Co-operation and defection: playing the field and the ESS

If food is patchily dispersed, food clumps being very rich, but rare and hard to find, each individual in a foraging flock then faces an evident dilemma: whether to co-operate and participate in the search, thus enhancing the rate by which rich patches are discovered, or to defect and let others do the searching, thus avoiding any possible expenditures and risks involved in the search (but enjoying the abundant resources once a rich patch is discovered). This conflict (and its possible solution) is treated as an example in the analysis of the synergistic n-player game presented in this paper. After deriving conditions for the existence of a mixed ESS in such games, the evolutionary stability of the mixed strategy against invasions by pure strategists, in particular against invasions by recognizable defectors, is analyzed. Whereas in any "degenerating" mixed-strategy model a recognizable defector can invade and spread, a "non-degenerating" model can sometimes yield a mixed ESS which is immune to such invasions.