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We consider a 3-player game in the normal form, in which each player has twoactions. We assume that the game is symmetric and repeated infinitely manytimes. At each stage players make their choices knowing only the averagepayoffs from previous stages of all the players. A strategy of a player in therepeated game is a function defined on the convex hull of the set of payoffs.Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. astrategy profile being resistant to deviations by coalitions. Constructedequilibrium strategies are safe, i.e. the non-deviating player payoff is notsmaller than the equilibrium payoff in the stage game, and deviating players'payoffs do not exceed the non-deviating player payoff more than a positiveconstant which can be arbitrary small and chosen by the non-deviating player.Our construction is inspired by Smale's good strategies described in\cite{smale}, where the repeated Prisoner's Dilemma was considered. In proofswe use arguments based on approachability and strong approachability typeresults.

Strong and safe Nash equilibrium in some repeated 3-player games