Nash equilibrium in multi-agent RL — what and when?

hard

Answer

$({\pi}_{1}, \;, \;{\pi}_{n})$
$In zero-sum games (Rock-Paper-Scissors, Chess, Go, StarCraft): minmax = maxmin = Nash.$
$Solved via self-play (AlphaZero) or fictitious play + best-response.$
$In mixed-motive / general-sum: multiple Nash equilibria + hard to find.$
$Related concepts: correlated equilibrium, coarse correlated equilibrium (used in AlphaStar).$

Check yourself — multiple choice

Random
Policy profile where no agent improves unilaterally; zero-sum: minmax = Nash, solved via self-play (AlphaZero) or fictitious play; general-sum multiple + hard
Same as PPO
Not real

Nash: no unilateral improvement; zero-sum via self-play; general-sum harder.

#multi-agent#theory

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