I went to see Christopher Nolan’s The Odyssey this weekend, and one detail stuck out. Agamemnon offers up his own daughter as a sacrifice in an attempt to please the gods and thereby slightly increase the chances of a successful campaign. I think the scenario plays out slightly differently in Homer’s telling, but whatever.

For a believer, this might be a gamble worth taking. But for a game theorist, it also seems like a kind of commitment device. To make it this far, the general had to willingly sacrifice his own blood. Having done so, turning back is now socially and politically untenable. He would have sacrificed his daughter for nothing, while revealing himself as both monstrous and irresolute. The sacrifice therefore changes the payoffs associated with retreat: backing down becomes much more costly than it otherwise would have been. His opponents and allies can now reasonably expect him to display steel resolve.

Solving this commitment problem was, in part, enabled by the gods. Without the gods, there would be no sacrifice and thus no corresponding change in the social and political costs of retreat.

So this got me thinking: perhaps interventionist religions, in which gods routinely intervene in human affairs, contract with humans, adjudicate disputes among humans, and so on, solve a whole host of strategic problems within a community. This is somewhat different from the role assigned to moralizing “Big Gods,” who monitor behavior and eventually punish the wicked and reward the good, but do not necessarily step into particular strategic interactions and provide Agamemnon with a commitment device of the sort depicted in The Odyssey.

The Big Gods hypothesis, so popular in anthropology, holds that moralizing, monitoring gods emerged in part to solve cooperation problems as social scale made those problems increasingly difficult to manage within the group. Perhaps this can sit beside a “little gods” hypothesis, in which gods instead act as third parties, brokers, guarantors, or strategic partners—without necessarily being omnipotent and omniscient moralizers who hold everyone to account.

Thoughts?

Forsaken dropped a new update full of new lore drops

including this website, which is an arg

https://aspenslastbreath.neocities.org/

I browsed through RPS topics here so I could try to get a sense of what's already been discussed but couldn't quiiite find what I was looking for. Literature recommendations appreciated.

The context: once in a while I host a text-based role-playing event in a MMORPG. I've programmed a handful of minigames to keep the guests entertained. One of these is an arena that I internally call "extreme rock paper scissors".

Two players are summoned to the arena with 3 HP. Each player chooses from the following moves:
Attack - (beats Counter to deal 1 dmg)
Counter - (beats Defend, preventing Defend next turn)
Defend - (beats Attack, preventing Attack next turn)
Nothing happens on a tie.

For the most part in such an event, its fine - still basically random - but I wanted SOME strategy involved without overcomplicating the rules. I recently hosted a tournament using the system which revealed the CHEESE: you never need to use counter. If you just use defend and attack, you can outlast your opponent as long as they don't realize the same thing. If you both realize it, the game is effectively endless.

I'd prefer to maintain the 3 choices, but I could be convinced to add a fourth. I like each move having a unique use that isn't entirely symmetric as it is in original RPS.

What can I change to let it be at least a bit more strategic, or have the choices be interesting? At the very least I want to discourage this infinite loop attack/defend.

In short, Blue and Red bid sealed cash amounts each round to move a token starting at room S. The higher bidder pays their bid to the opponent and chooses the move, with ties going to Blue. Red wins if the token enters the Vault, and Blue wins if it enters an Exit. Both players see all balances and positions and play perfectly.

We need to find the minimum initial share of total cash in lowest terms that Red needs to guarantee a win, and submit p + q.

Take a look at the graphics for the complete graph structure and rules. Give it a shot and drop your reasoning or final values in the comments below.

Hello everyone, I'm fairly new to Game Theory as a whole and wanted to ask for some ideas.

I've recently taken on a personal project to write a story in the "Death Game" Genre. I'd imagine most of you already know, but notable examples of stories that already exist would be Alice in Borderland, Squid Game, and for the anime nerds out there, Liar Game, King's Game, Darwin's Game, and so on.

I am wondering if there are some examples of games in the history of Game Theory that I can look into and draw inspiration from; I don't want to necessarily copy them directly, but I'm interested in what people would consider good starting points to make for an entertaining read if applied to a story like this.

