diff --git a/paper/src/chapters/03-methodology.tex b/paper/src/chapters/03-methodology.tex index 79e5ca7..2109814 100644 --- a/paper/src/chapters/03-methodology.tex +++ b/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: diff --git a/paper/src/graphics/banner.png b/paper/src/graphics/banner.png new file mode 100644 index 0000000..232186e Binary files /dev/null and b/paper/src/graphics/banner.png differ diff --git a/paper/src/graphics/banner.py b/paper/src/graphics/banner.py new file mode 100644 index 0000000..4b77f43 --- /dev/null +++ b/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") diff --git a/paper/src/graphics/banner.txt b/paper/src/graphics/banner.txt new file mode 100644 index 0000000..f4d3cb9 --- /dev/null +++ b/paper/src/graphics/banner.txt @@ -0,0 +1,23 @@ +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* ▽ ║ + ╚═══════════════════════════════════════════════════════════════╝