9 problems

The Bachet's game with lottery moves model is governed by the assumptions preceding the main theorem, including condition … is violated. The condition is used technically in the pr…

Let $\lambda_{\rm \max}:(0,1]^2\to[1,\infty)$ be the function measuring the maximum value associated with the game. Maximizer conjecture. The maximum value of…

Let $T_\infty=(h_1,h_2,\ldots)$ be a fixed partition with $h_1+h_2+\cdots=+\infty$, and let $v_{T_\infty,\lambda}(p)$ denote the value of the game from Theorem with discount parame…

An absorbing game has a limit value, and a rational absorbing game is one whose payoff and transition data are rational. A number is algebraic if it is a root of a nonzero polynomi…

Let $m\geq 1$. A rational absorbing game with $m$ actions per player is an absorbing game whose data are rational and in which each player has $m$ available actions. Maximal-degree…

Let $X^1,X^2,Y^1,Y^2,Z^1,Z^2$ be the payoff processes of a non-zero-sum Dynkin game, with payoff functions … … Define the regions…

Let $\Phi^N(t)$ be the finite-dimensional matrix-valued function defined by the Riccati system in the source, with entries $\Phi^{N,i,j}(t)$. Consider the associated functions…

Let $N$ be the number of players, and let $n^N(t)$ denote the number of players in state $0$ at time $t$ under the unique symmetric Markov perfect equilibrium for the $N+1$-player…

Let $v_\lambda$ denote the value vector associated with the parameter $\lambda>0$ in the stochastic game, and let $V$ be a finite set. Finite-limit-set conjecture. There exists a f…