Constructive comparison in bidding combinatorial games

07/23/2022

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by   Prem Kant, et al.

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A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game comparison techniques from alternating normal play, we propose an algorithmic play-solution to the problem of game comparison for a class of bidding games that include game forms that are defined numbers. We demonstrate a number of consequences of this result that, in some cases, generalize the classical results in alternating play (from Winning Ways and On Numbers and Games). We state a couple of thrilling conjectures and open problems for readers to dive into this promising path of bidding combinatorial games.