Main trends of research in the social and human ... - unesdoc - Unesco

558 Raymond Boudon
ignorant of the other’s decision. The decisions of each of the two players, taken
together, produce a particular pay-off for either. The position can be expressed
by means of a pay-off matrix.
B
C d
A
b (2, -2) (-595)
In this particular game, if A chooses a and B chooses c, player A gains 4 and
player B loses 4 (4 francs for example); if A chooses b and if B chooses c, A wins
2 and B loses 2, etc.
A game like this is distinguished by several special characteristics; in particu-
lar it is a game for two players and it is a zero-sum game. In other words the
gain of one player is always equal to the loss of the other, whatever the decisions
they take.
Zero-sum games for two players were the first to be studied systematically
and it has been possible to establish a number of important theorems with
regard to them. In the situation described above, there is little difficulty in
defining the rationality of the decisions. Thus, as soon as one assumes that the
actors are sufficiently perspicacious to understand that the game which they are
playing is represented by the matrix shown above, A will choose a as his strategy,
as it guarantees him a gain of 4 or 2 according to whether B plays c or d, these
results being more in his favour than what he would obtain by playing b. Simi-
larly, it is in the interest of B to play d. This game is said to have a saddle point,
and its final result will be (3, - 3).
But zero-sum games for two players, despite their theoretical importance,
must be considered mainly as notional cases. It is interesting to explore them,
not so much because they faithfully reproduce real situations as because they
present elementary cases, whose properties it is logical to study before going on
to the more complex. Indeed, although there are many games which can be’con-
sidered as being effectually games for two players - armed conflict for instance -
it is seldom that a social situation characterised by a collection of inter-connected
decisions can be represented as a zero-sum game. One need only take the in-
stance of military or diplomatic conflicts: let us suppose that decisions taken by
two players A and B (nations in the present case) issue in an atomic war: it is
obvious that in this case the result of the game is disastrous for both players.
Now, in the case of non-zero-sum games it is difficult to give-a formal definition
of the notion of rational decision. Take for example the two-player, non-zero-
sum game defined by the following matrix:
B
C d