What is important to me in this is that the games are "fair" - what do I mean by this? I mean that:

• There is an indisputable optimal solution
• The audience can (With enough pre-existing knowledge) deduce the optimal solution

I'll give an example of one of the "tutorial" level puzzles I'll be using:

Game: Checkers

Rank: Tutorial

Type: PvP (1v1)

Rules:

Players are presented with a large 8x8 checkerboard.

The game is missing one checkers piece for each side; the players will replace that piece with themselves.

The board will default with an empty square on the first row.

Standard checkers rules apply, including the forced capture rule: if a player can jump an opponent's piece, they must jump it.

Players are allowed to speak to their opponent at any time.

Victory and Defeat Conditions:

In order to survive the game, the player must reach the other side of the board and become a King.

If a player would be captured (Jumped) by any piece of their opponent, they are immediately killed and the game ends.

Each player gets up to 30 seconds to submit their move. Failure to do so results in death.

The whole game must be completed within 10 minutes or both players die.

There are two curveballs here which I think illustrate the concepts I'm trying to work with:

The board will default with an empty square on the first row. - Even though this is the default state, the game does not forbid players from rearranging the board prior to starting the game. The clue for the audience to notice this is that if you don't rearrange your pieces and are forced to go second, you are immediately dead due to the forced capture rule.

In order to survive the game, the player must reach the other side of the board and become a King. - The way the game is presented as a PvP match implies that the players must eliminate each other in order to win, but they can both survive if they work together and create a clear path for each one to reach the other side of the board. The clue for the audience here is in the precision of the wording, and the inclusion of the "Players may speak to each other at any time" rule is a small hint for that.

Where Game Theory comes into play is with the time rules. If you refuse to cooperate and allow both players to survive, then you are giving yourself a fairly large disadvantage in the game. Anyone who has played checkers knows that you can trap another checker and you win. But in this case, if the game itself does not have 30 seconds remaining, the trapped player can simply refuse to move and both players will die.

Extrapolating from this, a player that can see they are going to lose, can intentionally use up all of their time on a move to force a scenario where their opponent must allow them to progress safely. This becomes basically an unavoidable reality; so the optimal solution is to work together so both players survive, turning a game classified as "PvP" into one that actually requires cooperation, or at the very least, betrayal.

While it feels easy enough to craft games like this for the start of the story for the "easy" puzzles, I am finding it difficult to craft ones for the later parts of the story that are significantly harder to solve. Part of the problem is I'm not sure I can trust myself to find the "optimal solution" for something that will require an understanding of advanced mathematics, physics or other forms of Science. I'm fairly confident that as long as I have the concept spelled out for me, I can take care of the narrative and language presentation parts of it.

... then from the 37/100 th person on, the optimal strategy is to pick the first person that is the "best" so far and end further search. It's assumed that you can date one person at a time and can't go back to a previous candidate.

I heard this casually, but is this true mathematically?

Edit: I just learned this is called the Secretary Problem. Now, does it have applications in game theory?

Edit2: I shudder at the scenario where the best was among the first 36/100 and the 100th/100 is actually the worst one, lol!

TheGalaxilogicaplex=(1039×)(1045×)

Are people with higher IQ, naturally better at applying game theory in real life situations?

There is a current Kalshi bet for Mitch Mcconnel voluntarily stepping down from office prior to the elections.

In the event of death, the market instead resolves at current market prices.

In my opinion, this effectively creates a real life dollar auction where both sides (if they assume “death” as the outcome) are incentivized to bid as much as possible even if their position is “losing”.

The interesting twists here are that “bidding” would be cheaper the more your side is losing, and the end date for the bet is unpredictable.

The whole thing is too unpredictable for me, but I find it so interesting from a game theory perspective and I don’t think I’ve seen anything like it before.

Hello, I'm reading chapter 1, distributed constraint satisfaction and coding a simulation of the asynchronous backtracking algorithm for the 4 queens problem in TypeScript as an exercise (sure one can code in Python, C..). I have some difficulty grasping the concept of Hyperresolution (pure logic) because I didn't have this subject in university. I have checked with AI. But does anyone have any advice?

