Robust Value Maximization in Challenge the Champ Tournaments with Probabilistic Outcomes

Umang Bhaskar, Juhi Chaudhary, Sushmita Gupta, Pallavi Jain, Sanjay Seetharaman

Keywords: tournament value maximization, robust value, approximation algorithms, hardness of approximation, challenge the champ tournaments

TL;DR: We study value maximization in Challenge the Champ tournaments when matches may have probabilistic outcomes. We show the optimal robust value is hard to approximate, and give approximation algorithms for relaxations and restricted instance.

Abstract:

Challenge the Champ is a simple tournament format, where an ordering of the players --- called a seeding --- is decided. The first player in this order is the initial champ, and faces the next player. The outcome of each match decides the current champion, who faces the next player in the order. Each player also has a popularity, and the value of each match is the popularity of the winner. Value maximization in tournaments is previously studied when each match has a deterministic outcome. However outcomes are often probabilistic, rather than deterministic. We study robust value maximization in Challenge the Champ tournaments, when the winner of a match may be probabilistic. We seek to obtain a seeding to maximize the total value that is obtained, irrespective of the outcome of probabilistic matches. We show that even in simple binary settings, the optimal robust value --- which we term the
VNAR, or the value not at risk --- is hard to approximate. However if we restrict the matches with probabilistic outcomes, or allow adaptive algorithms which determine the order of challengers based on the outcomes of previous matches, we can obtain good approximations to the optimal VNAR.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1327