Sensorimotor interactions as signaling games

In our everyday lives, humans not only signal their intentions through verbal communication, but also through body movements (Sebanz et al. 2006; Obhi and Sebanz 2011; Pezzulo et al. 2013), for instance when doing sports to inform team mates about one’s own intended actions or to feint members of an opposing team. We study such sensorimotor signaling in order to investigate how communication emerges and on what variables it depends on. In our setup, there are two players with different aims that have partial control in a joint motor task and where one of the two players possesses private information the other player would like to know about. The question then is under what conditions this private information is shared through a signaling process. We manipulated the critical variables given by the costs of signaling and the uncertainty of the ignorant player. We found that the dependency of both players’ strategies on these variables can be modeled successfully by a game-theoretic analysis. Signaling games are typically investigated within the context of non-cooperative game theory, where each player tries to maximize their own benefit given the other player’s strategy (Cho and Kreps 1987). This allows defining equilibrium strategies where no player can improve their performance by changing their strategy unilaterally. These equilibria are called Bayesian Nash equilibria, which is a generalization of the Nash equilibrium concept in the presence of private information (Harsanyi 1968). In general, signaling games allow both for pooling equilibria, where no information is shared, and for separating equilibria with reliable signaling. In our study we translated the job market signaling game into a sensorimotor task. In the job market signaling game (Spence 1973), there is an applicant—the sender—who has private information about his true working skill, called the type. The future employer—the receiver—cannot directly know about the working skill, but only through a signal—for example, educational certificates—that are the more costly to acquire, the less working skill the applicant has. The sender can choose a costly signal that may or may not transmit information about the type to the receiver. The receiver uses this signal to make a decision by trying to match the payment—the-action—to the presumed type (working skill) that she infers from the signal. The sender’s decision about the signal trades off the expected benefits from the receiver’s action against the signaling costs. To translate this game into a sensorimotor task, we designed a dyadic reaching task that implemented a signaling game with continuous signal, type and action space. Two players sat next to each other in front of a bimanual manipulandum, such that they could not see each others’ faces. In this task, each player controlled one dimension of a two-dimensional cursor position. No other communication than the joint cursor position was allowed. The sender’s dimension encoded the signal that could be used to convey information about a target position (the type) that the receiver wanted to hit, but did not know about. The receiver’s dimension encoded her action that determined the sender’s payoff. The sender’s aim was to maximize a point score that was displayed as a two-dimensional color map The point score increased with the reach distance of the receiver — so there was an incentive to make the receiver believe that the target is far away. However, the point score also decreased with the magnitude of the signal—so there was an incentive to signal as little as possible due to implied signaling costs. The receiver’s payoff was determined by the difference between his action and the true target position that was revealed after each trial. Each player was instructed about the setup, their aim and the possibility of signaling. The question was whether players’ behavior converged to Bayesian Nash Equilibria under different conditions where we manipulated the signaling cost and the variability of the target position. By fitting participants’ variance of their signaling, we could quantitatively predict the influence of signaling costs and target variability on the amount of signaling. In line with our game-theoretic predictions, we found that increasing signaling costs and decreasing target variability leads in most dyads to less signaling. We conclude that the theory of signaling games provides an appropriate framework to study sensorimotor interactions in the presence of private information