Stability of Multi-Agent Learning in Competitive Networks: Delaying the Onset of Chaos

The behaviour of multi-agent learning in competitive network games is often studied within the context of zero-sum games, in which convergence guarantees may be obtained. However, outside of this class the behaviour of learning is known to display complex behaviours and convergence cannot be always guaranteed. Nonetheless, in order to develop a complete picture of the behaviour of multi-agent learning in competitive settings, the zero-sum assumption must be lifted. Motivated by this we study the Q-Learning dynamics, a popular model of exploration and exploitation in multi-agent learning, in competitive network games. We determine how the degree of competition, exploration rate and network connectivity impact the convergence of Q-Learning. To study generic competitive games, we parameterise network games in terms of correlations between agent payoffs and study the average behaviour of the Q-Learning dynamics across all games drawn from a choice of this parameter. This statistical approach establishes choices of parameters for which Q-Learning dynamics converge to a stable fixed point. Differently to previous works, we find that the stability of Q-Learning is explicitly dependent only on the network connectivity rather than the total number of agents. Our experiments validate these findings and show that, under certain network structures, the total number of agents can be increased without increasing the likelihood of unstable or chaotic behaviours.

Stability of Multi-Agent Learning: Convergence in Network Games with Many Players

The behaviour of multi-agent learning in many player games has been shown to display complex dynamics outside of restrictive examples such as network zero-sum games. In addition, it has been shown that convergent behaviour is less likely to occur as the number of players increase. To make progress in resolving this problem, we study Q-Learning dynamics and determine a sufficient condition for the dynamics to converge to a unique equilibrium in any network game. We find that this condition depends on the nature of pairwise interactions and on the network structure, but is explicitly independent of the total number of agents in the game. We evaluate this result on a number of representative network games and show that, under suitable network conditions, stable learning dynamics can be achieved with an arbitrary number of agents.