VIEWS: 7 PAGES: 14 POSTED ON: 7/9/2011 Public Domain
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, American Economic Review, Vol. 68, n.5, 896-908. [2] Dixit and Nalebuﬀ (1991), Thinking Strategically, Norton, New York. [3] Dougherty and Forsythe (1988), Complete information outcomes without com- mon knowledge, TARK WP. [4] EU Commission, Sony/BMG Case No COMP/M. 3333. [5] Green and Porter (1984), Noncooperative Collusion under Imperfect Price In- formation, Econometrica, Vol. 52, n.1, 87-100. [6] Herings, Peeters and Schinkel (2005), Intertemporal Market Division: A case of alternating monopoly., European Economic Review, Vol.49, 1207-1223. [7] Ivaldi, Jullien, Rey, Seabright and Tirole (2003), The Economics of Tacit Col- lusion, Final Report for DG Competition, European Commission. [8] MacLeod, Norman and Thisse (1987), Competition, Tacit Collusion and Free Entry, The Economic Journal, Vol. 97, n. 385, 189-198. [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. 14