Strategic interaction between futures and spot markets

We study an oligopolistic industry where firms are able to sell in a futures market at infinitely many moments prior to the spot market. A kind of Folk-theorem is established: any outcome between perfect competition and Cournot can be sustained in equilibrium. We then find that the Cournot outcome can be sustained by a renegotiation-proof equilibrium. However, this is not true for the competitive outcome. Furthermore, only the monopolistic outcome is renegotiation-proof if firms can buy and sell in the futures market. These results suggest, contrary to existing literature, that the introduction of futures markets may have an anti-competitive effect.     

Asymmetric knowledge flows and localization with endogenous R&D: A dynamic analysis

Empirical evidence suggests that technological spillovers also depend on the mode chosen by firms to serve the foreign market, since a closer location increases the degree of knowledge transmission. Therefore multinationals may want to locate subsidiaries near sources of technological innovation and domestic firms may take advantage of this closer location by absorbing more easily technological knowledge. Within this context we analyse the interaction between firms' international strategy and innovative performance by using a dynamic oligopoly model where knowledge flows increase with geographical proximity. Our results illustrate the relationship between firms' innovation and foreign expansion strategy when localized spillovers are considered.     

The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition

Abstract. We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.     

A NOTE ON MARKET COVERAGE IN VERTICAL DIFFERENTIATION MODELS WITH FIXED COSTS

With fixed costs of quality improvement, we find that a covered market outcome with an interior solution in the price stage is not a Nash equilibrium. When the degree of consumer heterogeneity is high (low) enough, an uncovered market outcome (a covered market outcome with a corner solution in the price stage) is the only Nash equilibrium. When the degree of consumer heterogeneity is moderate, both of the two market outcomes are Nash equilibria, but an uncovered market outcome yields higher social welfare than a covered market outcome with a corner solution in the price stage.     

Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

On the endogeneity of Cournot-Nash and Stackelberg equilibria: games of accumulation

We characterize equilibria of games with two properties: (i) Agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur; but (ii) they can only add to their initial amounts. The equilibrium set consists of just the Cournot-Nash outcome, one or both Stackelberg outcomes, or a continuum of points including the Cournot-Nash outcome and one or both Stackelberg outcomes. A simple theorem that uses agents’ standard one-period reaction functions and the one-period Cournot-Nash and Stackelberg equilibria delineates the equilibrium set. Applications include contribution, oligopoly, and rent-seeking games.     

Imitation—theory and experimental evidence

We introduce a generalized theoretical approach to study imitation and subject it to rigorous experimental testing. In our theoretical analysis we find that the different predictions of previous imitation models are mainly explained by different informational assumptions, and to a lesser extent by different behavioral rules. In a laboratory experiment we test the different theories by systematically varying information conditions. We find significant effects of seemingly innocent changes in information. Moreover, the generalized imitation model predicts the differences between treatments well. The data provide support for imitation on the individual level, both in terms of choice and in terms of perception. Furthermore, individuals’ propensity to imitate more successful actions is increasing in payoff differences.     

Imitation and the evolution of Walrasian behavior: Theoretically fragile but behaviorally robust

A well-known result by Vega-Redondo (1997) [18] implies that in symmetric Cournot oligopolies, imitation leads to the Walrasian outcome. We show that this result is not robust to the slightest asymmetry in costs, since every outcome where agents choose identical actions will be played some fraction of the time in the long run. We then conduct experiments to check this fragility. We obtain that, contrary to the theoretical prediction, the Walrasian outcome is a good predictor of market outcomes. Finally, we suggest a new theory based on a mix of imitation and other learning processes that explains subjects' behavior fairly well.     

The Cournot-Bertrand model and the degree of product differentiation

We consider a duopoly model with a Cournot-type firm and a Bertrand-type firm. Both survive and the equilibrium is stable when there is sufficient product differentiation. With no differentiation, only the Cournot-type firm survives, and the outcome is perfectly competitive.     

Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products

In this paper we consider a Cournot–Bertrand duopoly model with linear demand and cost functions and with product differentiation. We propose a dynamic framework for the study of the stability properties of this kind of mixed oligopoly game, a rather neglected topic in the existing literature despite its relevance. In particular, in this paper we highlight the role of best response dynamics and of an adaptive adjustment mechanism for the stability of the equilibrium.     

