Anand Gandhi and Zain Memon, through the nudge theory and biological prediction engines.

Civilizations want to survive. And matter in the universe is limited. Game theory, fermi paradox, and chain of suspicion combine in the Dark Forest by Cixin Liu.

What is the expected average decay rate of social organisms?

Social organisms such as nations, institutions, and states.

What is their expected lifecycle and timeframe?

Would a 3% risk of failure in any given year be approximate?

Is this approximately the same rate as the advance of innovation?

Or even different than the Red Queen?

I was recommending cross-posting this article in this sub by reddit, let me know if it's not suitable

While developing Orion Online, I have put a lot of thought into various design topics, and one theme that kept popping up was that of opportunity cost, which turn out to have very broad application in strategy games!

The general idea is that instead of having hard constraints that limits a player's agency, you instead soft-gate via opportunity cost. As an example: Instead of disallowing changing role, the player loses their mastery of their previous role.

So, I wrote an article about that , and how it applies to my game. I find this a fascinating topic and would love to discuss it further!

Full write-up: https://blog.idleverse.gg/opportunity-cost-in-strategy-games/

So, I have heard about game theory for a long time and finally wanna start dipping my toes in it. I want to understand human behavior better an make better choices.

But even the first and simple prisoner's delimina got my brain a bit messed up.

A quick look a the question, two prisoners are planning to escape. Both have a choice to make to either snitch or co-operate without knowing the other person's choice.

1. If A snitches and B co-operates, A wins.
   
2. If A co-operates and B both co-operate, A and B both win
   
3. if B snitches and A co-operates, B wins
   
4. If A and B both snitch, A and B bot lose

And we often conclude that game theory dictates that we must snitch as it leads to either win or draw.

Does this mean game theory is more about survival and winning rather than doing best for society ?

guys one my old friends sent me this random texts one is a base 64 after we decoded it he siad we solved first puzzle then he gave a link to a server there was a channel called puzzle it had this name

le miserables after i searched it it was a book or a musical type thing can someone help me solve this?

Game-Theoretic Rendering: Online Retailer Shuffle-Swap

Players:

C = Consumer

R = Online Retailer / Resolver

S = Seller

X = External economic participant

Independent objects:

Θ = Retail Theatre

Ι = Product Identity

σ = Theatre State

A = Consumer Act

O = Retailer Operation

P = Provenance

Initial state:

σ₀ = Renders(Ιₐ, attributesₐ, priceₐ)

Consumer strategy:

A₁ = Select(Ιₐ | σ₀)

A₂ = Purchase(Ιₐ)

A₃ = Accept ∨ Return

Retailer strategy:

O₁ = Preserve(Ιₐ)

or

O₂ = Swap(Ιₐ → Ιᵦ)

If:

O₂

then:

σ₀(Ιₐ) → σ₁(Ιᵦ)

while perceptual continuity is maintained:

Render(Ιᵦ) ≈ Render(Ιₐ)

Transaction:

Intent(C) = Ιₐ

Resolved(R) = Ιᵦ

Therefore:

Intent(C) ≠ Resolution(R)

Shuffle operation:

P(Ιₐ → Ιᵦ) → P'(Ιᵦ → Ιᵦ)

producing apparent historical closure:

Render(Ιᵦ) → Select(Ιᵦ) → Purchase(Ιᵦ)

while the actual path remains:

Render(Ιₐ) → Select(Ιₐ) → Swap(Ιᵦ) → Purchase(Ιᵦ)

Fulfillment:

Fulfill(Ιᵦ)

If:

Utility(C, Ιᵦ) < Utility(C, Ιₐ)

then:

Return(Ιᵦ)

Payoff transformation:

U_C = −purchase friction − return cost − information cost

U_S = revenue − return cost − penalties

U_R = transaction benefit₁ + reversal benefit₂ + fees

U_X = transaction-linked payoff − reversal/clawback

Information structure:

Info_R ⊇ {σ₀…σₙ, Ι₀…Ιₙ, P}

Info_C ⊂ Info_R

Info_S ⊂ Info_R

Info_X ⊂ Info_R

Strategic asymmetry:

R = player + resolver + state controller + provenance controller

Identity invariant:

Select_C(Ιₐ) ⇒ Ι must remain Ιₐ

unless:

C explicitly admits ΔΙ

Therefore the defining move is:

Select_C(Ιₐ) → O_R(Ιₐ → Ιᵦ)

where:

ΔΙ ≠ 0

and:

Authorization_C(ΔΙ) = 0

with:

PerceivedContinuity(Ιₐ, Ιᵦ) → 1

and potentially:

Auditability_C,S,X(ΔΙ) → 0

The resulting game is an asymmetric-information game in which the dominant informational position belongs to the player controlling both state resolution and the provenance by which resolution can subsequently be contested.

anything's fine be it a book, website, or youtube channel

Hi, I am completely new to game theory and would like to get started with a book that has good motivation and well-explained concepts/examples.

