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Convergence of naive iteration for a stateful, iterated tabular game

The value iteration operator $$\Psi(V) = max_{x \in \Delta^{m_s}} \min_{y \in \Delta^{n_s}} \sum_{ij} [A_{ij} + \gamma V(T_{s i j})] x_i y_j$$ is the Shapley operator for the game. When the discount ...
Brian Lins's user avatar
1 vote

Convergence of naive iteration for a stateful, iterated tabular game

The class of games you describe is called "stochastic games". There is a rich literature on algorithmic aspects of these games. Look for surveys and papers by Raghavan, Filar, and their co-...
Eilon's user avatar
  • 745
1 vote

Optimally betting a beta-biased coin

Let $\alpha_0$ bet the cutoff value of $\alpha$ as a function of $N$ and $\beta$ -- meaning that for $0<\alpha<\alpha_0$ it is better not to bet on the first coin flip while for $\alpha_0<\...
Claude Chaunier's user avatar

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