Strategic stiffening/cooling in the Ising game

The dynamic noisy binary choice (Ising) game of forward-looking agents on a complete graph is analysed. It is shown that strategic considerations lead to effective interaction strengthening (noise reduction) as compared to the myopic game. We show that strategic agents are able to come to consensus in the wider range of noise values than myopic ones. Effective population dynamics with time-dependent probabilities reflecting this strategic stiffening/cooling effect is described.