Civilization and the evolution of short sighted agents

We model an assurance game played within a population with two types of individuals -- short-sighted and foresighted. Foresighted people have a lower discount rate than short sighted people. These phenotypes interact with each other. We define the persistent interaction of foresighted people with other foresighted people as a critical element of civilization while the interaction of short sighted people with other short sighted people as critical to the failure of civilization. We show that whether the short sighted phenotype will be an evolutionary stable strategy (and thus lead to the collapse of civilization) depends on the initial proportion of short sighted people relative to people with foresight as well as their relative discount rates. Further we explore some comparative static results that connect the probability of the game continuing and the relative size of the two discount rates to the likelihood that civilization will collapse.