SlowGuess/NeurIPS_2023_OCR huggingface dataset:
This is a theoretical work that concerns with algorithm design in a competitive market, with the primary goal of learning a stable equilibrium. The consumer demand follows the multinomial logit model, and we assume that their price/reference price sensitivities are positive, i.e.,  $b_{i}, c_{i} > 0$ . The feasible price range  $\mathcal{P} = [\underline{p}, \overline{p}]$  is assumed to contain the unique SNE, with the lower bound  $p > 0$ . We have justified both assumptions in the main body of the paper (see the discussion below Eq. (3) and Proposition 3.1).
The convergence results in the paper assume the firms take diminishing step-sizes  $\{\eta^t\}_{t\geq 0}$  with  $\sum_{t = 0}^{\infty}\eta^{t} = \infty$  , which is common in the literature of online games (see, e.g., [15, 14, 40]). We also discuss the extension to constant step-sizes in Remark 5.3.