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We study price personalization in a two period duopoly with horizontally differentiated products. In the second period, a firm has collected detailed information on its old customers, using it to engage in price personalization. Customers, when returning to buy, may choose to incur a cost in order to access the standard offer of their previous provider in addition to its personalized offer and the standard offer of its rival. The analysis confirms that firms’ second period profits are boosted when consumers are active in this sense (being equal to perfect price discrimination ones when initial market hares do not differ too much) but it reveals that this advantage is dissipated and possibly over-dissipated by the resulting fierce first-period competition for the market. Two-period aggregate profits are smaller with active customers provided the consumers are naive and/or the firms patient enough. Consumers’ access to both personalized and standard firms’ offers which benefit the oligopolists in mature markets may plausibly hurt them in emergent ones. The equilibrium is shown not to depend on the level of the cost as long as it is below some critical value.
We consider a nondurable good monopolist that collects data on its customers in order to profile them and subsequently practice price discrimination on returning customers. The monopolist’s price discrimination scheme is leaky in the sense that an endogenous fraction of consumers choose to incur a privacy cost to conceal their identity when they return in the following periods. We characterize the Markov perfect equilibrium of the game under two alternative customer profiling regimes: full information acquisition (FIA) and purchase history information (PHI). In both cases, we find that, contrary to what could be expected, the monopolist’s aggregate profit is not monotonically increasing in the level of the privacy cost, but a U-shaped function of it, leading to ambiguous profit effects: a reduction in privacy costs increases the fraction of customers who choose to be anonymous (detrimental profit effect), but it also softens the firm’s introductory price, reducing the pace at which prices targeted to new customers fall over time (positive profit effect). When comparing results under FIA and PHI, we find that market expansion is faster, and more customers conceal their identity under FIA than under PHI. Equilibrium profits are also higher in the FIA case. Although equilibrium profits are U-shaped functions of the privacy cost in both profiling regimes, they tend to be globally decreasing with the privacy cost under PHI and globally increasing under FIA.
We consider a general equilibrium model with vertical preferences, where workers and consumers are differentiated respectively by their sensitivity to effort and their intensity of preference for quality. We consider a public monopoly, i.e. which is owned equally by all individuals. The question is under which conditions the firm will be privatized and at which rate/price. The decisions are taken through majority vote in a plurality system. When the firm is controlled by the State, the price is determined through a vote among all the population. Otherwise, the price is the one which maximizes the profit. We prove that, when the maximum disutility of working in the firm is higher than the maximum utility of consuming its output, privatization may emerge as a possible choice of the majority, even if no hypothesis is made on the efficiency of a private management relative to a public one.
A durable good monopolist faces a continuum of heterogeneous customers who make purchase decisions by comparing present and expected price-quality offers. The monopolist designs a sequence of price-quality menus to segment the market. We consider the Markov perfect equilibrium (MPE) of a game where the monopolist is unable to commit to future price-quality menus. We obtain the novel results that: (a) under certain conditions, the monopolist covers the whole market in the first period (even when a static Mussa–Rosen monopolist would not cover the whole market), because this is a strategic means to convince customers that lower prices would not be offered in future periods and that (b) this can happen only under the stage-wise Stackelberg leadership assumption (whereby consumers base their expectations on the value of the state variable at the end of the period). Conditions under which MPE necessarily involves sequentially trading are also derived.
Using a Markov-perfect equilibrium model, we show that the use of customer data to practice intertemporal price discrimination will improve monopoly profit if and only if information precision is higher than a certain threshold level. This U-shaped relationship lends support to a popular view that knowledge is good only if it is sufficiently refined. When information accuracy can only be achieved through costly investment, we find that investing in profiling is profitable only if this allows to reach a high enough level of information precision. Consumers expected surplus being a hump-shaped function of information accuracy, we show that consumers have an incentive to lobby for privacy protection legislation which raises the cost of monopoly's investment in information accuracy. However, this cost should not dissuade firms to collect some information on customers' tastes, as the absence of consumers' profiling is actually detrimental to consumers.
