The Player's Effect
Ronen Gradwohl, Omer Reingold, Ariel Yadin, Amir Yehudayoff

TL;DR
This paper investigates the influence of individual players on functions with inputs from multiple players, establishing bounds on the number of influential players and conditions under which players have positive effect.
Contribution
It provides a tight upper bound on the number of players with large effect under pairwise independence and explores conditions for the existence of players with positive effect.
Findings
Bound on the number of players with large effect under pairwise independence
Existence of small sets of players whose removal reduces effect
Conditions under which players have positive effect
Abstract
In a function that takes its inputs from various players, the effect of a player measures the variation he can cause in the expectation of that function. In this paper we prove a tight upper bound on the number of players with large effect, a bound that holds even when the players' inputs are only known to be pairwise independent. We also study the effect of a set of players, and show that there always exists a "small" set that, when eliminated, leaves every set with little effect. Finally, we ask whether there always exists a player with positive effect. We answer this question differently in various scenarios, depending on the properties of the function and the distribution of players' inputs. More specifically, we show that if the function is non-monotone or the distribution is only known to be pairwise independent, then it is possible that all players have 0 effect. If the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAuction Theory and Applications · Game Theory and Applications · Consumer Market Behavior and Pricing
