Alright y’all, hear me out: What if we took game theory and automata theory, smashed them together, and created a new framework to formalize games? 🎲🤔 Introducing: Game-Theoretic Automata (GTA).

The idea? Represent games as automata with: 1. States: Game positions (e.g., heaps in Nim, coin flip outcomes 🪙). 2. Transitions: Moves between states (player actions). 3. Players: Strategic agents (P₁ vs. P₂ vibes). 4. Winning Conditions: Explicit logic for victory. 5. Temporal Operators: ◯ (next), □ (always), ◇ (eventually)—so we’re not just playing games but encoding time like a boss.

Here’s a fun example: The Coin Flip Game

Let g ∈ Games where
∀gₓ ∈ g:
gₓ = {🪙, P, (s₀, s₁, s₂)}

where s₀ = unflipped, s₁ = 🪙↑, s₂ = 🪙↓

◯(s₀ → s₁ ∨ s₂)
□(s₁ ∨ s₂ → ¬s₀)

gₓ(w) where:
s₀ → turn(P₁)
w = 🪙↑ ∧ s₂ → Loss
w = 🪙↓ ∧ s₁ → Loss
w = s → Win

Now, combine this with Nim, where the optimal strategy is literally encoded using the XOR operation. NimSum(s) = a₁ ⊕ a₂ ⊕ … ⊕ aₙ Yes, folks, you can now flex on your friends with game-theoretic logic encoded into state machines. 💻♟️

Why does this matter? • AI/ML Applications: Train multi-agent systems with automata-based strategies. • Formal Verification: Verify adversarial system interactions as games. • Algorithm Design: Solve combinatorial problems in ways that would make von Neumann proud.

The future of formalizing games and strategy is literally a crossover episode between Game Theory and Automata Theory. Who’s ready to take this to the next level? 🚀

Thoughts? Questions? Memes? Let’s hear ‘em. 😂

Let g ∈ Games where
∀gₓ ∈ g:
gₓ = {🪙, P, (s₀, s₁, s₂)}

where s₀ = unflipped, s₁ = 🪙↑, s₂ = 🪙↓

◯(s₀ → s₁ ∨ s₂)
□(s₁ ∨ s₂ → ¬s₀)

gₓ(w) where:
s₀ → turn(P₁)
w = 🪙↑ ∧ s₂ → Loss
w = 🪙↓ ∧ s₁ → Loss
w = s → Win​​​​​​​​​​​​​​​​

https://reddit.com/link/1gzt31j/video/xll4e67my33e1/player

Hide and Sleep bloopers, credits to u/INUbis on youtube!
https://www.youtube.com/@inubis

https://reddit.com/link/1gre78q/video/9ssv0augdx0e1/player

https://preview.redd.it/dx290rutgvzd1.png?width=408&format=png&auto=webp&s=4f6da35f99ad92859e15f2c25ed780130929f0b8

Got this add and seemed familiar 💀