Figure 2 | Scientific Reports

Figure 2

From: α-Rank: Multi-Agent Evaluation by Evolution

Figure 2

Overview of the discrete-time macro-model. (a) Evolutionary concepts terminology. (b) We have a set of individuals in each population \(k\), each of which is programmed to play a strategy from set \({S}^{k}\). Under the mutation rate \(\mu \to 0\) assumption, at most one population is not monomorphic at any time. Each individual in a \(K\)-wise interaction game has a corresponding fitness \({f}^{k}({s}^{k},{s}^{-k})\) dependent on its identity \(k\), its strategy \({s}^{k}\), and the strategy profile \({s}^{-k}\) of the other players. (c) Let the focal population denote a population \(k\) wherein a rare mutant strategy appears. At each timestep, we randomly sample two individuals in population \(k\); the strategy of the first individual is updated by either probabilistically copying the strategy of the second individual, mutating with a very small probability to a random strategy, or sticking with its own strategy. (d) Individual in the focal population copies the mutant strategy. (e) The mutant propagates in the focal population, yielding a new monomorphic population profile.

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