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We show that in a variant of the Minority Game problem, the agents can reacha state of maximum social efficiency, where the fluctuation between the twochoices is minimum, by following a simple stochastic strategy. By imagining asocial scenario where the agents can only guess about the number of excesspeople in the majority, we show that as long as the guess value is sufficientlyclose to the reality, the system can reach a state of full efficiency orminimum fluctuation. A continuous transition to less efficient condition isobserved when the guess value becomes worse. Hence, people can optimize theirguess value for excess population to optimize the period of being in themajority state. We also consider the situation where a finite fraction ofagents always decide completely randomly (random trader) as opposed to the restof the population that follow a certain strategy (chartist). For a singlerandom trader the system becomes fully efficient with majority-minoritycrossover occurring every two-days interval on average. For just two randomtraders, all the agents have equal gain with arbitrarily small fluctuations.

Continuous transition of social efficiencies in the stochastic strategy Minority Game