1 research outputs found
Playing Games with Bounded Entropy: Convergence Rate and Approximate Equilibria
We consider zero-sum repeated games in which the players are restricted to
strategies that require only a limited amount of randomness. Let be the
max-min value of the stage game; previous works have characterized
, i.e., the long-run max-min value. Our first
contribution is to study the convergence rate of to its limit. To this
end, we provide a new tool for simulation of a source (target source) from
another source (coin source). Considering the total variation distance as the
measure of precision, this tool offers an upper bound for the precision of
simulation, which is vanishing exponentially in the difference of R\'enyi
entropies of the coin and target sources. In the second part of paper, we
characterize the set of all approximate Nash equilibria achieved in long run.
It turns out that this set is in close relation with the long-run max-min
value