Dove v Hawk

John Maynard Smith introduced the concept of the evolutionarily stable strategy (ESS), which demonstrates how different behavioural strategies become balanced within a population.

Maynard-Smith proposed a hypothetical case in which a member of a population could either be hawk or dove. When encountering another member of this population the hawk and dove would adopt divergent fighting strategies: the hawk would always fight vigorously whilst the dove would flee after putting up a nominal show of resistance. Points can be allocated to gauge the outcome of each encounter: for example, 50 points for a win, 0 for losing, minus 100 for being badly injured, and -10 for wasting time in a prolonged contest.

In a population of doves, no member of the population would be badly hurt but time would be wasted through drawn-out posturing. In a contest between two doves the winner would gain 50 points for victory, whilst losing 10 for wasting time. The loser would merely lose 10 points for wasting time. If the dove population was invaded by a hawk, the latter strategy would prove successful. Within a population of doves, the rogue hawk would win all of his fights scoring 50 points on each occasion (with no deduction for wasted time).

However, if the population swung to being comprised solely of hawks then the success of this strategy would be vastly diminished. Winning fights against a fellow hawk would yield 50 points, but there is also the possibility of losing and being badly injured which equals minus 100 points. In this population, a mutant dove would prosper as, whilst they would lose fights, they would never be hurt so would break even with 0 points.

It might be expected that the population would oscillate between being comprised solely of doves, to being comprised exclusively of hawks. Maynard-Smith demonstrated that what actually happened was that a stable equilibrium occurred when a certain amount of hawks and doves comprised the population, for example a hawk-dove ratio of 7:5 might yield an ESS. The average pay-off in the stable population is less than that in an all-dove population, but it has been demonstrated that the all-dove population is not stable, as it can be infiltrated by an aggressive hawk.

Hawk strategy, Spain 1982

At World Cup 2010 games will be played which reflect the trade-off required for the maintenance of an ESS, albeit at a much more complex level. Two teams adopting a complete dove strategy would yield the maximum pay-off, with flowing football undisturbed by crunching tackles and niggling fouls. However, the dove strategy could be easily broken down if infiltrated, so the incentive would be to switch to a hawk strategy in the pursuit of success. (An example from English club football is Manchester United adopting a hawk strategy to end Arsenal’s 49 game unbeaten streak back in 2004). But if the hawk team became faced with another hawk team, then the trade-off would be greatly diminished with players ending up injured and sent off, within a game bogged down in a heated and fruitless midfield battle.

As with the hypothetical example above, the aim is to field a team which comprises hawk and dove fighting strategies, so that parity can at least be attained with other sides. However, the successful team in South Africa may be the one which is able to exploit the subtle oscillations of the ESS which characterize cagey, well-matched international tournament fixtures.