We provide an algorithm to find the value and an optimal strategy of the solitaire variant of the Ten Thousand dice game in the framework of Markov Control Processes. Once an optimal critical threshold is found, the set of non-stopping states of the game becomes finite, and the solution is found by a backwards algorithm that gives the values for each one of these states of the game. The algorithm is finite and exact.The idea to find the critical threshold comes from the continuous pasting condition used in optimal stopping problems for continuous-time processes with jumps.
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium computation are known only for particular classes of continuous games, such as two-player polynomial games or games in which pure equilibria are guaranteed to exist. This contribution focuses on the computation and approximation of a mixed strategy equilibrium for the whole class of multiplayer general-sum continuous games. We vastly extend the scope of applicabilit…
Can agents be trained to answer difficult mathematical questions by playing a game? We consider the integer feasibility problem, a challenge of deciding whether a system of linear equations and inequalities has a solution with integer values. This is a famous NP-complete problem with applications in many areas of Mathematics and Computer Science. Our paper describes a novel algebraic reinforcement learning framework that allows an agent to play a game equivalent to the integer feasibility problem. We explain how to transform the integer feasibility problem into a game over a set of arrays with…
