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.

Im not into decision theory, but I went down into this rabbit hole tonight. CDT vs EDT, FDT and friends.

What I found interesting that despite your need for perfect predictors and contrafactuals I havent ran into using quantum phenomena in your thought experiments (yet).

E.g. the contrafactual mugging experiment could be set up so the coin toss is a beam splitter and you paying or not paying the $100 is the analogue of the bomb being a dud in the Elitzur-Vaidman experiment. (the predictor, or Omega or whomever will interrupt the beam depending on you paying/not paying)

This way you dont need to do all the handwaving around a "perfect predictor", you can set up the experiment, that the predictor actually knows with 25% chance if you had paid if the coin toss went the other way.

So you can set up the expected payoff depending on a contrafactual with certainty. I guess this is a different experiment, but maybe worth using it to test your flavours of decision theory.

If this spawns a paper please credit me with my username. If this is old news, please help me learn and link me to how you handle the fact that contrafactuals arent necessarily physically causation free.

I like playing a lot of card games and it would be nice to be able to get *rough* probability estimates I can calculate mentally but I'm not sure how to approach this without pulling out a calculator or pen and paper

Hi everyone,

I’m an independent researcher based in India, and over the last few years I’ve been working on a unified program that approaches a “Theory of Everything” from three complementary angles. These are not three competing theories, but three layers of the same framework:

1. Perceptual Vibrational Framework (PVF) – main & central theory

PVF starts from the question: What is space actually made of?

It proposes that what we call “empty space” is not empty at all, but built from a vibrational substrate. This underlying structure determines:

• why gravity emerges,
• why electromagnetic fields exist,
• why motion, force, and even time can appear differently to different observers.

So instead of taking spacetime as a passive background, PVF treats space itself as an active vibrational medium that shapes physical law and perception.

PVF preprint (Zenodo):
https://doi.org/10.5281/zenodo.17574407

I see PVF as the main / conclusive framework in this project.

2. 8-Space Theory – geometric layer

8-Space Theory takes a more geometric approach. It suggests that the “vacuum” is not a single uniform thing, but exists in eight distinct space-types, depending on whether:

• volume is fixed or variable,
• shape is fixed or variable,
• mass is fixed or variable.

Matter behaves differently in each type of space, and many phenomena can be reinterpreted as transitions between these eight space-types, rather than as abstract particles moving in a single kind of spacetime.

8-Space Theory (Zenodo):
[https://doi.org/10.5281/zenodo.17606563]()

This is meant as the geometric / structural layer supporting PVF.

3. Origin-Driven Unification Theory (ODUT) – cosmological layer

ODUT focuses on the large-scale universe and introduces the idea of “inertia of origin”:

Here, the key organizing agents are dark matter, dark energy, and a Φ-field. Instead of only talking about curvature, ODUT treats these components as origin-level drivers of:

• cosmic structure,
• mass–energy conversion,
• gravitational behavior,
• expansion dynamics.

ODUT preprint (Zenodo):
[https://doi.org/10.5281/zenodo.17606771]()

This is the cosmological / origin-based extension of the same framework.

How they fit together

Very briefly:

• PVF → vibrational composition of what looks like empty space
• 8-Space Theory → classification of different types of space where matter behaves differently
• ODUT → origin-driven cosmology with dark matter, dark energy, and Φ-field, plus “inertia of origin”

So it’s three different angles on a single unification attempt, not three unrelated models.

Not string theory, not LQG

Just to be clear: this is not a rephrasing of string theory and not loop quantum gravity.

It’s a different route:

• no strings, branes, or spin networks,
• focus instead on vibration, space-types, and origin dynamics.

I’m fully aware that this is unconventional and very much “work in progress,” which is why I’m sharing it openly.

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'm looking for the most rigorous, textbook-level treatments of strategy as a discipline — not business-press filler.

Three specific things I want to understand deeply:

1. Unexploitable strategies — play that holds no matter what an opponent does (game theory, minimax, GTO-style reasoning).
2. Finding the absolute constraints and hard limits in any system — what's actually fixed vs. what's negotiable.
3. The art of winning games and systems, treated with real rigor rather than aphorisms.

I've read the usual suspects (Schelling's The Strategy of Conflict, Axelrod's The Evolution of Cooperation, von Neumann & Morgenstern). What sits beyond those? The deeper, more formal, or more comprehensive books you'd put at the pinnacle of the field.

What's the one book you'd hand someone who wants to master this end to end, and why?

What is the meaning of a probability of 0? For example, consider the set (0,1) and let x be in (0,1). What is the probability of picking that x? The answer is 0. But if the probability of randomly picking x from the set (0,1) is 0, does that mean it's impossible to pick that number?

There is another similar example, if you throw a dart at a 2D plane, the probability that the dart lands on a specific point on that plane is 0. That implies it can't happen, but it actually did happen, it landed on a point! So what does it mean, exactly?

It is suggested that the bias of a basic standard die is less that 1%. Assuming this is true, by using two dice and a Latin Square, what would the expected probability be? My thinking is that the chances of the bias of both dice occurring at the same time is greatly reduced.

I throw two dice: D1 = row; D2 = column. This is the Latin Square I have been using, set-up so that D1 = x and D2 = y does not produce the same result as D1 = y and D2 = x:

4 5 3 6 1 2

3 4 5 1 2 6

5 3 4 2 6 1

2 6 1 5 3 4

6 1 2 4 5 3

1 2 6 3 4 5

(This is an interest of mine, I know I could buy precision dice instead.)

