Competition considered in Stephens’ game theory

In human experience, competition could be seen as the essence of a game, and competing against rivals provides the quintessential game sensation. But competition is also a key concept in the biological sciences. Ever since Darwin, its primary importance in shaping the morphology and behaviour of organisms through natural selection has been recognised.

This note is an attempt at explaining competition in terms of Dennis Stephens’ theory of games, a theory that he developed quite independently of evolutionists like Lewontin (1961) and Maynard Smith (1982). In his view, any activity of humans – or other living things – can be analysed as a game consisting of conflicting purposes in the broadest sense of that word, or postulates in his terminology. Stephens did not directly address the subject of competition in his only published book (Stephens, 1979) or in any of his notes that have survived, apart from closely linking it to the idea of conflict. He dismissed ‘compete’ as a games goal along with ‘win’, ‘achieve’ and ‘succeed’. A games goal is one that is meaningful only inside a game, and is therefore irrelevant to understanding the mechanism of games as viewed objectively from the outside, which was the main thrust of his work.

Living organisms compete because all individuals are attempting to secure the finite resources that they need to live and reproduce. In biology, competition is most broadly defined as a reciprocal negative interaction between organisms (Connell, 1990), or more narrowly as the tendency of neighbouring organisms to utilise the same resources (Grime, 1973). It is strongest between the most similar organisms: individuals of the same age class and sex within the same species, because similar organisms make similar demands on their environment for resources. It occurs at a lower level between different species whose ecological niches coincide or overlap.

While a predator/prey relationship between two species implies a negative feedback loop tending to equilibrium, a competitive relationship is positive feedback that may end in the elimination of one species from the niche (Margalef, 1968).

A distinction can be made between tacit and explicit competition. Tacit, indirect or blind competition is a ubiquitous fact, as when two birds are foraging for the same food in the same habitat without being aware of each other, or when the root systems of two trees are tapping the same subsoil aquifer.

Explicit competition begins when one organism reacts to the other as a competitor with the triggering of functions or behaviour directed at the competitor. In the field of ethology, explicit or overt competition for resources among animals is called aggression.

Wallace (1889) considered every organism to be in contest with its whole environment, including both physical influences and the biotic influences of the other organisms present. This is tacit competition.

On the other hand, Darwin had emphasised explicit, direct competition; not surprising since he was a capitalist whose ideas were influenced by Herbert Spencer. But an organism is not operating with a goal “to compete”, even tacitly. Its behaviour or functions are directed toward maximising its exploitation of the necessary resources, and consequently denying them to its competitors. Similarly, when businessmen brag about being competitive, they really mean that they can break their rivals.

At the threshold between tacit and explicit competition the game escalates and might be described as compulsive as neither player can withdraw without defeat.

Here is an example of a Stephensian games matrix, for the goal ‘to know’.

Know                          Be known

Not know                    Not be known

Each of the four postulates has a complement facing it horizontally, forming the active and passive voices of a transitive verb. It also has an opposite (vertically in this matrix) and an opposition (diagonally). Here the difference between ‘opposite’ and ‘opposition’ is crucial! Games occur on the two diagonals between opposition postulates, so there are two games possible in this matrix: Know versus Not Be Known, and Be Known versus Not Know.

Two men might each want to know what the other is doing, without letting him know what they are doing. This would be a compulsive game where each is trying to get dominance over the other by having superior knowledge. Competition is a state where they both want to achieve the same goal but are in a relationship of rivalry rather than co-operation.

In a compulsive game, every postulate adopted by self has a corresponding exclusion postulate, which is the negative of its complement (Stephens, 1993). It is so called because it excludes self from the effect he’s trying to have on the opponent. The exclusion postulate corresponding to Know is Not Be Known, which applies to self while the Be Known postulate applies to not-self. Conversely, the exclusion postulate of Be Known is Not Know.

So their game play converges toward a balance between the dual intentions of achieving their own goal and blocking an opponent from theirs. Explicit competition arises in a compulsive game because of the exclusion postulate.

‘Eat/Be eaten/Not eat/Not be eaten’ is the ubiquitous games matrix in biology. To survive, anything needs to eat, and also to avoid being eaten until it has completed its life cycle. The feral doves that my wife feeds in the garden provide an example of explicit competition among animals engaged in a compulsive game about eating. A dove that is accustomed to being fed grain at a certain point will attempt to drive any other dove away from that place. Sometimes it will put so much effort into stopping the other from eating that it forgoes its own meal. Because it is a compulsive game player, it cannot rationally co-operate with the other bird to let them both eat in peace.

Competitors must be sufficiently similar before explicit competition is triggered: they must be in the same class for the purposes of the game. Runners in a race compete only against other registered entrants, paying no attention to dogs, spectators or birds even if these are moving faster than them. And those doves actively compete with other doves, but not with birds of other species that are eating the same food. I’ve often seen them ignoring the sparrows that eat their grain while they fight among themselves.

We can say, with Stephens and Wallace, that competition is just something perceived by the observer of a game and need not be consciously intended by the players. Tacit competition between organisms just happens, and if evolution can be said to be “trying” to do anything, it’s trying to minimise competition that causes waste and inefficiency.

There is no competition between individuals who have complementary postulates, such as ‘’control’ and ‘be controlled’. Nor is there competition if they have opposite postulates, like ‘eat’ and ‘not eat’. Competition only occurs between players who are trying to occupy the same role in a game that has become compulsive. Such a game is reduced to each player’s own postulate and its opposition, which is also their exclusion postulate.

Games begin between two different types of player (such as predator and prey, or businessman and customer) with distinctly opposed goals, but as the game becomes compulsive the players end up as rivals or competitors who are trying to reach the same goal. Predator and prey species both have the intention to eat but not to be eaten, and converge on strategies that maximise their chances of getting a meal without becoming a meal. Even in a ritualised game like football, success depends on a dual strategy of attacking one set of goal posts while defending a similar goal at the other end of the field.

This competitive state is exacerbated when their goal is a games goal such as ‘to win’ – as can be seen in every ritualised game from tiddlywinks to international politics. Anyone mired in a game that has become compulsive might agree with C.S. Lewis’ devil that “to be” inevitably means “to be in competition.”

Competition is characteristic of the final phase of a game where the games postulate and exclusion postulate have become condensed together. There is a cycle in a game that runs from co-operation between individuals with complementary roles, to conflict between individuals with opposing roles, to competition between individuals with identical roles.

In the final analysis, competition is just a subset of opposition. Stephens was right to dismiss it with scant attention.

References

Connell, J.H. (1990) Apparent versus “real” competition in plants. In Grace, J.B. & Tilman, D. Perspectives on Plant Competition. 9-26. (Academic Press: San Diego).

Grime, J.P. (1973) Competition and diversity in herbaceous vegetation – a reply. Nature 244: 310-311.

Lewis, C.S. (1942) The Screwtape Letters. (Geoffrey Bles: London).

Lewontin, R. (1961) Evolution and the theory of games. J. Theor. Biol. 1: 382-403.

Margalef, R. (1968) Perspectives in Ecological Theory. (University of Chicago Press: Chicago)

Maynard Smith, J. (1982) Evolution and the Theory of Games. (Cambridge University Press: Cambridge).

Stephens, D. H. (1979) The Resolution of Mind. (privately published: Sydney).

Stephens, D. H. (1993) The Exclusion Postulate. Tape recorded 20 April 1993.

Wallace, A.R. (1889) Darwinism. (Macmillan: London).



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