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Revisiting the Bertrand Paradox via Equilibrium Analysis of No-regret Learners

Announce Type: replace Abstract: We study the discrete Bertrand pricing game with a non-increasing demand function. The game has $n \ge 2$ players who simultaneously choose prices from the set $\{1/k, 2/k, \ldots, 1\}$, where $k\in\mathbb{N}$. The player who sets the lowest price captures the entire demand; if multiple players tie for the lowest price, they split the demand equally. We study the Bertrand paradox, where classical theory predicts low prices, yet real markets often sustain high...

arXiv CS 9d ago

Earth from Above author returns with astonishing freshwater images

From Kenya's Tree of Life to a Svalbard glacier, these stunning photos are taken from a new book by Yann Arthus-Bertrand, whose The Earth From Above was a smash hit 25 years ago

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Week 4 of the 2026 Premier Lacrosse League season is June 5-6, as the league heads to American Legion Memorial Stadium in Charlotte. Four PLL games are on the schedule on Friday and Saturday, and the Carolina Chaos have one game each day. The 2026 WLL season also continues, as the Boston Guard take on the California Palms.

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Tonight, we’re staying in: Patrick Bruel cancels his summer shows

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