## Predictions based on game theory.

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Figures are generally photos, graphs and static images that would be represented in traditional pdf publications.

**(a)** Definition of Nash equilibria vs ‘no-partner’ strategies in two-players non-cooperative game. Nash equilibrium is determined by the intersection of the partners’ reaction curves—locus of optimal control action calculated for each value of the partner action [29] (blue and red lines). The ‘no-partner’ solution is determined as the optimal action calculated by each player by assuming that partner’s control is zero. **(b)** Simulated movements under Nash equilibria, ‘no-partner’ and unconnected conditions, for Player 1 (blue) and Player 2 (red). From top to bottom: movement paths, interaction force and interaction power profiles. **(c)** Interaction power, *P*_{i}, is defined as the scalar product of the interaction force (*F*_{i}) and the velocity(*V*_{i}). **(d)** Leader-follower strategy in the no-partner (left) and Nash strategy (right). The plots depict the Leadership index (LI) for both players and both via-points, calculated as the average power in the 300 ms interval (in gray) just before crossing the via-point by its homologous player.