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Alternating Monopoly and Tacit Collusion

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					       Alternating Monopoly and Tacit Collusion
                        Andrea Amelio∗and Sara Biancini†
                              Preliminary version


                                      May 14, 2005


                                          Abstract
      In this paper, we focus on the possibility of colluding in the time release of
      new goods. We consider a framework in which firms face uncertain demands
      and have information about the presence of present or future competitors’
      new products but not of their prices. We show that ATM (alternating time
      monopoly) may be Pareto improving with respect to classic tacit collusion
      and in some cases is the only equilibrium capable of sustaining tacit collusion.




Introduction
Tacit coordination or tacit collusion is one of the ways in which competition may
be threatened. In such a situation, firms are able to exert market power preventing
the emerging of the competitive equilibrium outcome. This doesn’t require commu-
nication between the parties as in the standard explicit collusion or official cartel,
but it can replicate the cartel outcome in terms of profits and price (or quantities).
So far the literature has widely investigated on many kind of collusive agreements,
starting from price and quantity coordination1 . Some of the factors which facilitate
collusion has been analyzed in order to derive policy recommendation, in particular
for merger control.
A natural extension to the classical price coordination model, has considered the
ability of sharing (tacitly or explicitly) the geographical market2 . Collusion, in this
case, takes the form of respecting exclusive territories, making firms able to extract
monopoly rent on their territory.
In some sense, geographical partition and temporal partition can be seen as two
  ∗
    GREMAQ, Toulouse University. E-mail: andrea.amelio@univ-tlse1.fr
  †
    GREMAQ, Toulouse University. E-mail: sara.biancini@univ-tlse1.fr
  1
    For a complete review of this issue, see Ivaldi, Jullien, Rey, Seabright and Tirole (2003)
  2
    See for instance Capozza and Van Order (1978) and MacLeod, Norman and Thisse (1987)

                                               1
analogue options to create a situation in which the firms are let alone on a certain
share of the market. Firms may alternate their presence on the market because they
have tacitely decided to share the time of activity. Either splitting geographically
the market enjoying half of the demand either splitting intertemporally the market
enjoying the total demand for a period of the time gives similar incentive to firms.
Very little work has been done so far on the ability of firms to share (tacitly or
explicitly) the market on an intertemporal basis. Nevertheless, we think that this
is likely to be an important coordination device in many markets. If we consider
for instance big firms producing highly homogeneous goods, some evidence has been
already put into attention concerning behaviors that seem to reproduce time co-
ordination (See the example of Coca-cola and Pepsi discount campaigns in Dixit
and Nalebuff (1991)). We claim media markets could be a particularly fertile envi-
ronment for this kind of coordinating behavior. TV stations often alternate their
prime shows (like movies, new TV-series or sports event) in order not to compete
on the same public. Movies which represent big events for the Majors are launched
by advertising campaigns which announce the time they will be on the screens with
important time lag. Music festivals are usually concentrated in precise seasons. In
all these examples, we see that the particular marketing strategy (big advertising
campaign for events in precise periods of the year, the month or the week) can serve
as a coordination device for firms operating in these sectors. This becomes more
important if other forms of coordination are indeed difficult to exploit, due to the
specificities of the markets. In a recent decision of the EU Commission (Sony/BMG
Case No COMP/M. 3333), the difficulty of observing the price of competitors has
been evocated as an element to be taken into account in order to assess the likelihood
of an existing collusive behavior. In particular, in media markets, deviations on the
final price is difficult to observe due, for instance, to the discount policies of the
distributor. Sometime this becomes just meaningless, due to some exogenous form
of price homogeneity (newspapers, cinema). The problem is that, when referring
to the difficulty to observe or change the price (to make retaliation credible) as an
impediment to coordination, one should first take into account viable alternatives
to coordination in prices, potentially capable of generating a collusive outcome. In
all media markets, the release of new products, in particular premium products,
is easily observed because they are systematically announced through advertising
campaigns. We think it is thus important to look at the specific opportunities of
collusion in markets displaying this mode of competition.
There are a very few contributions in the literature considering this idea of coor-
dinating on the time release of products. Time to market has rarely be considered
a strategic tool. Literature on R&D is concentrated on the fact that reducing the
”time to market” is a dominant strategy for all the firms, since it can assure the
possibility of enjoying temporary monopoly rent on the innovation. What has not
been considered insofar is the possibility that some kind of firms, having a portfolio
of new products, can deliberately choose to delay the introduction of new products
in order to get a more favorable period, perhaps a time in which she is the only

