The Myopic Barrier

In social dilemmas, agents can cooperate, defect, or take an individual solution — a guaranteed payoff that doesn’t depend on what others do. Most evolutionary game theory studies this under imitation dynamics: agents copy successful neighbors. But imitation assumes agents observe and compare payoffs across their network. Myopic best response assumes less — agents simply choose whichever strategy maximizes their payoff given their current neighborhood, without comparing themselves to others.

The dynamics differ fundamentally, and the difference matters for cooperation.

Under imitation dynamics, small neighborhoods promote cooperation — tight networks let cooperators cluster and protect each other from defectors. Under myopic best response, small neighborhoods can also promote cooperation, but with a twist: the individual solution creates an additional barrier. When an agent can guarantee a decent payoff alone, the benefits of cooperation must be significantly larger to justify the risk. Smaller neighborhoods make this barrier harder to overcome — cooperation requires greater benefits precisely where it’s most structurally favored.

The mechanism is double-edged. The same feature (small neighborhoods) that enables cooperative clusters also makes the individual solution more attractive, because the agent has fewer neighbors to cooperate with and thus less to gain from cooperation. The individual solution competes directly with cooperation for the agent’s strategy choice, and in small neighborhoods, the competition is tighter.

Multiple equilibria emerge on square lattices: individual solution dominance, cooperator-defector coexistence, or all three strategies coexisting. Which equilibrium prevails depends on neighborhood size, cooperation benefits, and individual solution cost — but the key finding is that the landscape under bounded rationality differs qualitatively from the landscape under imitation. Assuming agents imitate predicts different cooperation levels than assuming agents optimize locally.