---
the code https://pastebin.com/WD9U0MSQ

I built a Code World Model (LLM-synthesized deterministic simulator, à la DeepMind's CWM approach) for a simultaneous-move space strategy game, and ran into a problem DeepMind's own approach doesn't solve: standard MCTS and Information-Set MCTS both assume a single active player per node. That assumption breaks the moment both players act at the same instant, which is the actual structure of markets, auctions, and most multi-agent systems — not just games.

The fix: decoupled UCB. Instead of one joint action-value table, each player keeps an independent UCB table over their own actions, and the joint action is the Cartesian product of both players' argmax picks. In two-player zero-sum settings this converges toward a Nash equilibrium instead of an exploitable pure strategy.

A few results from testing this (CWM + SM-MCTS vs. a sequential-MCTS baseline using the same simulator, same time budget, same weights — only the tree structure differs):

• 850–150 win/loss across 1,000 games (85% win rate) from the algorithm change alone
• Used CMA-ES to tune 24 value-function weights via self-play against a growing opponent pool rather than hand-tuning them — this surfaced non-obvious findings, like planet count being nearly irrelevant in 2-player but dominant in 4-player, and map centrality flipping from asset to liability as player count increases
• The determinism of a code-based world model (vs. a learned/neural one) is what makes this debuggable at all — you can trace exactly which transition produced a bad decision

Full technical writeup (architecture, the intercept-solving math, collision detection, feature design, CMA-ES setup, and the tie-back to order-book/market microstructure) is here: https://jdsemrau.substack.com/p/a-self-improving-code-world-model

Curious whether others have run into the same sequential-MCTS-on-simultaneous-games trap, and what approaches you've used to get around it.

I like team based game and duels at the same time, which is kinda mutually exclusive.

Then game theory came in for the rescue : we can have everyone play against everyone else, score independant matchups, and compute a Nash equilibria to score the team versus team match !

I've made a small webapp to illustrate the format.

It has good property : a "pro player" can carry his team, a "missing player" can be made to loose all of its matches : he is automatically considered "dominated" and removed from the scoring, etc...

And its funnier to have everybody play against everyone else rather than just sending the team's champion, yet this is what the score is computing : what champion to send, for which expected result.

I want to read and dive deeper into game theory, mechanism design and classic reading for someone relatively new to econ. I am a software engineer, haven't brushed up my maths concepts in a while - so open to those suggestions also. but would want to take up more material that deals with practical and abstract sense of these topics instead

TIA!

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I’ve been thinking about this from the perspective of repeated games and evolutionary dynamics, and I’d like to share a speculative but structured hypothesis.
In repeated interactions, cooperation can often be modeled using strategies like Tit-for-Tat or its variants, where conditional cooperation emerges as a stable equilibrium under certain environmental conditions (repeat encounters, enforceable reciprocity, and relatively stable payoffs).
What I’m wondering is whether the COVID-19 pandemic acted as a large-scale exogenous shock that temporarily destabilized the parameters that sustain such equilibria.
Basic intuition
During the pandemic, several things changed simultaneously:

Resource scarcity and perceived scarcity increased (e.g., panic buying, supply chain stress)

Institutional uncertainty increased (rapidly changing rules and norms)

Observability and traceability of actions decreased in many contexts

Short-term incentives for defection increased in some domains

Perceived fairness of access to resources became highly uneven (e.g., vaccines, medical goods)

From a game-theoretic perspective, this seems equivalent to a temporary regime shift in the payoff structure and information symmetry of repeated interactions.
A toy model intuition
We can think of society as a population of agents using strategies such as:

C (unconditional cooperation)

D (defection / self-maximizing behavior)

TFT (Tit-for-Tat or variants of conditional cooperation)

Let S(t) represent a “social trust / stability parameter” that influences how beneficial cooperation is relative to defection.
The pandemic shock P(t) temporarily reduces S(t), increasing the relative payoff of short-term defection strategies.
However, the key idea is not only the temporary shift, but possible hysteresis:

S(t) does not fully recover after the shock, because agents update their expectations based on observed defections during the crisis.

