8 problems

Let $t$ be a time, let $h_t$ be the history at time $t$, and let $G_{t,\beta^v,\sigma^\nu}(t,h_t)$ and $G_{t,\sigma^v,\sigma^\nu}(t,h_t)$ denote the expected utilities when the foc…

Giannakopoulos–Koutsoupias conjecture. The straight-jacket auction is optimal for this auction problem.

Consider the pay-as-bid supply-function game with the strategy space restricted to $K$-Lipschitz supply functions, and suppose that the demand is affine. The affine-demand converge…

Consider the restricted game in which each agent's strategy is parametrized by a single parameter $p_i$, and suppose that the demand is linear. The piecewise supermodularity conjec…

Let $K$ be the Lipschitz constant defining the strategy space of supply functions, and let the equilibrium outcome be the resulting Nash equilibrium outcome of the pay-as-bid aucti…

General uniqueness conjecture. $\Sigma^*$ is the unique equilibrium for fewer bidders under a non-informative information structure, regardless of the specific parameters of the au…

Uniqueness conjecture. Fewer bidders are required for $\Sigma^*$ to be the unique equilibrium when the information structure is non-informative than when it is informative.

Revenue superiority conjecture. A revenue-maximizing potential helper prefers the pure bundle auction over both separate single-object subcarrier auctions and the naive multiple-ob…