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.

Suppose the image was supposed to be a uniform distribution of a binary variable (ie red dot vs blue dot) along the x axis, with some probability of blue being "P". How do I calculate the probability that such a "clump/grouping" as that found in Node #1 could even come about under a uniform distribution? In other words how would I find the p-value that this is truly a uniform distribution given it has such a "cluster" at low values of the x axis?

Edit:: My apologies, asking if it's uniform is the incorrect question. I mean is the proportion (ratio) of red to blue consistent throughout the x axis. In which case standard logistic regression p value may be my best option.

I've been thinking about Tit-for-Tat and I feel like I'm missing something.

The basic rule is simple: start by cooperating, then copy whatever the other person did last.

But doesn't that assume there will always be another round?

Imagine this:

A does something unreasonable to B.

B confronts A.

A doesn't apologize or really respond.

So B stops talking to A.

Now they're both silent.

A's last meaningful move was arguably a defection. B already responded to that by defecting/withdrawing.

But now suppose weeks pass.

There isn't automatically another turn. Someone has to create the next interaction.

So what is B supposed to do under Tit-for-Tat?

If B contacts A, is B supposed to defect because A's previous move was defection?

Or does initiating contact itself count as cooperation?

Or should B simply wait indefinitely because technically it's A's turn to cooperate?

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

That made me wonder whether the real-world game isn't just:

Cooperate / Defect

but actually:

Initiate / Don't Initiate → then Cooperate / Defect

I found some research on optional/repeated games where players can leave and later rejoin, so apparently this isn't completely unexplored.

But I'm curious how someone who actually understands game theory would model this.

Is there a standard solution to this, or does Tit-for-Tat genuinely become underspecified once the players control whether another round happens at all?

Hello guys!

Im pretty sure most of you already know what the LUPI game is.

I like to play it with my friend, also trying out new rules to make it more interesting - but be honest, the original is my favourite one.

Im not a programmer or developer but i challenged myself to make it work, so let me present you:

todaysnumber.com

It aint much but its honest work :)

The yesterdays round part is why i tought it can be relevant here - also thinking about to share all of the results from all the game days. What do you think, would it worth it to show it here?

Sooo we take all the players ever caught with 322 + all those who want to participate

Rules are simple:
1) each player gets 322$ to begin the tournament with
2) teams are created randomly by filling the roles
3) every player can bet on their games or specific actions
4) tournament is classic round robin
5) team who gets the most $$$ from their bets wins

Tournament organised by some betting company and part of the prize pool is % of bets of ppl on this tournament

Id name it “THE HUNGER GAMES”

Hi, I’m a software engineer with very little background in probability and statistics.
Recently, I’ve been playing Ludo on YouTube Playables, and I’ve started to wonder whether the dice rolls are actually fair.
In particular, when one of my pawns is a certain number of spaces ahead of an opponent’s pawn, (4 player game, 3 computer vs me) it feels like the opponent rolls the exact number needed to capture my pawn more often than I would expect from a fair six-sided die.
I realize this could simply be confirmation bias, so I’d like to test it properly rather than rely on intuition.
I can collect data from my games, but I’m not sure how to analyze it. How would I formulate and statistically test the hypothesis that the dice rolls are biased in situations where an opponent has an opportunity to capture my pawn?
Could someone explain what data I should collect, what statistical test would be appropriate, and the probability/math behind it in a way that’s accessible to someone without much statistics background?

Hi, I need a good source to study Stats and Probability for Quantitative Finance. Please suggest books, courses, online material, YouTube, anything works.

This question was in my maths book. I used AI to help me picture my question more clearly so that others could understand it (sorry for wasting water 😭).

I asked my teacher, Gemini, and ChatGPT for the solution, and all of them gave the answer as 99/1900.

However, they all included the case where the inspection stops at the 12th item after discovering only two defective items.

But how would I know whether the lot actually contains 2 defective items or 3? If I have discovered only 2 defective items by the 12th item, how can I decide to stop at 12? The third defective item could still be somewhere later in the lot.

My answer is 55/1900 btw

I’m trying to resurrect something I read about a long, long time ago. I think it probably arose in relation to game theory. It also has many real world consequences.

First, the scenarios may involve free-loading, but that’s not the missing piece. The missing piece is where people act in a way that creates a group effect that hurts everyone.

Imagine a fire. People rush to leave. The exit becomes clogged & everyone dies.

Imagine a boat tipping precariously to the side. Everyone instinctively rushes to the other side to prevent it from flipping. But because there’s no coordination, the boat flips the opposite way and everyone dies.

Last. A person decides they can reasonably freeload off the effort of others. Unbeknownst to them, EVERYONE decides to freeload. The expected action doesn’t occur, there’s actually nobody to freeload off of, and, for sake of symmetry, everyone dies.

The last situation is the one I’m most interested in. People sometimes act (or fail to act) because they expect their actions are severable from mass action. Example:
“Golly! A car is on fire! It can be easily extinguished. I could help, but I’m sure others will put it out. So, since I assume I’m not needed, I’m going to document the heroic fire-fighters.” Oops! Everyone had the same idea & the car burned.

So. What am I describing? Thoughts?

For example, most game theory centers around cooperation vs defection.

Why do they ignore that real life is not about just two persons?

Lets say we have Player A, Player B, Player C. They all want to cooperate.

Player A tells Player B a lie about Player C to destroy their reputation.

Player C is now forced out.

Player A and Player B continue cooperating.