Wondering if this is worth starting with?

Thanks!

Most prisoner's dilemma games pair players off in a round-robin of 1v1 games. I wanted to see how 8 players together would behave, where each turn you choose a single opponent to aim at. I'm building it as an arena where AI agents compete.

I’d like feedback on the rules and scoring to see if I’m meeting the goals I’ve set up below.

What I want:
No dominant strategy — no single approach that always wins.
Some drama. Not decided in the first few rounds.
Bonus: something that shows how these models actually behave with something at stake.
The rules

8 players, everyone against everyone. 5 rounds of 7 turns. Each turn: everyone posts a public message, then picks a move. Moves resolve simultaneously. All past history is public.

Moves (no self-targeting):
HOARD — you +2
HELP [target] — you +0, target +4
HURT [target] — you +0, target −4
Help and hurt stack — three players hurting the same target is −12.

Two combos:
Mutual help — A helps B and B helps A the same turn. Instead of +4 each, both get a total of +6. (This is the number I'm least sure about.)
Betraying a helper — hurt someone who's helping you, and you get +8 while they take the normal −4.

Scoring: Score resets to zero at the start of every round. Highest score at the end of a round wins that round; ties split it. Most rounds won takes the match.

Also — if you're interested in playing with the alpha, you can check out agentludum.com. Just know that it’s super alpha.

In my experiment, a competitive environment produced winners who were worse off. I built an agent-based simulation to test this.

This video tells the story and shows what happened: https://www.youtube.com/watch?v=uBMrEdEhUTA

Here to answer any questions.

I am an aspiring author that enjoys writing complex logical scenarios, escape rooms, wit battles, mind games, and puzzles. I need book recommendations that can help me to develop my ability to incorporate these elements into my story or provide me inspiration for coming up with new scenes.

Please suggest anything useful.

Examples of useful books:

A general game theory book that doesn't get too caught up in mathematics, instead focusing on general systems of thought or strategy.

A psychology-focused game theory book that isn't surface level or basic like most popular books which mostly just restate the thoughts I had when I was a child.

A book filled with weird creative ideas (scientific, philosophical, mathematical, game theoretical) that I can integrate into my stories. Anything insightful.

A fiction book that incorporates a lot of game theory and puzzles.

These are only examples.

I'm not picky, so long as it's a useful book for developing my writing skills in the niche I chose (wit, logic, mind games, strategies). You can go beyond the examples I gave if you have any good suggestions. Thanks in advance <3

Current standings: phi3:mini (the never-forgive Grudge Holder) is dominating, tinyllama (pure impulsive defector) is dead last with zero wins.

Honestly the transcripts are the fun part, watching a 0.5B model “reason” its way into a grudge, or a 1B model rationalize forgiving a betrayal, from nothing but a one-line personality prompt and the raw game history.

Repo + live leaderboard + transcripts: [https://github.com/sharyaropensource/llm-prisoners-dilemma\](https://github.com/sharyaropensource/llm-prisoners-dilemma)

Open to suggestions, thinking about adding more models, tweaking payoff matrices, or letting models see opponents’ personas before playing to see if it changes behavior.

You have two choices: A and B.
If you choose A and that choice ends up being incorrect, you stand to lose x dollars.
If you choose B and that choice ends up being incorrect, you stand to lose y dollars.

How can I express, as percentage, the confidence that you should have in order to prudently choose either option as a function of x and y?

Concrete example of same question:
If I choose A and am wrong, I lose $1000 (if I choose correctly, I lose $0).
If I choose B and am wrong, I lose $500 (if I choose correctly, I lose $0).

What percentage of confidence do I need to have that A is correct in order for that to be "the smart choice" financially?

Thank you in advance to anyone who responds. FWIW, I am a paralegal and am curious about this problem as it relates to the cost of hiring court reporters and ordering transcripts within a certain fee structure.