R&D games in a Cournot duopoly with isoelastic demand functions: A comment

In a recent paper, Tramontana (Economic Modelling, 27; 350-357, 2010) investigates the stability properties of a Cournot Duopoly game when the demand function is isoelastic. In this note, we show that for some well known applications of two-stage Cournot games (D. Aspremont and Jacquemin, American Economic Review, 78, 1122-1137, 1988) an isoelastic demand function can guarantee both the existence and the uniqueness of a Nash Equilibrium even in cases where existence is not obtained with linear demands.     

A continuum of commitment

We examine a generic three-stage game for two players with alternating moves, where the first player can choose the level of adjustment cost to be paid in the last period to modify the action she announced in the first period. In the resulting continuum of commitment options, convexifying the choice between first-mover and second-mover advantage in pure strategies, we characterize when an intermediate adjustment-cost level is chosen in equilibrium. We show that the wastefulness of the adjustment cost may be in the players’ best interest, improving both of their individual net payoffs over making any fraction of the adjustment cost a side-payment from the first to the second player.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

Elastic demand, sunk costs and the Kreps–Scheinkman extension of the Cournot model

Summary. The paper shows that, with any rationing mechanism between the efficient and proportional extremes, the Kreps-Scheinkman two-stage quantity-price game reduces to the Cournot model if demand is uniformly elastic and if all costs are sunk at the first stage, thus providing positive results to set against existing negative statements. Received: May 24, 1995; revised version: March 6, 1997     

Rational expectations equilibria of economies with local interactions

We consider general economies in which rational agents interact locally. The local aspect of the interactions is designed to represent in a simple abstract way social interactions, that is, socioeconomic environments in which markets do not mediate all of agents’ choices, which might be in part determined, for instance, by family, peer group, or ethnic group effects. We study static as well as dynamic infinite horizon economies; we allow for economies with incomplete information, and we consider jointly global and local interactions, to integrate e.g., global externalities and markets with peer and group effects. We provide conditions under which such economies have rational expectations equilibria. We illustrate the effects of local interactions when agents are rational by studying in detail the equilibrium properties of a simple economy with quadratic preferences which captures, in turn, local preferences for conformity, habit persistence, and preferences for status or adherence to aggregate norms of behavior.     

Skating on thin ice: rule changes and team strategies in the NHL

Abstract.  In an effort to stimulate a more exciting and entertaining style of play, the National Hockey Association (NHL) changed the rewards associated with the results of overtime games. Under the new rules, teams tied at the end of regulation both receive a single point, regardless of the outcome in overtime. A team scoring in the sudden-death 5-minute overtime period would earn an additional point. Prior to the rule change in the 1999–2000 season, the team losing in overtime would receive no points while the winning team earned 2 points. This paper presents a theoretical model to explain the effect of the rule change on the strategy of play during both the overtime period and the regulation time game. The results suggest that under the new overtime, format equally powerful teams will play more offensively in overtime resulting in more games decided by a sudden-death goal. The results also suggest that while increasing the likelihood of attacking in overtime, the rule change would have a perverse effect on the style of play during regulation by causing them to play conservatively for the tie. Empirical data confirm the theoretical results. The paper also shows that increasing the rewards to a win in regulation time would prevent teams from playing defensively during regular time.     

Why shops close again: An evolutionary perspective on the deregulation of shopping hours

This paper introduces a new perspective on the deregulation of shopping hours based on ideas from evolutionary game theory. We study a retail economy where shopping hours have been deregulated recently. It is argued that first, the deregulation leads to a coordination problem between store owners and customers, and second, the ‘solution’ to this problem depends on the specific cost structure of stores and the preferences of customers. In particular, it may happen that, even if extended shopping hours are Pareto efficient, stores and customers do not succeed in coordinating on this equilibrium. The analysis explains the observation in Germany, where shopping hours have been deregulated recently, that store owners tend to go back to the former shopping hours again. Moreover, it emphasizes the important role of advertisement campaigns as a signalling device.     

Exclusion via Non‐Exclusive Contracts

We establish that non‐linear vertical contracts can allow an incumbent to exclude an upstream rival in a setting that does not rely on the exclusivity of the incumbent's contracts with downstream firms or any limits on distribution channels available to the incumbent or rival. The optimal contract we describe is a three‐part quantity discounting contract that involves the payment of an allowance to a downstream distributor and a marginal wholesale price below the incumbent's marginal cost for sufficiently large quantities. The optimal contract is robust to allowing parties to renegotiate contracts in case of entry.