Symmetries are important in bargaining games. Symmetric games represent situations in which every person at the negotiating table is essentially equal, in the sense that each faces the same set of possible gains or losses. In other words, the payoff I receive if I follow s and you follow s′ is the same as the payoff you would receive if I followed s′ and you followed s.

Important as symmetric games are, many games played in real life are asymmetric. On the African savannah, competition between impala and leopards provides a striking example of a naturally occurring asymmetric game. Leopards are carnivores, capable of running at speeds exceeding 60 miles an hour. Impala, a type of African antelope, are herbivores and possess great leaping abilities: long jumps exceeding 11 meters have been recorded, as well as jumps of more than 3 meters in height. These differences in natural endowments between the two species give rise to key asymmetries in the strategy sets available to members of each species during an interaction. Leopards try to kill and eat impala, but impala do not try to kill and eat leopards. The differences in the individual strategy sets are reflected in the possible payoffs to each player: impala face death if they choose the wrong strategy in an encounter, whereas leopards merely face going hungry for a bit longer.

In the social world, many types of interaction are asymmetric.