# EEG Pattern Classification of Picking and Coordination Using Anonymous Random Walks
## 1 Introduction  
Tacit coordination games are games where two or more individuals are trying to select the same solution out of the same set of options without any communication between [1]. In games and problems of this kind, where there are several Nash equilibria points, classical game theory recommends choosing the options at random (i.e., picking) [2]. According to this analysis of classical game theory, in tacit coordination games, the predicted chance of successful coordination is \(\frac{1}{N}\), where \(N\) is the number of Nash equilibrium points. Despite this assumption, experimental studies have shown that human coordination abilities are significantly higher than \(1/N\) (e.g., [3; 4; 5; 6; 7]). This difference between the predicted results by classical game theory and actual performance stems from the fact that classical game theory considers only the rewards associated with each solution, which is the same for all Nash equilibrium points, regardless of cues such as color, size, shape and spatial location [8; 9; 10]. These cues may affect the preference of the player, who may choose the more prominent solution to the game. The more salient solutions are known as focal points [8; 9; 10]. Until now, research combining tacit coordination games with electrophysiological measures was mainly based on spectral analysis (e.g., [11; 12; 13]). Another tool that can describe the dynamics of activation during cognitive tasks is coherence. EEG coherence (e.g., [14; 15; 16]) measures the similarity between two different signals, recorded simultaneously at different sites of the scalp, based on the normalized cross-power spectrum per frequency of the two signals. Thus, it measures the degree of synchronization between their oscillatory activities. Using these two methodologies, we can provide complementary insights intothe dynamics of brain activation and reveal important patterns of neurological activity accompanying tacit coordination. Power spectrum analysis is an important part of EEG analysis and enables the extraction of key discriminative features associated with different cognitive processes. In contrast, EEG coherence enables the examination of functional and morphological connections between brain regions [17]. In a previous study [11], we tried to differentiate between three cognitive states, resting state, picking and coordination, by using EEG power spectrum measures. However, in that study, we constructed a complex model that was based on a deep CNN combined with a transfer learning method and involved only frontal and pre-frontal electrodes. The resultant model was a weighted combination of all frontal electrodes based on the use of a genetic algorithm. In contrast, in the current study, we would like to differentiate between the three abovementioned conditions using coherence patterns that are manifested throughout the scalp and involve all the electrodes using graph theory. Previous studies have used various EEG classification methods to predict different clinical states and humans' behavioral patterns, such as sleep disorders [18], Alzheimer's [19] and upcoming emergency brakings during simulated driving [20]. Some of the studies used the fact that the EEG recording includes a large number of electrodes that have a spatial relationship between them, according to their location on the scalp, and used graph theory to improve the classification results (e.g., [21; 22; 23]). In the current study, we have transformed the raw EEG signals into a graph. Each graph contained 16 nodes (equivalent to the 16 EEG channels) while the arcs between nodes were determined by coherence analysis. To assign each graph (16 EEG epochs) into its appropriate label, we have constructed a hierarchical classifier. In the first stage, we have distinguished between the resting-state condition and the other two cognitive tasks, namely picking and coordination. This task was accomplished by a relatively simple feature embedding process in which the graph was represented by a low-dimensional vector (e.g., [24; 25; 26]).