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Abstract Social dilemmas are situations in which collective welfare is at odds with individual gain. One widely studied example, due to the conflict it poses between human behaviour and game theoretic reasoning, is the Traveler’s Dilemma. The dilemma relies on the players’ incentive to undercut their opponent at the expense of losing a collective high payoff. Such individual incentive leads players to a systematic mutual undercutting until the lowest possible payoff is reached, which is the game’s unique Nash equilibrium. However, if players were satisfied with a high payoff -that is not necessarily higher than their opponent’s- they would both be better off individually and collectively. Here, we explain how it is possible to converge to this cooperative high payoff equilibrium. Our analysis focuses on decomposing the dilemma into a local and a global game. We show that players need to escape the local maximisation and jump to the global game, in order to reach the cooperative equilibrium. Using a dynamic approach, based on evolutionary game theory and learning theory models, we find that diversity, understood as the presence of suboptimal strategies, is the general mechanism that enables the jump towards cooperation.