6 problems

Let $S=\{s_3,s_2,s_1\}$ with $s_3<s_2<s_1$. Let $o_{\mathrm{zs}}$ denote the zero-sum scoring-play outcome and let the antagonistic self-interest game use AvA tie-breaking. Three-a…

Let $S$ be a two-action subtraction set, let $o_{\mathrm{zs}}(h)$ be the zero-sum scoring-play outcome at heap size $h$, and let $o^1_{\mathrm{AvA}}(h),o^2_{\mathrm{AvA}}(h)$ be th…

Let ${\mathrm{TB}}$ be the total budget, and let a unitary game be a game in the class defined by the paper. Associate to it the corresponding 0-bidding automaton $\mathcal{A}$, wh…

Let $\Gamma$ be a ruleset, with $\mathcal{B}$ its set of allowed bids and $\mathcal{U}$ the class of rulesets having the uniqueness properties. Suppose that all weights are nonnega…

Let $mathcal{PT}{-x}$ be the set of scoring-play game positions in which every node has value $x0$ and the initial score is $0$. Write $Gcong 0$ for equivalence to the zero game a…

The u-value conjecture. All input-setting games can only involve the $u$-values