S Akash

S Akash, Pratik Gajane

We study two-player zero-sum games (TPZSGs) with bandit feedback under fairness constraints requiring every action to be played with probability at least $α/m$. Existing instance-dependent results target $\textit{pure}$ Nash equilibria, while fairness generically produces $\textit{mixed}$ equilibria, a harder learning target. Our key technical tool is a reparametrization: every fair strategy decomposes as $p = (α/m)\mathbf{1} + (1-α)\widetilde{p}$ with $\widetilde{p} \in Δ_m$, and substituting into the payoff form yields $p^{\top}Aq = \widetilde{p}^{\top}\widetilde{A} q$ for a fair payoff matrix $\widetilde{A} := (1-α)A + α\mathbf{1} c^{\top}$, where $c_j = \tfrac{1}{m}\sum_i A(i,j)$ is the column-mean vector. The fair game on $A$ is then equivalent to a standard zero-sum game on $\widetilde{A}$, so equilibrium existence, KKT structure, and LP basis stability reduce to classical results applied to $\widetilde{A}$. We derive the fair minimax value, fair Nash equilibrium, fair regret, and a clean dual representation showing the price of fairness is at most $α(1-1/m)$ and vanishes whenever the unconstrained equilibrium already has full support. Our main result is an $\widetilde{O}(T^{2/3})$ regret bound for an Explore-Then-Commit algorithm, $\texttt{Fair-ETC-TPZSG}$, applicable to general mixed fair equilibria, together with a discussion of why naive action elimination does not readily improve it. When the fair equilibrium has a single dominant action, equivalently when $\widetilde{p}^{\star}$ is a vertex of $Δ_m$, the bound sharpens to instance-dependent $\widetilde{O}(1/\widetildeΔ(α)^{2})$, where $\widetildeΔ(α)$ is the LP-margin gap.

Nitish Kumar, Sannu Kumar, S Akash et al.

With the rapid proliferation of online sports journalism, extracting meaningful pre-game and post-game insights from articles is essential for enhancing user engagement and comprehension. In this paper, we address the task of automatically extracting such insights from articles published before and after matches. We curate a dataset of 7,900 news articles covering 800 matches across four major sports: Cricket, Soccer, Basketball, and Baseball. To ensure contextual relevance, we employ a two-step validation pipeline leveraging both open-source and proprietary large language models (LLMs). We then utilize multiple state-of-the-art LLMs (GPT-4o, Qwen2.5-72B-Instruct, Llama-3.3-70B-Instruct, and Mixtral-8x7B-Instruct-v0.1) to generate comprehensive insights. The factual accuracy of these outputs is rigorously assessed using a FactScore-based methodology, complemented by hallucination detection via the SummaC (Summary Consistency) framework with GPT-4o. Finally, we propose SUMMIR (Sentence Unified Multimetric Model for Importance Ranking), a novel architecture designed to rank insights based on user-specific interests. Our results demonstrate the effectiveness of this approach in generating high-quality, relevant insights, while also revealing significant differences in factual consistency and interestingness across LLMs. This work contributes a robust framework for automated, reliable insight generation from sports news content. The source code is availble here https://github.com/nitish-iitp/SUMMIR.