                                          2
one active. This can be the case in markets in which bringing a new good into the
market requires some time (for instance to reach the potential customers trough
advertising) and consumers are willing to buy new goods repetitively, unrespective
to their consumption behavior in the past (consumers are willing to buy a new disc,
movie, newspaper at every period).
The first paper, to our knowledge, to take the possibility of alternating monopolies
into account is Dougherty and Forsythe (1988), which looks more generally to the
possibility of reproducing first best outcomes relaxing common knowledge assump-
tions. They consider a simplified problem in which there is no time discount and they
find that alternating strategies can be a decentralize way to reach a collusive out-
come sustainable without any side-payment. Omitting to put a time discount factor
in the model seems very restrictive, since any alternating strategy presumes some
player ”waiting”. The discount factor will play an important role in our analysis,
as in other intertemporal games, as we will see. This intuition about the possibility
of sharing the market intertemporally has not been further developed until very re-
cently. Nevertheless, some empirical and experimental studies have started to check
for the possibility of this kind of equilibrium to emerge in a market situation. Zil-
lante (2004) present an experiment trying to test the emerging of time coordination.
The results are mixed and difficult to interpret, especially because there is still a lack
of theoretical knowledge about what are the characteristics which make a market
exposed to this kind of collusive behavior.
From a theoretical point of view Herings, Peeters and Schinkel (2005) have con-
tributed to the analysis of this issue considering the emerging of an alternating
monopoly as a Markovian equilibrium in a symmetric duopoly in which also the
Cournot equilibrium is sustainable. Their aim is to show that this equilibrium can
emerge in a Markovian set, without employing any notion of collusive behavior,
such as retaliation strategies. Firms just play a strategy of the form ”entry at t with
probability 1 if you are not already in the market” and ”exit at t with probability
1 if you were in the market at t − 1”. Of course, this simple strategy works in a
symmetric monopoly. The equilibria has been numerically simulated for some values
of the intertemporal discount factor δ. The natural question is why a firm should
play this game in a more complicated setting in which they have some memory and
can sustain more sophisticated decentralized collusive equilibria as in the classic
tacit collusion models. For the realism of the model, it seems necessary to show
some situation in which this way of colluding is indeed the one which firms could
rationally choose as a response to a particular environment.
One very natural application is the Green and Porter (1988) framework, in which
firms suffer from shocks in demand which make impossible to distinguish perfectly
the deviation of a rival from an exogenous negative shock on demand. Zillante (2003)
compares one possible example of equilibrium with stochastic demand (symmetric
firms, retaliation period equal to T=1) with the alternating monopoly outcome. He
shows that ATM can be chosen over some standard collusive equilibrium. This is
not further developed, since the main aim of this paper is to perform an empirical

                                           3
investigation (using data on the US baseball card industry), in order to detect some
empirical evidence on the existence of alternating strategies.
Aim of our paper is to put forward a theoretical investigation of a form of tacit
collusion based on alternating monopoly. We show how demand uncertainty can
favor the emerging of an alternating monopoly, as opposed to other standard forms
of tacit collusion. The intuition is that ATM can solve the uncertainty problem
relying on fewer or cheaper information (the presence of the competitor in the mar-
ket as opposed to the price or the quantity produced by the competitor). We show
under which conditions on time impatience and degree of inefficiency of retalia-
tion strategies (related to uncertainty about demand) ATM may dominate classical
price coordination. The paper also aims to analyze robustness of this new collusive
equilibrium. Insofar, in the few examples quoted above, only the symmetric cost
case has been considered. This facilitates the individuation of the candidate ATM
equilibrium (each firm produces one period out of two). The drawback is that it
restricts the analysis to a very specific situation. The reminder of the paper deals
with extensions of the basic model, trying to enrich the framework, therefore the
complexity of the market, and looking at how the ATM equilibrium performs under
these additional assumptions. We show that under asymmetry in costs, the peculiar
characteristics of an ATM (alternating the presence on the market over discrete pe-
riods) is a less flexible collusion device than colluding on the instantaneous market
shares, rising doubts about the possibility of this collusive practice to be successful
under cost asymmetries.
Afterwards, we consider a N firms framework and we look at the efficiency property
of ATM. Contrarily to the previous extension, we found that ATM seems to respond
better to an increase of players in the collusive agreement.


