An Electrophysiological Model for Assessing Cognitive Load in Tacit Coordination Games

Previously, it was shown that some people are better coordinators than others; however, the relative weight of intuitive (system 1) versus deliberate (system 2) modes of thinking in tacit coordination tasks is still not resolved. To address this question, we have extracted an electrophysiological index, the theta-beta ratio (TBR), from the Electroencephalography (EEG) recorded from participants while they were engaged in a semantic coordination task. Results have shown that individual coordination ability, game difficulty and response time are each positively correlated with cognitive load. These results suggest that better coordinators rely more on complex thought process and on more deliberate thinking while coordinating. The model we have presented may be used for the assessment of the depth of reasoning individuals engage in when facing different tasks requiring different degrees of allocation of resources. The findings as well as future research directions are discussed.

Level-K Classification from EEG Signals Using Transfer Learning

Tacit coordination games are games in which communication between the players is not allowed or not possible. In these games, the more salient solutions, that are often perceived as more prominent, are referred to as focal points. The level-k model states that players’ decisions in tacit coordination games are a consequence of applying different decision rules at different depths of reasoning (level-k). A player at Lk=0 will randomly pick a solution, whereas a Lk≥1 player will apply their strategy based on their beliefs regarding the actions of the other players. The goal of this study was to examine, for the first time, the neural correlates of different reasoning levels in tacit coordination games. To that end, we have designed a combined behavioral-electrophysiological study with 3 different conditions, each resembling a different depth reasoning state: (1) resting state, (2) picking, and (3) coordination. By utilizing transfer learning and deep learning, we were able to achieve a precision of almost 100% (99.49%) for the resting-state condition, while for the picking and coordination conditions, the precision was 69.53% and 72.44%, respectively. The application of these findings and related future research options are discussed.

Coordination and Equilibrium Selection in Games: The Role of Local Effects

We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules – the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

Coordination Games on Weighted Directed Graphs

We study strategic games on weighted directed graphs, where each player’s payoff is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed nonnegative integer bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. We identify natural classes of graphs for which finite improvement or coalition-improvement paths of polynomial length always exist, and consequently a (pure) Nash equilibrium or a strong equilibrium can be found in polynomial time. The considered classes of graphs are typical in network topologies: simple cycles correspond to the token ring local area networks, whereas open chains of simple cycles correspond to multiple independent rings topology from the recommendation G.8032v2 on Ethernet ring protection switching. For simple cycles, these results are optimal in the sense that without the imposed conditions on the weights and bonuses, a Nash equilibrium may not even exist. Finally, we prove that determining the existence of a Nash equilibrium or of a strong equilibrium is NP-complete already for unweighted graphs, with no bonuses assumed. This implies that the same problems for polymatrix games are strongly NP-hard.

Institutions and their strength

Institutions can be strong or weak. But what does this mean? Equilibrium theories equate institutions with behavioural regularities. In contrast, rule theories explicate them in terms of a standard that people are supposed to meet. I propose that, when an institution is weak, a discrepancy exists between the regularity and the standard or rule. To capture this discrepancy, I present a hybrid theory, the Rules-and-Equilibria Theory. According to this theory, institutions are rule-governed behavioural regularities. The Rules-and-Equilibria Theory provides the basis for two measures of institutional strength. First, institutions that pertain to coordination games solve problems of information. Their strength is primarily a matter of the expected degree of compliance. Second, institutions that concern mixed-motive games solve problems of motivation. Their strength can be measured in terms of the weight people attribute to its rule.

Emergent Prosociality in Multi-Agent Games Through Gifting

Coordination is often critical to forming prosocial behaviors -- behaviors that increase the overall sum of rewards received by all agents in a multi-agent game. However, state of the art reinforcement learning algorithms often suffer from converging to socially less desirable equilibria when multiple equilibria exist. Previous works address this challenge with explicit reward shaping, which requires the strong assumption that agents can be forced to be prosocial. We propose using a less restrictive peer-rewarding mechanism, gifting, that guides the agents toward more socially desirable equilibria while allowing agents to remain selfish and decentralized. Gifting allows each agent to give some of their reward to other agents. We employ a theoretical framework that captures the benefit of gifting in converging to the prosocial equilibrium by characterizing the equilibria's basins of attraction in a dynamical system. With gifting, we demonstrate increased convergence of high risk, general-sum coordination games to the prosocial equilibrium both via numerical analysis and experiments.