Coevolution in Coordination Games

González-Casado, Miguel Angel. (Supervisors: Sanchez, Anxo; San Miguel, Maxi)
Master Thesis (2022)

In this thesis we assess the role of the network’s temporal evolution in reaching coordination and in equilibrium selection for Coordination Games. Specifically, we analyze what happens if, while agents play the game, they are able to sever some of their current connections and connect with others. We focus on two update rules: Replicator Dynamics (RD) and Unconditional Imitation (UI). We investigate the effect of this coevolution of the network both on a Pure Coordination Game (PCG), in which choices are equivalent, and on a General Coordination Game (GCG), for which there is a risk-dominant action and a payoff-dominant one. First, we observe that, as we increase the probability to rewire links, there is a transition from a regime in which the system fully coordinates in a single connected component to a regime in which the system fragments in two connected components, each one coordinated on a different action (either if both actions are equivalent or not). The nature of this fragmentation transition is different for both selection rules. Second, both for RD and UI in a GCG, for some values of the parameters the system is able to fully coordinate on the payoff-dominant action. Surprisingly, for the RD rule the system was only able to coordinate on the risk-dominant action in the absence of coevolution. For the UI rule the system was already able to coordinate on the payoff-dominant action in the absence of coevolution, but the region of the parameter space in which it is able to do so widens due to coevolution. Hence, coevolution enhances coordination on the payoff-dominant action for both update rules.

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