A randomized strategy in the mirror game
Uriel Feige

TL;DR
This paper improves the memory efficiency of a strategy for the mirror game, enabling Alice to secure a high-probability tie with significantly reduced memory usage, from nearly square root of N to polylogarithmic scale.
Contribution
The paper presents a modification of Garg and Schneider's strategy that reduces Alice's memory requirement to polylogarithmic in N while maintaining a high probability of tying.
Findings
Achieves a strategy with O((log N)^3) memory for Alice.
Maintains a high probability (at least 1 - 1/N) of tying in the mirror game.
Significantly improves previous memory bounds for Alice's strategy.
Abstract
Alice and Bob take turns (with Alice playing first) in declaring numbers from the set . If a player declares a number that was previously declared, that player looses and the other player wins. If all numbers are declared without repetition, the outcome is a tie. If both players have unbounded memory and play optimally, then the game will be tied. Garg and Schneider [ITCS 2019] showed that if Alice has unbounded memory, then Bob can secure a tie with memory, whereas if Bob has unbounded memory, then Alice needs memory linear in in order to secure a tie. Garg and Schneider also considered an {\em auxiliary matching} model in which Alice gets as an additional input a random matching over the numbers , and storing this input does not count towards the memory used by Alice. They showed that is this model there is a strategy for Alice that ties with…
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Taxonomy
TopicsStochastic processes and statistical mechanics · Data Management and Algorithms · Cryptography and Data Security
