S. B. WOLF 319
that of a perfectly competitive market, despite imperfect
competition. On the surface, this equilibrium is extre-
mely different from that of the Cournot model, where
firms exercise market power as a negative function of the
elasticity of demand and the number of firms in the mar-
ket, resulting in an equilibrium price and quantity above
and below, respectively, that of the competitive equilib-
rium3 ([2], p. 243; [1], p. 23). However, the outcomes of
the Cournot and Bertrand models are thematically inter-
changeable; regardless of whether price or quantity is
chosen as a variable, static markets under imperfect
competition will generate an equilibrium total profit well
below that reached in a monopoly.
Without prior knowledge of whether the game will be
repeated, neither firm engages in collusive behavior be-
cause both seek to maximize profits in the current period.
However, these static models are highly questionable
both in their implications and assumptions. The Bertrand
model, it could be said, implies that agents seek to beat
their competitors at all costs, even if it means the com-
plete destruction of the profitability o f the entire industry;
it therefore assumes that agent utility is a function of
profit alone. If the Bertrand model were to be examined
using utility functions that in part depended on the
strength and profitability of the industry as a whole,
would that allow for the possibility of a cooperative
equilibrium between non-cooperative ag ents? This matter
requires further investigation. Yet the most blatant criti-
cism of the static oligop oly mod els is that the assumption
of a one-shot game interaction is extremely unrealistic,
no matter the industry; therefore, to assess cooperative
behavior in a more useful way, we much analyze these
markets in a dynamic context, with the present knowl-
edge that repeated games will occur in the future.
4. Tacit Collusion in Dynamic Oligopoly
In considering dynamic oligopoly, we allow for the mul-
tiple repetitions of the game-theoretic interaction in ques-
tion; agents are aware of this rep etition, so payoffs in the
current period take into account profits from future peri-
ods. To begin, we forgo the Bertrand assumption that the
firm with the lowest price will supply the entire market,
and instead move towards a Cournot equilibrium in
which price is below monopoly level bu t above marginal
cost. Yet rather than focusing on either price or o utput as
the competitive variable, let us consider them as two
sides of the same coin; joint restriction of output and
growth of prices will increase total profit while an indi-
vidual firm lowering prices and increasing output above
the monopoly level will steal market share from its com-
petitors—though not necessarily reducing their sales to
zero.
With all this in mind, we can now examine tacit collu-
sion in and of itself as the occurrence of cooperative ac-
tions in repeated non-cooperative games. Consider an
oligopoly market in which each firm has set its price
equal to the monopo ly price level and restricted outpu t to
its share of the monopoly quantity. Industry profit is
maximized and the market is an optimum collusive equi-
librium; however, any one firm could increase its indi-
vidual profit at the cost of total profit in the next period
by setting price below the collusive level and increasing
output according to the demand curve, maximizing indi-
vidual profits given the price and output choices of its
competitors. This threat of competitive behavior is al-
ways present in collusive equilibrium. However, each
firm is aware that any deviation from the collusive out-
come will, depending on the ability of other firms to de-
tect and swiftly respond, set off a price war that will
generate heavy losses in future periods. Thus, for each
individual firm, the decision to defect from the collusive
equilibrium in a given period depends entirely on the
tradeoff between current and future profit.
There are several factors identified by the literature
that are critical to evaluating this tradeoff. First, a poten-
tial defector must be able to evaluate the profits in the
long term associated with maintaining a cooperative
equilibrium. Assuming market demand and cost condi-
tions will be roughly the same across periods, firms will
earn a collusive profit
M in every period in which all
firms maintain the monopoly price and total output.
However, it is a fundamental theme in economics that the
value of a given income in the current period is much
greater than the value of the same amount in successive
periods; the present value of expected future profits must
reflect this by discounting future cash flows. This dis-
count rate—represented by r—will often reflect the cost
of capital per period for the firm. Firms with high levels
of capital depreciation and thus larger capital costs will
more heavily discount the present value of future inco me;
these firms will be less likely to maintain a collusive
equilibrium. Furthermore, the size of the discount rate r
is significant in determining not only the present value of
maintaining a collusiv e equilibrium in future periods, but
also how costly the future losses of profit caused by pun-
ishment will be relative to the immediate gains obtain-
able by defecting.
3The reason for this is that, in the Cournot model, individual firms set
quantities of output given perceptions that its rival will sell a fixed
quantity. The demand curve faced by each firm is much less elastic
than those in the Bertrand model, where a firm can win full share o
the market by undercutting its competitors even by a miniscule
amount making for an extremely elastic demand. (Church & Ware [2],
. 270).
Next, the immediate payoff associated with defecting
from the collusive equilibrium is the increased profit
level
R obtained by the firm that increases output and
decreases price while other agents maintain monopoly
level price and output. Th e size of this augmented payoff
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