Information Theoretic Approach for Modeling Bounded Rationality in Networked Games

Bounded rationality of networked interactions lead to non-optimal equilibria. The rationality of a self-interested player is determined by the incoming information from the opponents on their strategies and pay-offs. In this work, we attempt to model the heterogeneously distributed bounded rationality of networked players using the directed information flow, measured using the transfer entropy. In order to compute the non optimal equilibrium, we use the Quantal Response Equilibrium (QRE) model that entails a rationality parameter, which we define as a function of transfer entropy. We then compute the average divergence of the network of strategic interactions from that of the Nash Equilibrium, which we term as the 'system rationality', in order to compare and contrast the varying network topologies on their influence on the rationality of players. We observe that the networks demonstrate higher system rationality when the rationality values of players are derived from on the average information flow from neighboring nodes, compared to when the rationality is computed based on the specific information flow from each opponent. Further, we observe that the scale-free and hub-and-spoke topologies lead to more rational interactions compared to random networks, when the rationalities of the interactions are computed based on the average incoming information flow to each node. This may suggest that the networks observed in the real-world may adopt scale-free and hub-and-spoke topologies, in order to facilitate more rational interactions among networks of strategic players.