banner addition

paper/src/chapters/03-methodology.tex

@@ -316,6 +316,7 @@ This yields two centroid-like heuristics that guide contamination estimation at
 In implementation, we maintain an alternating game-history stack (our \textit{Limbo} stack) and execute it explicitly every epoch with exactly two transitions: first the platform publishes a price vector (leader move), then the market responds with trajectory-derived demand (follower move).
 
 % Mention discretized action space and the clipping and over shotting in continuous action spaces
+% Also talk about catastrophic economics, we add termination on bankrupcy or zero demand so market collaps
 
 \subsubsection{Ambiguity Set Construction}
 We define an ambiguity set $\mathcal{U}_\epsilon(\hat{P}_N)$ centered around our empirical reference distribution $\hat{P}_N$ (derived from the generator $\mathcal{G}$). We utilize the Wasserstein distance metric to define the set of plausible demand distributions the agent might face:

paper/src/graphics/banner.py

@@ -0,0 +1,14 @@
+from PIL import Image, ImageDraw, ImageFont
+
+text = open("banner.txt", "r", encoding="utf-8").read()
+font = ImageFont.truetype("DejaVuSansMono.ttf", 18)
+
+dummy = Image.new("RGB", (1, 1))
+d = ImageDraw.Draw(dummy)
+bbox = d.multiline_textbbox((0,0), text, font=font)
+w, h = bbox[2]-bbox[0], bbox[3]-bbox[1]
+
+img = Image.new("RGB", (w+20, h+20), "white")
+d = ImageDraw.Draw(img)
+d.multiline_text((10,10), text, font=font, fill="black")
+img.save("banner.png")

paper/src/graphics/banner.txt

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+Actors                            Trajectories
+■════■   interact  ┌────────────┐     ┌──┐
+║Agent──────┬──────▻Web Platform├──┐  │τ1│  ┌▻Q (demand estimate)─┐
+║Human──────┘      └──────△─────┘  └──▻..│──┘                     │
+╚════■                    │           │τK│                        │
+  △                       │           └──┘                        │
+  │motivate               │                                       │
+  └────────┐              │Setting    ┌──┐      Pricing Engine    │
+ ▲     ┌──┐│              │Prices     │p1│     ┌──────────────┐   │
+ │   ┌─┘  ││              └───────────┤..│◅────│▒▒▒▒▒▒▒▒▒▒▒▒▒▒│◅──┘
+ │   │    └──┐                        │pN│     └─────┬──┬─────┘
+ │ ┌─┘       │                        └──┘           │  │
+ └─┴─────────┴─▶                                     │  │
+ Private Valuations                                  │  │
+                                                     │  │
+ ╔═══════════════════════════════════════════════════╧══╧════════╗
+ ║ Training Loop / SAC PPO DQN A2C                               ║
+ ║ ■═════════════════════════════■                               ║
+ ║ Q̂_t,i = Σ_s Σ_k ω(a_s,k) · 1[i_s,k = i]                     │ ║
+ ║ f(τ') from KL( T' || T_H ) and KL( T' || T_A )              │ ║
+ ║ α* = argmin_{α ∈ Aε(α0)} [ Revenue(p, Q^α) - λ·COI_leak ]   │ ║
+ ║ r_t = Revenue - λ·f(τ') | a*                                ▽ ║
+ ╚═══════════════════════════════════════════════════════════════╝