Symmetric Oligopoly Research Articles

Bertrand‐Cournot profit reversal under non‐commitment process innovation

AbstractWe provide a new reason for Bertrand‐Cournot profit reversal. In a symmetric oligopoly, we show that firms get higher profits under Bertrand competition compared to Cournot competition under non‐commitment process innovation if the products are sufficiently differentiated and there is positive knowledge spillover. As the number of firms increases, the degree of product differentiation over which the profits are higher under Bertrand competition can increase. Higher outputs under Bertrand competition compared to Cournot competition generate higher R&D investments under the former than the latter, which is responsible for our result.

The impact on market outcomes of the portfolio selection of large equity investors

We study the portfolio selection of large investors who own equity of the firms competing in a symmetric oligopoly. An investor’s objective is to maximize the value of its portfolio accounting for the impact of its interests on the managerial incentives. We show that in a stationary equilibrium the portfolios of large investors soften competition, increasing the price markup and profits.

Price and non-price competition in an oligopoly: an analysis of relative payoff maximizers

Do firms that engage in relative payoff maximizing (RPM) behavior always choose a strategy profile that results in tougher competition compared to firms that engage in absolute payoff maximizing (APM) behavior? We address this question by way of a simple model of symmetric oligopoly where firms simultaneously select a two-dimensional strategy set consisting of a price variable and a non-price (i.e., quality) variable. Our results show that equilibrium solutions of RPM and APM are distinct. It is further shown that the standard result of Nash equilibrium in oligopoly, namely, that the non-price variable is used to soften price competition, survives also when firms are concerned with relative payoff considerations.

Rules of origin and uncertain compliance cost

This study considers the role of the cost uncertainty associated with meeting the rules of origin (ROO) in a free trade area/agreement (FTA). While the literature tends to overlook the cost uncertainties of ROO compliers, we show that the uncertain production costs resulting from meeting the ROO yield the coexistence of compliers and non-compliers in symmetric oligopoly firms. We also show that the regime in which compliers and non-compliers coexist is not the best one for an FTA importer, while it may be the best one for world welfare. We also discuss the case that uncertain production costs are firm-specific.

Endogenous Mergers and Leadership Acquisition in Cournot Oligopolies

I set up an endogenous merger model in which, whenever fi rms agree to join in a coalition, the new entity acquires the leadership in a symmetric Cournot oligopoly. I first explore the case of a single merger and show that, despite being such merger pro table irrespective of the number of participants, only two endogenous equilibria are possible: either a bilateral coalition or an n - 1-fi rm coalition. I then allow for multiple coalitions and show that merger waves often occur as a fi rms' response to the exclusion of monopolization. In other cases, even if monopolization is allowed, the grand coalition does not form and at least one fi rm prefers to act as a follower. The model provides an explanation of why bilateral mergers are observed in almost every industry, even where synergies are unlikely and why it is possible to observe a single large entity behaving as a market leader. Furthermore, it provides a justi fication of the strategic nature of merger waves as a response to the exclusion of monopolization. I also check how my results vary with different ex-ante merger policies. Moreover, it is shown that bilateral mergers between identical fi rms generating no synergies can be bene ficial to both consumers and producers.

Delegation and Incentives under Evolutionarily Stable Conjectures

Existing results show that in a homogenous Cournot duopoly, commitment by delegation harms profit. This conclusion presupposes that market conduct is the same whether incentives are aggressive or accommodating. We study delegation and incentives under evolutionarily stable conjectures and show how performance pay co-determines market conduct. In fact, in equilibrium with evolutionarily stable conjectures, we show that commitment through delegation leads to a profit increase. Manipulation of managerial incentives produces less competition and therefore benefits firms' owners even in symmetric homogenous oligopoly. Copyright © 2016 John Wiley & Sons, Ltd.

Price and Non-Price Competition in Oligopoly An Analysis of Relative Payoff Maximizers

Do firms under relative payoff s maximizing (RPM) behavior always choose a strategy profile that results in tougher competition compared to firms under absolute payoffs maximizing (APM) behavior? In this paper we will address this issue through a simple model of symmetric oligopoly where firms select a two dimensional strategy set of price and a non-price variable known as quality simultaneously. In conclusion, our results show that equilibrium solutions of RPM and APM are distinct. We further characterize the comparison between these two equilibrium concepts. In particular, RPM does not always lead to stricter competition compared to the Nash equilbrium (APM). In fact, the comparison between two equilibrium concepts is influenced by the parameters of demand curve and cost function. The conditions, derived in this paper, determine under which circumstances RPM induces more competition or less competition w.r.t the price or non-price dimension.

