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Motor coordination: when two have to act as one.

Braun DA, Ortega PA, Wolpert DM - Exp Brain Res (2011)

Bottom Line: In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements.Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach.Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering, Computational and Biological Learning Laboratory, University of Cambridge, Cambridge, UK. dab54@cam.ac.uk

ABSTRACT
Trying to pass someone walking toward you in a narrow corridor is a familiar example of a two-person motor game that requires coordination. In this study, we investigate coordination in sensorimotor tasks that correspond to classic coordination games with multiple Nash equilibria, such as "choosing sides," "stag hunt," "chicken," and "battle of sexes". In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements. Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach. We found that on the majority of trials coordination was achieved. Compared to the proportion of trials in which miscoordination occurred, successful coordination was characterized by several distinct features: an increased mutual information between the players' movement endpoints, an increased joint entropy during the movements, and by differences in the timing of the players' responses. Moreover, we found that the probability of successful coordination depends on the players' initial distance from the Nash equilibria. Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.

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Model simulations. (Row 1) Endpoint distribution of the diffusion process for the different games after 50 time steps. Thousand eight hundred draws are shown. (Row 2) Histogram over simulated endpoints. The histograms are similar to the experimental ones—compare Fig. 3. Analogous to the experimental data, endpoints can be classified as coordinated and miscoordinated. (Row 3) Joint entropy of the position distributions of player 1 and player 2. During the movement, the joint entropy is elevated in successful coordination trials (blue) compared to miscoordinated trials (green). This is a similar pattern observed in the experimental data—compare Fig. 4. (Row 4) Mutual information between the position distributions of player 1 and player 2. At the end of the movement, the mutual information is elevated in successful coordination trials (blue) compared to miscoordinated trials (green). The same pattern is observed in the experimental data—compare Fig. 4. (Row 5) Temporal difference in convergence time. In coordinated trials, the difference in time when the players converge to their final position is increased compared to miscoordinated trials. The same pattern is observed in the experimental data—compare Fig. 5
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Fig6: Model simulations. (Row 1) Endpoint distribution of the diffusion process for the different games after 50 time steps. Thousand eight hundred draws are shown. (Row 2) Histogram over simulated endpoints. The histograms are similar to the experimental ones—compare Fig. 3. Analogous to the experimental data, endpoints can be classified as coordinated and miscoordinated. (Row 3) Joint entropy of the position distributions of player 1 and player 2. During the movement, the joint entropy is elevated in successful coordination trials (blue) compared to miscoordinated trials (green). This is a similar pattern observed in the experimental data—compare Fig. 4. (Row 4) Mutual information between the position distributions of player 1 and player 2. At the end of the movement, the mutual information is elevated in successful coordination trials (blue) compared to miscoordinated trials (green). The same pattern is observed in the experimental data—compare Fig. 4. (Row 5) Temporal difference in convergence time. In coordinated trials, the difference in time when the players converge to their final position is increased compared to miscoordinated trials. The same pattern is observed in the experimental data—compare Fig. 5

Mentions: Finally, we devised a simple computational model to investigate qualitatively a potential computational basis of some of the features characteristic for within-trial coordination (see “Methods” for details). The computational model can be thought of as a diffusion process through the payoff landscape and is a standard model in physics. In a physical system, the payoff would correspond to an energy surface and the players could be thought of as particles moving stochastically in this energy landscape, trying to move downhill (lower forces and hence higher payoff). Diffusion models have also been previously applied to understand coordination in iterative classic coordination games (Crawford 1995). In our simulations, the initial positions of the players were drawn from a distribution similar to the initial distribution observed experimentally. We then simulated diffusion in the payoff landscape, assuming that each player estimates a noisy version of how the spring stiffness varies with their lateral movement (local payoff gradient) and tries to move downhill. Importantly, there are no lateral forces in the experiment, which means the modeled “downhill movement” does not correspond to the robot forces that are pushing against the subjects’ forward motion, but represent the subject’s voluntary choice following a noisy gradient in spring-constant space (compare Fig. 2). This model allows us then to determine the final distribution of positions of each player (Fig. 6, top row). The model captures the increased relative occurrence of the Nash equilibria by showing that coordinated solutions occur much more frequently than miscoordinated solutions (Fig. 6, second row). The model accounts for the most frequent pattern of coordination in all games, with the exception of the increased probability of the experimentally observed [swerve, swerve] solution in the chicken game. As observed in the experimental data, the model also accounts for an increased joint entropy during the movement between the positions of the players in successful coordination trials as opposed to miscoordinated trials (Fig. 6, third row). The model also captures that the mutual information between the two players’ position should be increased at the end of the trial in case of successful coordination (Fig. 6, fourth row). Finally, the model captures the increased difference in decision time in successful coordination trials compared to miscoordinated trials (Fig. 6, bottom row). However, there are also important features that are not captured by the diffusion model that are discussed below.Fig. 6


Motor coordination: when two have to act as one.

