Ji Ho Bae

A sink equilibrium without local sources whose content is not an attractor

Biggar and Papadimitriou showed that a local source in a sink equilibrium prevents the content of the sink from being an attractor of the replicator dynamic and asked whether the converse holds: must every unstable sink equilibrium contain a local source? We answer this question...

An ordinal characterization of universal fictitious-play convergence (C73-11)

An infinitary ordinal characterization of universal simultaneous fictitious-play convergence for finite normal-form games, covering every initial profile and every legal tie choice. The result is a mathematical characterization, not a finite decision algorithm. Contents. Original...

Local convex certificates for one-sided-information game values (C73-8)

Local convex-capital certificates characterize bounded Borel payoffs admitting a value at every prior in one-sided-information games. This deposit includes the hand manuscript and the later Claude-developed BorelValue Lean project at its pinned public commit, including the superh...

A counterexample to the coalition LP conjecture for metric distortion

Charikar and Ramakrishnan conjectured that normalizing an optimal solution of their coalition linear program gives a randomized voting rule attaining their proposed metric-distortion bounds. We give a counterexample with four candidates and 25 voters. The linear program has a uni...

Exact zCDP for k-Ary Randomized Response

This note gives a self-contained exact zero-concentrated differential privacy (zCDP) characterization of k-ary randomized response for every integer k >= 2 and every privacy parameter epsilon >= 0. It proves that the necessary endpoint condition identified by Harrison and Manuran...

Closed certificates for fixed mirror-descent convergence (C73-15)

Closed-certificate trees and countable-ordinal rankings characterize convergence of fixed mirror-descent rules for the canonical regularizer and step-schedule class. The stated criterion is infinitary. Contents. Original proof PDF and LaTeX source, a complete research archive wit...

A nonminimizing limit of the uncorrected noisy game (C73-25)

A counterexample to minimizing selection for the uncorrected noisy game in the catalogue's stated admissible-penalty class. The construction uses a shrinking boundary cutoff and a vanishing interior term. The narrower pure decreasing-boundary-cutoff variant is not claimed. Conten...

Local capital geometry for maxmin concavification (C73-17)

A local-capital-geometry characterization of equality between the informed-player maxmin and concavification at every prior. The additional Lean project formalizes the criterion using the nonrevealing lower value; its README explains the relationship to the complete-information g...