Team-Nash equilibrium (TNE) predicts the outcomes of such coordinated interactions.

Let a two-player Markov game where both players affect the transition. As we have seen in Section 2.1, in the case of unilateral deviation from joint policy Let a (possibly correlated) joint policy ˆ σ . By Lemma A.1, we know that Where the equality holds due to the zero-sum property, (1). An approximate NE is an approximate global minimum. An approximate global minimum is an approximate NE.

One such example is two-player zero-sum Markov games, in which efficient ways to compute a Nash equilibrium are known. Inspired by zero-sum polymatrix normal-form games (Cai et al., 2016), we define a class of zero-sum

Insuch applications, a team of agents aim to maximize a joint expected utility through a single global reward.

Agent 1's action is resolved first. Figure 8: An example of Agent 1 using the "clean" action while facing East. The "main" beam extends directly in front of the agent, while two auxiliary A beam stops when it hits a dirty river tile. The Sequential Social Dilemma Games, introduced in Leibo et al. [2017], are a kind of MARL All of these have open source implementations in [Vinitsky et al., 2019]. The cleaning beam is shown in Figure 8a.