1       The benchmark: tacit collusion with demand
        uncertainty
To formalize the idea of an alternating monopoly, we need to build a framework
which we use as a benchmark and later to suppose that the firms insist in an equi-
librium which involve alternation.
We consider a simplified market in which to symmetric firms compete in prices in
a Bertrand framework.3 . The goods are substitutes and are produced at a constant
marginal cost c, normalized to zero. Therefore the consumers will buy from the firm
which sets the lower price and demand is split in halves if firms charge the same
price.

Assumption 1 The demand is uncertain and in every period there are two possible
states of nature.
    3
    Insofar, we restrict the analysis to the case in which there are two firms. Note that one of the
extensions in the paper analyzes a framework with N firms.


                                                4
Demand is stochastic and with probability α there is no demand (”low state”). With
probability (1 − α), the demand is positive (”high state”) and it is equal to D(p).
The realizations of the demand are i.i.d. over time. We denote with pm and Πm
respectively the monopoly price and the monopoly profit.

Assumption 2 Prices are not observable by firms.

Under these assumptions, each firm does not observe the reason of a low demand.
This could be due to the realization of the ”low state” or to a competitor’s price
cut. This specification restricts the attention to a situation in which at each period
firms make either zero profit or the monopoly profit. However, this simplification
allows us to focus more on the nontrivial signal extraction problem that firms face.
Given the information structure of the game, each firm cannot surely understand
the reason of a low demand. Each firm could be victim of ”bad luck” since the state
of nature is low indeed or she could be victim of a price cut but again each firm is
not able to distinguish that.

Assumption 3 The time horizon is infinite.

Firms interact for a infinite number of periods. Given this assumption, we want
to look at a collusive tacit equilibrium in which, in the collusive phase, the firms
coordinate on charging the monopoly price pm until a firm makes zero profit (this
event is observed by both firms).

Assumption 4 Firms play a trigger strategy.

The occurrence of zero profit triggers the punishment phase which is the Bertrand
outcome. We assume that firms stick to the punishment phase forever. This is one
of the possible equilibrium strategies which sustain collusion, and it is the one which
indeed maximizes the scope of collusion.
If we suppose that at time t, the game is in the collusive phase, the net present value
V + of the firms is thus4 :

                                           Πm
                         V + = (1 − α)        + δV +     + αδV −
                                            2
and in the punishment phase:

                                         V − = 0.
In this model, the participation of the firms to a collusive agreement is straightfor-
ward since a noncollusive situation will determine zero profit. However, the firms
can have incentive to deviate from the collusive agreement. Therefore, we must add
  4
   Note that since there are no asymmetries between the two firms, it is optimal to share the
market in equal shares.



                                             5
in the analysis a condition that states that no firm finds deviation attractive. This
is given by the incentive constraint:

                            V + ≥ (1 − α)(Πm + δV − ) + αδV − .
The previous equation simply states that the net present value in the collusive phase
must be bigger than the expected value of the profit from deviation and a retaliation
period which lasts forever. The threshold above which a collusive equilibrium is
sustainable is thus:
                                                 1
                                      δ ∗ (α) =
                                            2(1 − α)
therefore collusion is sustainable for δ ≥ δ ∗ .
It is worth noticing that for every length of the punishment period this equilibrium
doesn’t exist if the level of demand uncertainty is high (α ≥ 1 ). On the contrary, if
                                                               2
α < 1 , tacit collusion is sustainable and the previous condition holds.
      2