Braun DA, Ortega PA, Wolpert DM - Exp Brain Res (2011)

Model simulations. (Row 1) Endpoint distribution of the diffusion process for the different games after 50 time steps. Thousand eight hundred draws are shown. (Row 2) Histogram over simulated endpoints. The histograms are similar to the experimental ones—compare Fig. 3. Analogous to the experimental data, endpoints can be classified as coordinated and miscoordinated. (Row 3) Joint entropy of the position distributions of player 1 and player 2. During the movement, the joint entropy is elevated in successful coordination trials (blue) compared to miscoordinated trials (green). This is a similar pattern observed in the experimental data—compare Fig. 4. (Row 4) Mutual information between the position distributions of player 1 and player 2. At the end of the movement, the mutual information is elevated in successful coordination trials (blue) compared to miscoordinated trials (green). The same pattern is observed in the experimental data—compare Fig. 4. (Row 5) Temporal difference in convergence time. In coordinated trials, the difference in time when the players converge to their final position is increased compared to miscoordinated trials. The same pattern is observed in the experimental data—compare Fig. 5
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Fig6: Model simulations. (Row 1) Endpoint distribution of the diffusion process for the different games after 50 time steps. Thousand eight hundred draws are shown. (Row 2) Histogram over simulated endpoints. The histograms are similar to the experimental ones—compare Fig. 3. Analogous to the experimental data, endpoints can be classified as coordinated and miscoordinated. (Row 3) Joint entropy of the position distributions of player 1 and player 2. During the movement, the joint entropy is elevated in successful coordination trials (blue) compared to miscoordinated trials (green). This is a similar pattern observed in the experimental data—compare Fig. 4. (Row 4) Mutual information between the position distributions of player 1 and player 2. At the end of the movement, the mutual information is elevated in successful coordination trials (blue) compared to miscoordinated trials (green). The same pattern is observed in the experimental data—compare Fig. 4. (Row 5) Temporal difference in convergence time. In coordinated trials, the difference in time when the players converge to their final position is increased compared to miscoordinated trials. The same pattern is observed in the experimental data—compare Fig. 5
Mentions: Finally, we devised a simple computational model to investigate qualitatively a potential computational basis of some of the features characteristic for within-trial coordination (see “Methods” for details). The computational model can be thought of as a diffusion process through the payoff landscape and is a standard model in physics. In a physical system, the payoff would correspond to an energy surface and the players could be thought of as particles moving stochastically in this energy landscape, trying to move downhill (lower forces and hence higher payoff). Diffusion models have also been previously applied to understand coordination in iterative classic coordination games (Crawford 1995). In our simulations, the initial positions of the players were drawn from a distribution similar to the initial distribution observed experimentally. We then simulated diffusion in the payoff landscape, assuming that each player estimates a noisy version of how the spring stiffness varies with their lateral movement (local payoff gradient) and tries to move downhill. Importantly, there are no lateral forces in the experiment, which means the modeled “downhill movement” does not correspond to the robot forces that are pushing against the subjects’ forward motion, but represent the subject’s voluntary choice following a noisy gradient in spring-constant space (compare Fig. 2). This model allows us then to determine the final distribution of positions of each player (Fig. 6, top row). The model captures the increased relative occurrence of the Nash equilibria by showing that coordinated solutions occur much more frequently than miscoordinated solutions (Fig. 6, second row). The model accounts for the most frequent pattern of coordination in all games, with the exception of the increased probability of the experimentally observed [swerve, swerve] solution in the chicken game. As observed in the experimental data, the model also accounts for an increased joint entropy during the movement between the positions of the players in successful coordination trials as opposed to miscoordinated trials (Fig. 6, third row). The model also captures that the mutual information between the two players’ position should be increased at the end of the trial in case of successful coordination (Fig. 6, fourth row). Finally, the model captures the increased difference in decision time in successful coordination trials compared to miscoordinated trials (Fig. 6, bottom row). However, there are also important features that are not captured by the diffusion model that are discussed below.Fig. 6

Bottom Line: In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements.Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach.Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering, Computational and Biological Learning Laboratory, University of Cambridge, Cambridge, UK. dab54@cam.ac.uk

ABSTRACT
Trying to pass someone walking toward you in a narrow corridor is a familiar example of a two-person motor game that requires coordination. In this study, we investigate coordination in sensorimotor tasks that correspond to classic coordination games with multiple Nash equilibria, such as "choosing sides," "stag hunt," "chicken," and "battle of sexes". In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements. Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach. We found that on the majority of trials coordination was achieved. Compared to the proportion of trials in which miscoordination occurred, successful coordination was characterized by several distinct features: an increased mutual information between the players' movement endpoints, an increased joint entropy during the movements, and by differences in the timing of the players' responses. Moreover, we found that the probability of successful coordination depends on the players' initial distance from the Nash equilibria. Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.

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