On nonrenewable resource oligopolies: The asymmetric case

We give a full characterization of the open-loop Nash equilibrium of a nonrenewable resource game between two types of firms differing in extraction costs. We show that (i) there almost always exists a phase where both types of firms supply simultaneously, (ii) when the high cost mines are exploited by a number of firms that goes to infinity the equilibrium approaches the cartel-versus-fringe equilibrium with the fringe firms acting as price takers, and (iii) the cheaper resource may not be exhausted first, a violation of the Herfindahl rule, that may be detrimental to social welfare.     

Nonlinear pricing in spatial oligopoly

A model of duopoly competition in nonlinear pricing when firms are imperfectly informed about consumer locations is analyzed. A continuum of consumers purchase a variable amount of a product from one of two firms located at the endpoints of the market. At the Nash equilibrium in quantity-outlay schedules, consumers buy the same quantities as they would from the same firm if it were a monopolist facing the same informational asymmetries, but they receive greater surplus. Hence, no efficiency gains result from competition. If consumers have the option to reveal their locations and have the firms deliver the goods, all consumers choose to reveal their locations in equilibrium. Thus, the inefficiencies from information asymmetries may not arise because firms can deliver the good to consumers. In contrast, with a monopoly seller, consumers have no incentives to reveal their locations.     

Divisionalization and Delegation in Oligopoly

We consider a model where oligopolistic firms create independent divisions or franchises, which subsequently delegate output decisions to managers. We show that the number of firms required to make divisionalization privately profitable is greater in our model than in previous pure divisionalization models. However, in contrast with pure delegation models, we show that the subgame perfect Nash equilibrium approaches perfect competition as divisionalization costs tends to zero, even with a small fixed number of firms.     

Convergence to Walrasian equilibrium with minimal information

We consider convergence to Walrasian equilibrium in a situation where firms know only market price and their own cost function. We term this a situation of minimal information. We model the problem as a large population game of Cournot competition. The Nash equilibrium of this model is identical to the Walrasian equilibrium. We apply the best response (BR) dynamic as our main evolutionary model. This dynamic can be applied under minimal information as firms need to know only the market price and the their own cost to compute payoffs. We show that the BR dynamic converges globally to Nash equilibrium in an aggregative game like the Cournot model. Hence, it converges globally to the Walrasian equilibrium under minimal information. We extend the result to some other evolutionary dynamics using the method of potential games.

     

Bargains Followed by Bargains: When Switching Costs Make Markets More Competitive

In markets where consumers have switching costs and firms cannot price‐discriminate, firms have two conflicting strategies. A firm can either offer a low price to attract new consumers and build future market share or a firm can offer a high price to exploit the partial lock‐in of their existing consumers. This paper develops a theory of competition when overlapping generations of consumers have switching costs and firms produce differentiated products. Competition takes place over an infinite horizon with any number of firms. This paper shows that the relationship between the level of switching costs, firms' discount rate, and the number of firms determines whether firms offer low or high prices. Similar to previous duopoly studies, switching costs are likely to facilitate lower (higher) equilibrium prices when switching costs are small (large) or when a firm's discount rate is large (small). Unlike previous studies, this paper demonstrates that the number of firms also determines whether switching costs are pro‐ or anticompetitive, and with a sufficiently large (small) number of firms switching costs are pro‐ (anti‐) competitive.     

Product Differentiation, Strategic Divisionalization, and Persistence of Monopoly

This paper analyzes the strategic incentive of oligopolists to create autonomous rival divisions when products are differentiated. We consider a two-stage game where firms choose the number of autonomous divisions in the first stage and all the divisions engage in Cournot competition in the second. It is shown that product differentiation ensures the existence of an interior subgame perfect Nash equilibrium (SPNE), and the equilibrium number of divisions increases with the degree of substitution among products and the number of firms. Further, if divisions are allowed to divide further, they always will, which leads to total rent dissipation. Thus, parent firms have incentives to unilaterally restrict their divisions from further dividing. In the free-entry equilibrium, it is found that the possibility of setting up autonomous divisions is a natural barrier to entry. Incumbents may persistently earn abnormally high profits. In the cases where product differentiation is difficult, the only pure-strategy free-entry SPNE is the monopoly outcome even if the entry cost is relatively low.     

