14 problems

A finite deterministic graphical game (DG game) with a unique cyclic outcome is considered, together with the rank vector $r$ whose entry $r_i$ counts the terminal outcomes that ar…

Consider the given imbalanced $(m,2k+1)$-RPS game and a Nash equilibrium $N$. Let $P_i(S)$ be the probability that player $i$ plays $S$, and let $P_i(T_p)$ be the probability that…

For $t,k\in\mathbb{N}$, let $r_1,\dots,r_{k-1},s$ be variables in $(0,1)$, and let $E_i(R)$, $E_i(P)$, $E_i(S)$, $E_s(P)$, $E_s(S)$, $E_p(R)$, $E_p(P)$, and $E_p(S)$ be the expecte…

Let $m\text{ in }\mathbb{N}$ denote the number of players, and let $E_i(R)$, $E_i(P)$, and $E_i(S)$ denote the expected payoffs associated with the strategies used in the paper. No…

The imbalanced $(m,2n+1)$-RPS is constructed from the paper's imbalanced $(m,3)$-RPS construction by iterated blow-ups. A game is strongly playable when it has the property defined…

Stationary payoff comparison conjecture. The stationary expected individual payoffs satisfy

Let an $n$-person deterministic graphical game be play-once if every player makes at most one move during a play. The game is Nash-solvable if it has a Nash equilibrium in pure sta…

Let $x$ be a position in the exact slow game $\operatorname{NIM}(n,n-1)$ played by $\ell$ players in a fixed cyclic order. A move reduces $n-1$ positive entries by $1$ and leaves o…

Consider the exact slow game NIM$(n,n-1)$ for $\ell$ players: a position is a non-negative $n$-vector, players move cyclically, and on each move a player keeps one entry unchanged…

A finite game is specified by its players, strategy sets, and payoff functions, and a Nash equilibrium is a strategy profile from which no player can profit by unilaterally deviati…

Boundary-utility conjecture. The following condition is sufficient: for all $\mathbf{p}\notin\mathcal{S}$,

Gurvich–Obraztsova conjecture. There is a chess-like game with no Nash equilibrium in pure stationary strategies satisfying condition (C).

Consider games with Nash equilibria and evolutionary dynamics, including multi-population dynamics. Broad elimination conjecture. For many other dynamics, including multi-populatio…

Consider games sufficiently close in payoff space to game … , but the paper's proof does not extend because its rescaling lemma requires a very specific payoff structure.