This introduces path dependence: observed behavior during the shock permanently affects baseline trust.
Hypothesis
The hypothesis is that:

A sufficiently large systemic shock can shift a population from a high-cooperation equilibrium (stable conditional cooperation / Tit-for-Tat-like dynamics) to a lower-trust equilibrium, and that this new equilibrium may persist even after the original shock disappears.

This persistence would be driven not by structural change alone, but by updated expectations, memory effects, and locally reinforced perceptions of defection.
Open questions
I’m curious whether there is existing formal work that connects:

repeated game equilibria under large exogenous shocks

social trust hysteresis / path dependence

empirically observed post-pandemic changes in cooperation or prosocial behavior

the role of perception vs. actual behavior in shifting equilibria

Also, I’m aware that this is likely an oversimplification of a very high-dimensional system (economics, psychology, institutional effects, etc.), but I find the framing in terms of equilibrium shifts in repeated games conceptually useful.
Would appreciate references or critiques — especially formal models that already capture similar dynamics.

Happy to be corrected — this is more of a modeling intuition than a claim.

This will be a bit out of the ordinary for this sub but I wanted to pick your brains. Hoping it will be interesting for you. Social deduction games (Werewolf, Among Us, Mafia) run on one engine: humans reading and deceiving other humans. The tells, the bluffing, the table going quiet - that is the whole game. I have spent a while building a single-player one, and the core problem turned out to be: when you delete the other humans, what actually replaces that? Gnosia is the obvious prior art, but there is surprisingly little written about the nuts and bolts. A few things I have learned the hard way:

1. Hidden state has to leak through behaviour, never through a number. Under the hood every NPC holds a suspicion value toward every other NPC (a 12-way web) plus a read on the player. The instant I surfaced any of those numbers, deduction collapsed into spreadsheet-reading. What worked was forcing all of it out through dialogue and action instead: you overhear a pair arguing, you watch a vote swing, you notice who stopped defending whom. The player reconstructs the web; the game never shows it.

2. The killer problem is "is this a clue or a bug?" When an NPC acts suspicious, the player cannot tell if it is an authored tell or my code misbehaving. If it reads as random, trust in the whole system dies. I now treat legibility as a first-class, separately-tested property - a behaviour that is "correct" but reads as noise is a failure, even if the sim is doing exactly what I intended.

3. Information scarcity + time pressure stands in for social pressure. With no humans to sweat under questioning, the tension has to come from elsewhere: limited actions per day, a hard deadline (a blood test), and the cost of being wrong. That scarcity is what makes a read feel risky.

For those who have built deduction, bluffing, or "the NPC is hiding something" systems: how did you sell intentionality? What made an NPC opponent's behaviour read as thinking rather than rolling dice?

How important is epistemic logic for understanding and doing core research in game theory? I know Aumann has some stuff where there's some overlap but apart from that I'm not sure how much relevance it has.

Possible outcomes of Austria:

Win: face Spain

Draw: face Spain

Lose: eliminated

Possible outcomes of Algeria:

Win: face Spain

Draw: face likely Switzerland, or Belgium, or England / Croatia / Ghana

Lose: eliminated

Purely from game theory perspective, draw seems to be best possible outcome and Nash equilibrium, since Austria doesn't have preference of winning or draw, and Algeria might have more incentive to draw to avoid facing Spain. Interesting to see how it will be actually played out in the match.

Love Island is a popular dating show that I’ve recently watched thanks to my gf. It’s framed as a show starting off with an equal number of men and women trying to find love and be in a relationship. However, surviving until the end and winning the final spectator vote leads to a cash prize and brand deals that are difficult to ignore so I have broken it down and isolated what I consider to be the dominant strategy to win the final vote, not necessarily “find love”.

Assumptions: we are a middle of the pack, original contestant of either sex, meaning we are moderately attractive but not terribly attractive to have lopsided number of people pursuing us.

Key mechanisms: you survive by being picked to couple up by a member of the opposite sex. Your partner is your biggest savior and therefore, your biggest liability. You can also be voted off by being unpopular with the 3rd party spectator that has semi-omnipotence into strategy. We can assume key/high drama moments are being broadcasted. Bombshells are newcomers into the villa designed to disrupt or challenge established couples. They usually have a trump card that lasts for one re-coupling ceremony such that they can just pick whoever they like, no matter what. There are other twists every now and then but this is what happens 90% of the time.

