Myopic Best Response as a Double-Edged Mechanism in Networked Social Dilemmas with Individual Solutions

Abstract

Myopic best-response dynamics (MBRD) capture agents' bounded rationality and can generate evolutionary outcomes that differ from those produced by widely examined imitation dynamics. In this study, we apply MBRD to a three-strategy social dilemma -- the snowdrift game with an individual solution -- in which not only defection but also an individual solution that guarantees a safe, constant payoff can undermine cooperation. Monte Carlo simulations show that, on a square lattice, the evolutionary dynamics result in distinct equilibria, including the dominance of the individual solution, the coexistence of cooperators and defectors, or all-strategy coexistence. By combining simulations with a simple heuristic that approximates the transition condition between the dominance of the individual solution and the all-strategy coexistence, the analysis reveals a dual role of neighborhood size. Specifically, smaller neighborhoods can promote cooperation even when the individual solution is relatively inexpensive; however, achieving cooperation under these conditions requires greater benefits from cooperation. Notably, this hindrance to cooperation contrasts with evolutionary outcomes observed under imitation dynamics. Analysis of local strategy configurations explains the transition between the all-strategy coexistence and the coexistence of cooperators and defectors while showing that this transition is absent in a one-dimensional lattice. These observations indicate that the persistent availability of individual solutions constitutes an additional inhibiting factor of cooperation in populations of boundedly rational agents.