Rationalizability and efficiency in an asymmetric Cournot oligopoly

This paper studies rationalizability in a linear asymmetric Cournot oligopoly with a unique Nash equilibrium. It shows that mergers favor uniqueness of the rationalizable outcome. When one requires uniqueness of the rationalizable outcome maximization of consumers' surplus may involve a symmetric oligopoly with few firms. We interpret uniqueness of the rationalizable outcome as favoring a dampening of strategic ‘coordination’ uncertainty. An illustration to the merger between Delta Air Lines and Northwest shows that a reallocation of 1% of market share from a small carrier to a larger one has implied a lower production volatility over time, yielding a 1.5% decrease in the coefficient of variation of number of passengers.

Supply function equilibria for uniform price auction in oligopolistic markets

We consider game-theoretic models related to the supply function auction for electricity markets. We determine the set of supply function equilibria (SFE), introduced by Klemperer and Mayer (Econometrica 57:1243–1277, 1989), for a symmetric oligopoly with linear demand, fixed marginal cost and capacity constraint. This set depends on the maximum random shock of the demand function. We also study the best response dynamics and show that in general it does not converge to any SFE. We find out sufficient conditions for the convergence and conclude on the optimal parameters of the auction.

Evolutionary Stability in Asymmetric Oligopoly

It is a very well-known result that in terms of evolutionary stability the long-run outcome of a Cournot oligopoly market with fi nitely many fi rms approaches the perfectly competitive Walrasian market outcome (Vega-Redondo, 1997). However, in this paper we show that an asymmetric structure in the cost functions of fi rms may change the long-run outcome. Contrary to Tanaka (1999) we show that the evolutionarily stable price in an asymmetric Cournot oligopoly needs not equal the marginal cost, it may rather equal a weighted average of (diff erent) marginal cost. We apply a symmetrization technique in order to transform the game with asymmetric fi rms into a symmetric oligopoly game and then extend Schaff er’s defi nition (1988) of a fi nite population ESS (FPESS) to this setup. Moreover, we show that the FPESS in this game represents a stochastically stable state of an evolutionary process of imitation with experimentation.

Evolutionarily Stable Quality and Price in Oligopoly: A Comparison with Nash

The article proposes an evolutionary game theoretical analysis of quality and price competition in oligopoly. Using the notion of a finite population evolutionarily stable strategy (FPESS) defined by Schaffer (1989), the relative payoff maximizing behavior is compared with the absolute payoff maximizing behavior. In the literature of IO on quality competition, two different assumptions are made about the nature of cost function. First, firms produce quality mostly with fixed costs and second, quality is produced by variable costs. Therefore, in the context of a symmetric oligopoly game where each firm has two dimensional strategy set of price and quality, the present paper attempts to answer a question regarding the equivalence of FPESS and Nash equilibrium. In conclusion, whether firms produce quality with fixed costs or variable costs, our results show that Nash equilibrium, FPESS and competitive equilibrium are distinct. Moreover, this paper provide a generalization of evolutionary game setup of Tanaka (2000) where we obtain not the same equilibrium price comparison between Nash and FPESS from the one that attained in Tanaka (2000, proposition 2).

The asymptotic core, nucleolus and Shapley value of smooth market games with symmetric large players

We examine the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector in a transferable utility (TU) market game. We provide sufficient conditions for the asymptotic core and the nucleolus to coincide with the unique TU competitive payoff distribution. This equivalence results from nucleolus of a finite TU market game belonging to its core, the core equivalence in a symmetric oligopoly with identical atoms and single-valuedness of the core in the limiting smooth game. In some cases (but not always), the asymptotic Shapley value is more favourable for the large traders than the nucleolus, in contrast to the monopoly case (Einy et al. in J Econ Theory 89(2):186–206, 1999), where the nucleolus allocation is larger than the Shapley value for the atom.

The Welfare Effects of Mobile Termination Rate Regulation in Asymmetric Oligopolies: The Case of Spain

We examine the effects of mobile termination rate regulation in asymmetric oligopolies. We do this by extending existing models of asymmetric duopoly and symmetric oligopoly where consumer expectations about market shares are passive. We first calibrate product differentiation parameters using detailed data from the Spanish market from 2010. Next, we predict equilibrium outcomes and welfare effects under alternative scenarios of future termination rates. Lowering termination rates typically lowers profits of all networks and improves consumer and total surplus.