2       The Alternate Time Monopoly (ATM)
Consider now, in the same framework as before, an equilibrium in which firms in
the collusive phase alternate the presence of them in the market. Suppose firm 1 is
in the market only in odd periods and firm 2 in even periods.
Assumption 5 Each firm is able to see if the competitor is selling in the market.
This assumption states that firms are informed whether a competitor is (or it will be)
active at a certain period of time. This is compatible with a situation in which firms
cannot observe prices but at least they can see whether the competitors are actively
participating to the market selling their products. We can also think that collecting
information about the release of products is cheaper than gathering information
about prices.
This assumption is crucial because it allows each firm to solve the signal-extraction
problem. The trade-off is therefore between the cost of the inefficiency related to
the signal-extraction problem and the costs of being out of the market one period
over two subject to the incentive of not breaking the collusive agreement5 . The net
present value of firm 1 is thus:

                           V1+ = (1 − α)(Πm + δ 2 V1+ ) + αδ 2 V1+
and the value of firm 2 is thus:

                                   V2+ = (1 − α)(δΠm + δ 2
    5
    The issue of whether this particular arrangement ”one period in-one period out” is the optimal
one, is undertaken in the asymmetric cost paragraph. However, we can state here that given the
symmetric nature of the two firms the relevant equilibrium is an arrangement of the type ”one
period in-one period out”

                                                  6
                                   V2+ ) + αδ 2 V2+ .
The two firms face different time constraints which are respectively:

                      V1+ ≥ (1 − α)Πm + δ(1 − α)Πm + δ 2 V1−
for firm 1 and

                              V2+ ≥ (1 − α)Πm + δV2−
for firm 2. Vi− = 0 for i = 1, 2. Both incentives
    constraints describe the situation in which the two firms deviate and decide to
be active in the market during the period out of the tacit agreement enjoying the
expected monopoly profit undercutting the competitor but suffering for all the future
periods the retaliation, which consists on a Bertrand zero profit equilibrium.
At equilibrium, the threshold above which the two firms can sustain collusion is:
                                             √
                                      ∗        5−1
                                     δAT M =        .
                                                2
                      ∗
Therefore for δ ≥ δAT M the collusion with an alternate monopoly equilibrium is
sustainable.
                                   ∗                                              ∗
Comparing the two thresholds δAT M and δ ∗ , the first important point is that δAT M
doesn’t depend on the demand uncertainty parameter α. As already said, the activ-
ity of firms is a disposable information for firm themselves and therefore alternation
allows to solve firms’ signal-extraction problem. On the other hand, the equilibrium
is given by an alternating strategy which imposes firms to wait in non-releasing pe-
riods. This has a cost, depending on the time impatience represented by discount
factor δ. The independency of the ATM equilibrium from the level of uncertainty in
the economy does not constrain the existence of the equilibrium to a certain range
of α, as it does happen for the benchmark equilibrium. As previously said, the
benchmark equilibrium exists for level of α strictly less that 1/2. We can therefore
conclude that when the signal extraction problem is very severe the alternating is
the equilibrium that prevails since it is the only one which exists.
We now concentrate on the range of α in which both the equilibria exist. It is
straightforward to notice that when there is no uncertainty of demand (α = 0),
the standard collusion equilibrium in which the two firms are both active in the
                                          ∗
market is easier to sustain (δ ∗ (0) < δAT M ). The burden of alternation is not com-
pensate by any other gain. On the contrary, when the uncertainty of demand is very
high the burden of waiting one period is offset by a gain in the resolution of the
signal-extraction problem which makes easier to collude on the base of an alternate
presence in the market.
To complete the analysis, we draw a picture (See the Figure) in which we summarize
the results.


                                           7
The graph shows four regions. Region I is the area in which only the benchmark
equilibrium is feasible. For values of α relatively small, the signal extraction problem
(”retaliation or bad luck”) of the benchmark agreement is relatively small. The
signal extraction problem is not severe and the discount δ is not high enough to
make feasible an alternate equilibrium.
Region IV is the opposite situation. The demand shock, and consequently the signal
extraction problem, is very severe and the benchmark collusion is not sustainable.
Only ATM is sustainable. Firms are willing to alternate and still enjoy the monopoly
profit solving the information problem which causes the failure of the standard
benchmark agreement.
Regions II and III are hybrid zones in which both equilibria are feasible. Therefore,
in this situation both equilibrium could arise.
One possible way to determine what is likely to happen in these undeterminate
regions is to compare the value of the firms in the two cases. In fact, if both
equilibria are feasible but one is more profitable, one can expect firms to converge
on this. The net present values of firms (Vi+ for i = 1, 2 and V + respectively)
are different. The comparison of the different net present values between the two
collusive equilibrium gives the following two conditions:

                                  2(1 − α)δ − δ 2 ≤ 1
and

                                 1 ≤ 2δ − (1 − 2α)δ 2 .




