Predictions based on game theory.
(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  (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, Pi, is defined as the scalar product of the interaction force (Fi) and the velocity(Vi). (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.