Players in Axelrod and Hamilton's model of cooperation were not only in a Prisoner's Dilemma, but by definition, they were also trapped in a dyad. But animals are rarely so restricted and even the option to interact with third parties allows individuals to escape from the Prisoner's Dilemma into a much more interesting and varied world of cooperation, from the apparently rare 'parcelling' to the widespread phenomenon of market effects. Our understanding of by-product mutualism, pseudo-reciprocity and the snowdrift game is also enriched by thinking 'beyond the dyad'. The concepts of by-product mutualism and pseudo-reciprocity force us to think again about our basic definitions of cooperative behaviour (behaviour by a single individual) and cooperation (the outcome of an interaction between two or more individuals). Reciprocity is surprisingly rare outside of humans, even among large-brained 'intelligent' birds and mammals. Are humans unique in having extensive cooperative interactions among non-kin and an integrated cognitive system for mediating reciprocity? Perhaps, but our best chance for finding a similar phenomenon may be in delphinids, which also live in large societies with extensive cooperative interactions among non-relatives. A system of nested male alliances in bottlenose dolphins illustrates the potential and difficulties of finding a complex system of cooperation close to our own.