This paper investigates duopoly competition when horizontally differentiated firms are able to make personalized product-price offers to returning customers, within a behavior-based discrimination model. In the second period, firms can profile old customers according to their preferences, selling them targeted products at personalized prices. Product-price personalization (PP) allows firms to retain all old customers, eliminating second-period customer poaching. The overall profit effects of PP are shown to be ambiguous. In the second period, PP improves the matching between customers’ preferences and firms’ offers, but firms do not make any revenues in the rival’s turf. In the Bertrand outcome, second-period profits only increase for both firms if the size of their old turfs are not too different or initial products are not too differentiated. However, the additional second-period profits may be offset by lower first-period profits. PP is likely to increase firms’ overall discounted profits when consumers’ (firms’) discount factor is low (high) and firms’ initial products are exogenous and sufficiently different. When the location of initial products is endogenous, profits are hurt because of an additional location (strategic) effect aggravating head-to-head competition in the first period. Likewise, when a fraction of active consumers conceals their identity, PP increases second-period profits at the cost of aggressive first-period price competition. Finally, we show that the room for profitable PP enlarges considerably if firms rely on PP as an effective device to sustain tacit collusive outcomes, with firms credibly threatening to respond to first-period price deviations with second-period aggressive relocations of their standard products.
This paper was accepted by Matthew Shum, marketing.
We study price personalization in a two period duopoly with vertically differentiated products. In the second period, a firm not only knows the purchase history of all customers, as in standard Behavior Based Price Discrimination models, but it also collects detailed information on its old customers, using it to engage in price personalization. The analysis reveals that there exists a natural market for each firm, defined as the set of customers that cannot be poached by the rival in the second period. The equilibrium is unique, except when firms are ex-ante almost identical. In equilibrium, only the firm with the largest natural market poaches customers from the rival. This firm has highest profits but not necessarily the largest market share. Aggregate profits are lower than under uniform pricing. All consumers gain, total welfare is higher herein than under uniform pricing if firms’ natural markets are sufficiently asymmetric. The low quality firm chooses the minimal quality level and a quality differential arises, though the exact choice for the high quality depends upon the cost specification.
This paper accounts simply for the link between higher education and the productive economy through educated workers. We study a model of vertical successive monopolies where students/workers acquire qualification from a University then “sell” skilled labor to a monopoly which itself sells its final product to consumers, linking through quality the education sector to the labor and output markets. We determine the optimal share the State should keep in the University to compensate for the market imperfections, while taking into account the inefficiencies of public management. The resulting partially privatized University fixes the tuition fees so as to maximize a weighted sum of profits and social welfare. We derive the optimal public share under the hypothesis that the State may subsidize the tuition fees/University losses, then under the constraint that the University should make a nonnegative profit. We prove that in both cases, the State should keep a substantial share (higher under the first hypothesis) in the University, unless public management is too inefficient in which case the University's management should be completely private.
The citizen candidate models of democracy assume that politicians have their own preferences that are not fully revealed at the time of elections. We study the optimal delegation problem which arises between the median voter (the writer of the constitution) and the (future) incumbent politician under the assumption that not only the state of the world but also the politician's type (preferred policy) are the policy-maker's private information. We show that it is optimal to tie the hands of the politician by imposing both a policy floor and a policy cap and delegating him/her the policy choice only in between the cap and the floor. The delegation interval is shown to be the smaller the greater is the uncertainty about the politician's type. These results are also applicable to settings outside the specific problem that our model addresses.
This paper shows that the platforms’ private information on demand may explain the empirical observation that platforms like Amazon resell high-demand products, while acting as marketplace for low-demand goods. More precisely, the paper examines the strategic interaction between a seller and a better informed platform within a signalling game. We consider that the platform may choose between two distinct business models: act as a reseller or work as a pure marketplace between the buyers and the seller. The marketplace mode, which allows to internalize the spillover between the platform’s sales and the seller’s direct sales is always preferred for a low-value good. The reselling mode, which allows the platform to take advantage of its private information, may be selected in the case of high-value goods provided that (i) the externalities between direct sales and platform sales are not too strong and (ii) the difference between consumers’ willingness to pay for the high and the low-value goods is large enough. Under these conditions, the game displays a Least-Cost Separating Equilibrium in which the platform works as a marketplace for low-demand goods, while it acts as a reseller in the case of high-demand goods.
Under triopoly and Cournot competition, we study an infinite horizon Markov perfect equilibrium merger game in which in each period one of the firms (“the Buyer”) selects a bid price and then the two sellers accept or reject this offer with some probability. The possibility of a “war of attrition” equilibrium in which the seller who outlasts the other is then able to sell in the following period at a greater price, is a distinct feature of the model. Delayed monopolization is all the more likely when the discount factor is small and the ratio duopoly/ triopoly profits is important. Two other equilibria are shown to be possible: an unmerged and an immediate monopolization equilibrium. Each equilibrium is shown to correspond to a different set of parameter values. The two special cases of linear and constant price elastic demand functions are fully characterized.