A Strategic Approach to Software Protection*

This paper demonstrates that there is a strategic reason why software firms have followed consumers' desire to drop software protection. We analyze software protection policies in a price-setting duopoly software industry selling differentiated software packages, where consumers' preference for particular software is affected by the number of other consumers who (legally or illegally) use the same software. Increasing network effects make software more attractive to consumers, thereby enabling firms to raise prices. However, it also generates a competitive effect resulting from feircer competition for market shares. We show that when network effects are strong, unprotecting is an equilibrium for a noncooperative industry.     

Collusive equilibria with switching costs: The effect of consumer concentration

I study the ability of two competing firms to set collusive prices in markets where consumers have switching costs. In consumer markets (with a small number of consumers), I find an antifolk result in which collusion, in the presence of switching costs, does not arise with patient firms. Patient firms compete aggressively and consumers expect a large utility. A collusive equilibrium is unstable because a deviating firm incorporates the future consumer utility in its deviating price. Also, consumers have a strategic impact so, with the prospects of large utility, they decide to switch to destabilize the firms' collusive agreement. These results do not eventuate in markets with a large number of consumers. In mass markets (a continuum of consumers), a single consumer lacks a strategic impact to destabilize a collusive agreement and a deviating firm cannot appropriate the consumer utility when deviating from collusion. Collusion, then, becomes straightforward to achieve. We show that for any number of consumers, switching costs make collusion easy to sustain.     

Signaling Quality in an Oligopoly When Some Consumers Are Informed

This paper considers a signaling game between two competing firms and consumers. The firms have common private information concerning their qualities, and some of the consumers are informed about the firms' qualities. Firms use prices and uninformative advertising as signals of quality. The model reveals that in the separating equilibrium, prices are first climbing and then declining with the proportion of informed consumers, while the expenditure on uninformative advertising is declining. Firms' profits are highest when the proportion of informed consumers is at an intermediate level. Pooling equilibria exist if the proportion of informed consumers is below a certain threshold.     

Imitation and price competition in a differentiated market

We study the stable market outcome that evolves in a spatially differentiated market when price-competing firms choose actions by imitation of the most profitable firm. We compare and contrast the stable outcomes under two imitation procedures: one, where each firm immediately imitates the most profitable firm, and the other when a firm imitates another firm only if it is more profitable while being “sufficiently similar” (in context of the market segment it operates in) or “sufficiently close”. In either case, the symmetric pure strategy Nash equilibrium is always a stable outcome. However, when imitation of the most profitable firm is immediate and market differentiation is ‘moderate’, states with prices lower than the Nash equilibrium are also stable. In contrast, when imitation of the most profitable firm is more gradual and market differentiation is below a threshold, states with prices above the Nash equilibrium are also stable. Thus, while competitive evolutionary pressure in this imitation based model does result in the Nash equilibrium always being stable, other outcomes may be stable as well. Interestingly, the states that are stable under gradual imitation give the firms a higher profit than the stable states under immediate imitation.     

Tax Competition with Heterogeneous Firms

Abstract

This paper studies tax competition in an economic geography model that allows for agglomeration economies with trade costs and heterogeneous firms. We find that the Nash equilibrium involves a large country charging a higher tax than a small nation. Lower trade costs lead to an intensification of competition, a drop in Nash tax rates and a narrowing of the gap. Since large, productive firms are naturally more sensitive to tax differences in our model, large firms are the crux of tax competition in our model. This also means that tax competition has consequences for the average productivity of big and small nations' industries; by lowering tax rates, a small nation can attract high-productivity firms.     

A differential game in a duopoly with instantaneous incentives

In this paper, we study a differential game in which two competing firms exploit a public renewable resource that is relevant from a landscape point of view. We consider a policy maker that provides an instantaneous incentive to the firms in order to prevent the resource exhaustion during the whole extraction period, which coincides with the harvesting license period. We compute an open-loop Nash equilibrium of the differential game, showing that it coincides with a linear feedback Nash equilibrium. Finally, we compute the value of the incentive that leads to the maximization of social welfare considering the incentive both as a pure transfer and as a cost.     

