Ashwin Goyal

Ashwin Goyal, Drashthi Doshi, Swaprava Nath

Motivated by the fact that the worth of a coalition may depend on the order in which agents arrive, Nowak and Radzik (1994) (NR) introduced cooperative games with generalized characteristic functions. We study such temporal cooperative games (TCGs), where the worth function v is defined on sequences of agents π rather than sets S. This order sensitivity necessitates a re-examination of axioms for reward sharing. NR and subsequent work proposed several axioms; the resulting solution concepts are still inherently order-oblivious and closely tied to the Shapley value. In contrast, we focus on sequential solution concepts that explicitly depend on the realized order π. We study reward-sharing mechanisms satisfying incentive for optimal arrival (I4OA), which promotes orders maximizing total worth; online individual rationality (OIR), which ensures agents are not harmed by later arrivals; and sequential efficiency (SE), which requires that the worth of any sequence is fully distributed among its agents. These axioms are intrinsic to TCGs, and we characterize a class of reward-sharing mechanisms uniquely determined by them. The classical Shapley value does not directly extend to this setting. We therefore construct natural Shapley analogs in two worlds: a sequential world, where rewards are defined for each sequence agent pair, and an extended world, where rewards are defined per agent, consistent with the NR framework. In both cases, the axioms of efficiency, additivity, and null player uniquely characterize the corresponding Shapley analogs. But, these Shapley analogs are disjoint from the class of solutions satisfying the sequential axioms, even for convex and simple TCGs.

Devendra Swami, Yash Phogat, Aadiraj Batlaw et al.

Upon film premiere, a major form of speculation concerns the relative success of the film. This relativity is in particular regards to the film's original budget, as many a time have big-budget blockbusters been met with exceptional success as met with abject failure. So how does one predict the success of an upcoming film? In this paper, we explored a vast array of film data in an attempt to develop a model that could predict the expected return of an upcoming film. The approach to this development is as follows: First, we began with the MovieLens dataset having common movie attributes along with genome tags per each film. Genome tags give insight into what particular characteristics of the film are most salient. We then included additional features regarding film content, cast/crew, audience perception, budget, and earnings from TMDB, IMDB, and Metacritic websites. Next, we performed exploratory data analysis and engineered a wide range of new features capturing historical information for the available features. Thereafter, we used singular value decomposition (SVD) for dimensionality reduction of the high dimensional features (ex. genome tags). Finally, we built a Random Forest Classifier and performed hyper-parameter tuning to optimize for model accuracy. A future application of our model could be seen in the film industry, allowing production companies to better predict the expected return of their projects based on their envisioned outline for their production procedure, thereby allowing them to revise their plan in an attempt to achieve optimal returns.