                                           8
If these conditions hold, the net present values of the ATM is bigger than the one
of the benchmark case 6 . These two conditions (dashed line) split in two the hybrid
region delimiting Region II and Region III. Regions II is the area in which the
benchmark dominates the alternate collusive equilibrium. In fact, V + is negatively
affected by uncertainty, which triggers the possibility of inefficient retaliation (with
probability α, retaliation occurs even if no firm has deviated form the collusive
behavior). When α is relatively small, the probability of inefficient retaliation is
thus small and the value of the firm is grater under the benchmark (for any δ ≤ 1).
In Zone III is the opposite holds.


3       Cost Asymmetries
Cost asymmetries are a common feature of many markets and in order to check the
robustness of the ATM, we try to embed this assumption into the original model.
Suppose the two firms have asymmetric marginal costs ci , i ∈ {H, L} and we do
the same analysis to verify the property of the alternate equilibrium under this
extension.
This enriched framework generates some structural difficulties to the ability of the
firm to collude. Denoting cL the marginal cost of the more efficient firm and cH
the one of the less efficient, we define the profit of the firm as (p − ci )D. In order
to simplify the exposition we take inelastic demand D and a reservation price of
consumers which is constant and equal to r. Therefore, the monopoly price is pm = r
and the firms identify this as the optimal price to charge consumers whatever the
marginal costs are. The main effect that the costs asymmetry assumption generates
is that the more efficient firm suffers from a lack of incentive in participate in the
collusion, due to the more restricted ability of the less efficient one to punish the
eventual deviation. In a Bertrand model, retaliation does not push the more efficient
firm to zero profit. The best that the less efficient can do is to charge a price equal
to cH leaving to the more efficient firm a positive profit (cH − cL )D. In order to
reduce this incentive problem, we focus on an equilibrium in which the market share
of firm L, namely β, is increased above one half, in order to react to its increased
incentive to deviate.
                                                                                  +
Suppose that at time t the game is in the collusive phase, the net present value VL
of the more efficient firm is thus:

                        +                           +      −
                       VL = (1 − α) (r − cL )βD + δVL + αδVL
and in the punishment phase:

                       −                           −      −
                      VL = (1 − α) (cH − cL )D + δVL + αδVL .
    6
     Note that the first one is always verified for all the values of α < 1/2 and δ in the interval
[0,1].



                                               9
In the same way, in the collusive agreement, the net present value of the less efficient
firm is thus:

                  +                                 +      −
                 VH = (1 − α) (r − cH )(1 − β)D + δVH + αδVH
and in the punishment phase:

                                              −
                                             VH = 0.
For the reasons mentioned above, the firm H will have less power to discipline firm
L, since the retaliation is less effective. The incentive constraint of the low-cost firm
is thus:

                       +                          −        −
                      VL ≥ (1 − α)((r − cL )D + δVL ) + αδVL
and for the high-cost firm:

                      +                          −        −
                     VH ≥ (1 − α)((r − cH )D + δVH ) + αδVH .
As already said, in order to improve the collusive agreement partially solving the
asymmetries between the two firms, the market share of firm L, namely β is increased
above > 1/2. We restrict the attention to the market share β ∗ which maximizes the
payoff of firm L, keeping firm H efficient in the collusive agreement and as a result
of the maximization, β ∗ = (1 − α)δ. The new threshold above which tacit collusion
is sustainable is thus:
                                                     1
                              δ ∗ (γ, α) =
                                               (2 − γ)(1 − α)
            H −c
where γ = cr−cLL represents a degree of asymmetry in the industry7 . This is consis-
tent with the stylized model since it is a generalization of the previous threshold.