The size of stable cartels: An analytical approach

In this paper, we revisit the size of stable cartels in a symmetric oligopoly model with a Cournot fringe. Konishi and Lin (1999) make a conjecture on the size of stable cartels. Due to algebra complexity, they test the conjecture by conducting numerical simulations. We provide an analytical approach to determine the size of stable cartels, and show that the size of stable cartels is slightly larger than the one in their conjecture. Furthermore, we find that the uniqueness of the stable cartel in Konishi and Lin (1999) could not always hold.

Asymmetric Bertrand-Edgeworth Oligopoly and Mergers

This paper investigates mixed strategy equilibria in a capacity-constrained price competition among three firms. It is shown that the equilibria in an asymmetric oligopoly are substantially different from those in a duopoly and symmetric oligopoly. In an asymmetric triopoly, it is possible that (i) a continuum of equilibria exists and that (ii) the lowest price of the smallest firm is higher than that of the others and the smallest firm earns more than the max-min profit in undominated strategies. In particular, the second finding sheds light on a new pricing incentive in Bertrand competitions. As an application, the equilibrium characterizations give rise to a new class of merger paradoxes.

Asymmetric Bertrand-Edgeworth Oligopoly and Mergers

This paper investigates mixed strategy equilibria in a capacity-constrained price competition among three firms. It is shown that the equilibria in an asymmetric oligopoly are substantially different from those in a duopoly and symmetric oligopoly. In an asymmetric triopoly, it is possible that (i) a continuum of equilibria exits and that (ii) the lowest price of the smallest firm is higher than that of the others and the smallest firm earns more than the max-min profit in undominated strategies. In particular, the second finding sheds light on a new pricing incentive in Bertrand competitions. As an application, the equilibrium characterizations give rise to a new class of merger paradoxes.

Tacit collusion and capacity withholding in repeated uniform price auctions

This article analyzes tacit collusion in infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity‐constrained firms. Under two popular definitions of the uniform price, when each firm sets a price‐quantity pair, perfect collusion with equal sharing of profit is easier to sustain in the uniform price auction than in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this outcome. Even when firms may set bids that are arbitrary finite step functions of price‐quantity pairs, in repeated uniform price auctions maximal collusion is attained with simple price‐quantity strategies exhibiting capacity withholding.

Collusion under monitoring of sales

Collusion under imperfect monitoring is explored when firms' prices are private information and their quantities are public information; such an information structure is consistent with several recent price‐fixing cartels, such as those in lysine and vitamins. For a class of symmetric oligopoly games, it is shown that symmetric equilibrium punishments cannot sustain any collusion. An asymmetric punishment is characterized that does sustain collusion and it has firms whose sales exceed their quotas compensating those firms with sales below their quotas. In practice, cartels could have performed such transfers through sales among the cartel members.

CHARACTERIZATION OF COURNOT EQUILIBRIA IN A MARKET WITH NETWORK EFFECTS

Market equilibria are difficult to describe in markets with network effects because they often involve an upward sloping demand curve and/or multiple equilibria. In the framework of symmetric Cournot oligopoly, I investigate for a minimal set of conditions and thus extend the standard equilibrium analysis by Amir (Games and Economic Behavior, Vol. 15 (1996), pp. 132–148) and Amir and Lambson (Review of Economic Studies, Vol. 67 (2000), pp. 235–254) to these kinds of markets.

Stochastically stable states in an oligopoly with differentiated goods: equivalence of price and quantity strategies

This paper presents results on a stochastically stable state (or long-run equilibrium) in evolutionary dynamics based on imitation of strategies by firms in a symmetric oligopoly with differentiated goods. We consider both quantity setting and price-setting oligopoly games, and define a globally surviving strategy (GSS). It is a strategy that can invade any configuration where the population monomorphically adopts some other strategy, and closely related to a finite population evolutionarily stable strategy (ESS), defined by Schaffer (Schaffer, M.E., Evolutionarily stable strategies for a finite population and a variable contest size, Journal of Theoretical Biology 132, 1988, 469–478). In a quantity-setting oligopoly, the unique GSS output is equal to the unique finite population ESS output, and is a stochastically stable strategy. In a price-setting oligopoly, the unique GSS price is equal to the unique finite population ESS price, and is a stochastically stable strategy. The GSS in a quantity-setting oligopoly and that in a price-setting oligopoly are equivalent. Therefore, stochastically stable states in both cases coincide.