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Extra resources for Distributed strategic learning for wireless engineers
A common correlation scheme in a one-shot game is the following: each player chooses his/her action according to his/her observation of the value of the same public signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from the recommended strategy (assuming the others don’t deviate), the distribution is called a correlated Cournot/Nash equilibrium. A set is said to be convex if it is empty or it contains all the convex combinations of its elements.
Deﬁned in a probability space. The selected state wt is perfectly and ˜ t) publicly known. Then, the perfectly-known state simultaneous-act game G(w is played. Note that, in this context, the actions at time t are dependent on the state wt . 6 Unknown State Dynamic Games We consider dynamic games where the players have an opportunity to act several times. Additionally, the dynamic game can be under uncertainty; that is, the game can have a state which changes randomly from time slot to another.
R j w∈W We denote the game by ˜ j4 )j∈N ). G4 = (N , (Aj )j∈N , W, (R The equilibria of G4 are called maximin robust equilibria. 5. Worse-case Cournot/Nash equilibrium if (i) there exists w∗ (x) such that rj (w∗ (x), x) = inf rj (w, x), w and (ii): rj (w∗ (x), x) = max rj (w∗ (xj , x−j ), xj , x−j ) xj The choice of the set W plays an important role in the ˜ j (H, A) = Worse-case Cournot/Nash equilibrium. For example, if R log det I + 1 N0 j ∈N Hj∗ Pj Hj , and Hj ∈ Cn×n , then ˜ j (H, A) = 0. inf R H Therefore everything is optimal, which does not reﬂect the solutions to the mutual information optimization.