3.1    ATM with Cost Asymmetries
In the case of ATM, firms have to share the time of permanence in the market. In
the case of asymmetry, they could share unevenly the periods of activity in order to
make coordination feasible for every type of firm. In other words, firms coordinate on
sharing the infinite number of periods providing asymmetric allocations of periods.
As in the benchmark case, we look for the periods’ optimal share which, intuitively,
gives more periods to the more efficient firm still making the less efficient firm willing
to participate.
Call T and S the number of periods in which, respectively,the firm L and firm H
stay in the market. We focus on a type of equilibrium in which the more efficient
  7                                 1
   Note that we assume γ ≤ 2 −   (1−α)δ .   This insures no to have the incentive constraint of the
more efficient binding.




                                                10
firm decides to be active in the market for the first T periods and the less efficient
one the last S periods8 . Therefore, the two firms’ values are:
                                    T −1
                  +                                                 +              +
                 VL    = (1 − α)(          δ i (r − cL )D + δ T +S VL ) + αδ T +S VL
                                    i=0

and
                                    S−1
                  +                                                +              +
                 VH    = (1 − α)(         δ i (r − cH )D + δ T +S VH ) + αδ T +S VH .
                                    i=0

It is easy to see that the value of the more efficient firm increases with T and de-
creases with S while it is the opposite for the less efficient one. As in the benchmark
firm L has more incentive to deviate. In order to sustain collusion it will have to
satisfy the following incentive constraint:
                                     T
                   +                                                −              −
                  VL   ≥ (1 − α)(          δ i (r − cL )D + δ T +2 VL ) + αδ T +2 VL
                                    i=0
                                     −                        −      −
where, as in the benchmark case, VL = (1 − α) (cH − cL )D + δVL + αδVL . Sym-
metrically, the less efficient one’s incentive constraint is:

                          +                          +        +
                         VH ≥ (1 − α)((r − cH )D + δVH ) + αδVH
           −
where VH = 0. It is important to remark that both the collusive payoffs of the
two firms decrease with the sum T + S. We look for an equilibrium which increases
as much as possible the number of T periods in which the more efficient firm is
active, maintaining the sum T+S minimal. This consists in a situation in which the
efficient firm has the maximal incentive to collude and the less efficient firm wants
to participate without waiting to much to be active. The optimal time share will be
T ∗ (δ, γ) and S ∗ (δ).
We have thus seen that the peculiarity of ATM (the necessity for the firms to stay
out in some periods) induces a difficulty in determining the optimal time share. The
discrete nature of the periods of activity make them a less flexible instrument with
respect to the instantaneous market share β of the benchmark.
For a low level asymmetry close enough to zero, we can restrict the attention to the
standard ATM: firms still alternate at every period9 .
   8
     We can also think about other more complicated types of alternation. However, we think that
we should stick to simple alternation strategy. Alternate periods of activity seems to us one of the
simplest types.
   9
     The maximization in order to find the optimal active time length T ∗ (δ, γ) and S ∗ (δ) is rather
complex. Insofar, we have focused on little costs asymmetries represented by γ and to solve
the maximization problem we use an heuristic method mixed by consideration concerning the
simplicity of the tacit agreement. By studying the problem with γ close enough to zero and trying
alternatives which are close enough to the one considered under symmetric costs, we concluded that
the symmetric costs ATM still the best arrangement for little costs asymmetries too. (Preliminary)



                                                   11
For this case, the best strategy consists of T ∗ (δ, γ) = S ∗ (δ) = 1. Therefore the
threshold for little cost asymmetry is thus:

                        ∗             5 − 6γ + γ 2 − (1 − γ)
                       δAT M (γ) =
                                           2(1 − γ)
which is a generalization of the previous ATM threshold in case of perfect cost
symmetry.
It is possible to compare this threshold with the one of the benchmark. In order
to run the comparison, we start by looking at the two optimized (with respect the
asymmetry γ) equilibria for little asymmetry in the economy. Both the thresholds
highlight positive derivatives with respect the asymmetry. Cost asymmetries make
collusion more difficult both in the benchmark and in the case of ATM. However,
                                                              ∗ (γ,α) ∂δ ∗    (γ)
it possible to show that for little asymmetry and α given, ∂δ ∂γ < AT M . This
                                                                           ∂γ
implies that there is still a threshold of α under which the ATM equilibrium is the
only one feasible but it adapts less efficiently than the benchmark when the cost
asymmetry increases. This shows that both the collusive equilibria are weaken by
a cost asymmetry but the optimal market share agreement reacts better than the
ATM equilibrium to cost asymmetry.