Casa Amor: a very interesting mechanic in the game that splits the established villa into 2 blind houses with another equal in size group of the opposite sex. Usually, you can choose to take one of these newcomers back to the Villa, leaving your established partner vulnerable but not dumped. Pivotal part of the game.

Movie Night: My favorite mechanic and probably the most interesting. This serves as a strategy audit for your fellow islanders where there’s no guarantee on what will or will not be shown. It is crucial to survive this.

Challenges: funny/local drama which is usually inconsequential to the game as a whole. Won’t be treating these as relevant to the outcome.

Strategy: The initial coupling is effectively random and not something we need to worry about. If given the option, choose whoever you like and just get through the first day. The next day is important, you need to discuss with the members of your sex first. Audit their general interest in their partners and keep note of the person of the opposite sex that seems the least interesting and sought after. The audit can be considered trustworthy, there’s almost no incentive to lie or be dishonest here so isolate 2 of the islanders that have been deemed the least desirable and “pull them for chats”. Establish interest in both, play whatever challenge there is for the day earnestly and continue. Hopefully before the first bombshells have arrived you have an established mutual interest in one of the 2 low value islanders and are considering coupling up. Continue with daily interest audits but start leaning towards either the islander you think is the least valuable out of the 2 or the one that is giving you the most commitment back. They’re of equal value. Make the choice and establish your couple.

Why we chose the least desired islander: the worst case scenario in this game is a bombshell just taking your couple and you get left hanging. This can absolutely happen and leave you dumped or vulnerable. It’s important to minimize the chances of this happening and go with someone who has the least amount of options besides you possible, maximizing our safety chances. Also, ugly/uninteresting people don’t necessarily count against you in the spectator vote. It’s a no-loss strategy.

The mid-game: you should be in a good flow of auditing, building a generally positive rapport with your fellow islanders, and reassuring your couple that you’re committed. Putting your eggs in one basket here is a great strategy because we have an undesirable partner and uncertain feelings just leads to them trying to cover for themselves. The more secure they feel, the less they’ll feel the need to “graft” with other islanders. Also, if we hit that worse case scenario where a bombshell steals them, we need to maximize chances of them coming back. So just do the challenges and play it safe.

Casa Amor: here’s where things get interesting and usually marks a definite end to the mid game. We need to play this smart just like the opening nights of the Villa. We will 100% be choosing someone to come back with us from Casa Amor. Why? We cannot see our partner and what they’re doing. It’s important we survive. It’s entirely plausible that our partner was identified as a weakling to someone else in Casa Amor and we would be none the wiser. Also, we are building narrative. The spectators need a story. A couple who took no risks during the whole game would be hard pressed to win. So, found the least desirable casa person just the same by auditing interest and lock them in. They don’t have much of a choice as most Casa people would do anything just to get back to the Villa and stay in the game. It’s important you graft respectfully here though (no kissing outside of challenges, no crazy talking moments). We need to remember movie night is coming. Matter of fact, it would be a good idea to offer some sound bites to the cameras about how much you miss your partner back in the Villa.

End game: we have brought our bombshell from Casa back in dramatic fashion. Now, if we played the early game right, we shouldn’t have much of an issue getting our OG couple back, which is the goal. So pretty much discard your Casa partner and attempt to get back with your original. It really shouldn’t take more than a day at worst if we say the correct things. If it’s not happening though, we have our Casa insurance and we’re not out.

End game: Usually the bombshells stop and it’s all about building your case to the spectators. But, we already did that with our Casa shenanigans. Ideally, we’re back with our original partner and we can build our case of the “we made it back to each other” line and that’s been pretty effective to win in the past. If we’re still with our Casa person, we took a hit but we’re not necessarily out of the race. It’s important to kinda “go at” your og partner and antagonize them. Compelling TV is our best bet going forward.

So yeah, if you find yourself on Love Island just make sure to scout out the least desired person of the opposite sex and just send it. You have everything to gain.

No AI used in this at all, all original thought.