Price Dispersion and Consumer Reservation Prices

We describe firm pricing when consumers follow simple reservation price rules. In stark contrast to other models in the literature, this approach yields price dispersion in pure strategies even when firms have the same marginal costs. At the equilibrium, lower price firms earn higher profits. The range of price dispersion increases with the number of firms: the highest price is the monopoly price, while the lowest price tends to marginal cost. The average transaction price remains substantially above marginal cost even with many firms. The equilibrium pricing pattern is the same when prices are chosen sequentially.     

Trading equilibrium in a public good economy with smooth preferences and a mixed measure space of consumers

Lindahl and Nash equilibria are often used in the theory of public good. Shitovitz and Spiegel (1998) present an example of 2-person economy with one private good and one pure public good, where the core efficient Lindahl allocation does not Pareto dominate the (inefficient) Nash allocation. In this paper we introduce the new concept of Trading equilibrium for a general public good economy with smooth preferences and a mixed measure space of consumers. We obtain that this economy admits a unique Trading equilibrium. Moreover, the Trading equilibrium induces a core allocation that strictly Pareto dominates the Nash allocation.     

Endogenous mechanisms and Nash equilibrium in competitive contracting games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.     

Competition with Aftermarket Power When Consumers Are Heterogeneous

We study a model of competitive foremarkets and partly monopolized aftermarkets. We show that high aftermarket power prompts firms to engage in inefficiently aggressive below‐cost pricing in the foremarket. This inefficiency is driven by the presence of consumers with valuations below marginal cost. While for intermediate aftermarket power their presence leads to a competition‐softening effect, for high aftermarket power firms attract increasing numbers of unprofitable consumers by aggressively pricing below cost. For high aftermarket power, firms' equilibrium profits can therefore be decreasing in aftermarket power but are always higher than for low aftermarket power. If firms engage in price discrimination by bundling the foremarket and aftermarket goods or by reducing their aftermarket power, they avoid selling to unprofitable consumers but also reduce the competition‐softening effect. This decreases firms' equilibrium profits but increases consumer and social welfare.     

Endogenous vertical structure and trade policy in an import-competing market

We examine the endogenous determination of a vertical market in an import-competing market with import tariff. We show that if firms commit to vertical organization before the government's commitment to trade policy, the home and foreign firms choose vertical separation and vertical integration, respectively, at equilibrium under Bertrand competition. Under Cournot competition, the subgame perfect Nash equilibrium entails both firms separating their retailers. Comparing profits between Bertrand competition to Cournot competition, we find that upstream manufacturer's profit can be higher under Bertrand competition with integration than under Cournot competition with separation when comparing foreign upstream manufacturer's profit.     

Is having a unique equilibrium robust?

We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n  -player finite games with a unique correlated equilibrium is open, while this is not true of Nash equilibrium for n>2$n>2$. The crucial lemma is that a unique correlated equilibrium is a quasi-strict Nash equilibrium. Related results are studied. For instance, we show that generic two-person zero-sum games have a unique correlated equilibrium and that, while the set of symmetric bimatrix games with a unique symmetric Nash equilibrium is not open, the set of symmetric bimatrix games with a unique and quasi-strict symmetric Nash equilibrium is.     

Mixed oligopoly, foreign firms, and location choice

We investigate a mixed market in which a state-owned, welfare-maximizing public firm competes against n domestic private firms and m foreign private firms which are all profit-maximizing. A circular city model with quantity-setting competition is employed. We find that the equilibrium location pattern depends on m. All private firms agglomerate in the unique equilibrium if m is zero or one. Two foreign firms induce differentiation between domestic and foreign private firms. More than two foreign firms yield differentiation among the foreign firms. Regardless of n and m, agglomeration of all domestic private firms appears in equilibrium. We provide several conditions in which eliminating the public firm from the market enhances social welfare. We extend the basic model and investigate three issues concerning multiple public firms, inefficiency of the public firm, and entries by private firms. We obtain some additional implications of welfare and equilibrium locations.     

Multi-store competition: Market segmentation or interlacing?

This paper develops a model for multi-store competition between firms. Using the fact that different firms have different outlets and produce horizontally differentiated goods, we obtain a pure strategy equilibrium where firms choose a different location for each outlet and firms' locations are interlaced. The location decisions of multi-store firms are completely independent of each other. Firms choose locations that minimize transportation costs of consumers. Moreover, generically, the subgame perfect equilibrium is unique and when the firms have an equal number of outlets, prices are independent of the number of outlets.