4    N Firms (very preliminary)
In this section, we want to look at a case in which the market has more players. As
in the cost asymmetric the benchmark and the ATM will react differently to this
additional assumption and we expect that both the strategies are worse-off by the
raise of the players. However, it is interesting to see in relative terms which one
reacts better.
Suppose the market is less concentrated, the number of firm is equal to N and they
are symmetric. Intuitively, the collusive equilibrium is more difficult to arise since
every firms a decreasing share of the monopoly profit as the number of the firm
increases. Therefore, the incentive to deviate is stronger the more are the firms in
the markets. The threshold above which collusion is sustainable in the benchmark
model becomes:

                                                 N
                            δ ∗ (N, α) =
                                           (N − 1)(1 − α)
which is again a generalization of the stylized model. As in the case of asymmetric
costs, collusion is more difficult to sustain.
The ATM equilibrium is affected in the same way. In analogy with the duopoly case,
we take simple symmetric alternating strategies in which each firm enters in turn
for one period and then wait until each firm has been on the market one period.
If there is entry of two firms at the same period, retaliation occurs. In this case,
firms participating to the collusive agreement has to wait more and therefore firms


                                           12
are more tempted to deviate. The analysis in this particular equilibrium gives a
threshold which is determined implicitly by the following equation10 :

                                      ∗N
                                     δAT −1 = 1 − δAT M .
                                         M
                                                   ∗N

                 ∗
The threshold δAT M (N ) is obviously a function of N and as we have been expecting
it is increasing in N . Therefore, ATM is consistent with the common view, that
the more are the players in the market the more is difficult to sustain collusion.
However, if we compare the two thresholds of the different equilibrium we notice
        ∗ (N,α)  ∂δ ∗    (N )
that ∂δ ∂N > AT M . This means that the less the market is concentrated, the
                      ∂N
more the firm will tend to prefer the ATM equilibrium.


5      Conclusion and policy implication (very prelim-
       inary)
Aim of this paper is to study a specific way of colluding (ATM) which is consistent
with markets showing some particular features. We have shown that the difficulty
of observing prices and the existence of particular marketing strategies providing
easy (or very cheap) information about other dimensions of activity of the firms
(release of new products), can offer an opportunity of tacit collusive behavior of
different nature with respect to classical price coordination. ATM is one of the
possible tacit agreements which firms operating in those market can put in place.
This can be important from policy point of view, for instance in merger policy, where
the potential for tacit coordination is to be taken into account. The results of this
paper suggest to policymakers the potential importance of less known types of tacit
collusive agreement for merger clearing decisions.




  10
     The equation comes from the incentive constraint of the last firm active in the market. This
is the most stringent condition to meet, therefore it is the relevant one.




                                              13
References
 [1] Capozza and Van Order (1978), A Generalized Model of Spatial Competition,
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 [2] Dixit and Nalebuff (1991), Thinking Strategically, Norton, New York.

 [3] Dougherty and Forsythe (1988), Complete information outcomes without com-
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 [4] EU Commission, Sony/BMG Case No COMP/M. 3333.

 [5] Green and Porter (1984), Noncooperative Collusion under Imperfect Price In-
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 [6] Herings, Peeters and Schinkel (2005), Intertemporal Market Division: A case
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 [7] Ivaldi, Jullien, Rey, Seabright and Tirole (2003), The Economics of Tacit Col-
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 [8] MacLeod, Norman and Thisse (1987), Competition, Tacit Collusion and Free
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 [9] Zillante (2003), Spaced-Out Monopolies: A Theory of Alternating Products Re-
     lease Times, Working Paper.

[10] - (2004), Intertemporal Collusion with Multiperiod Siganlling, Working Paper.




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