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Concave Pro-rata Games: Uniqueness of equilibrium
Authors:
(1) Nicholas A. G. Johnson ([email protected]);
(2) Theo Diamandis ([email protected]);
(3) Alex Evans ([email protected]);
(4) Henry de Valence ([email protected]);
(5) Guillermo Angeris ([email protected]).
Table of Links
1.1 Symmetric pure strict equilibrium
2 Batched decentralized exchanges
1.2 Uniqueness of equilibrium
Positivity of equilibria. First we will show that f(v) > 0 for every 0 < v < w. To see this, note that the function f is bounded from below by all of its chords, as it is a concave function. Note that the chord with endpoints (0, 0) and (z, f(z)) lies above the x-axis, except at (0, 0), while the chord with endpoints (z, f(z)) and (w, f(w)) = (w, 0) lies above the x-axis, except at (w, 0), which leads to the final result.
This paper is available on arxiv under CC BY 4.0 DEED license.
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