Sampling equilibrium, with an application to strategic voting

We suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist candidate can win the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.