Narrow Results

Based on the oligopoly game theory, a dynamic duopoly Cournot model with bounded rationality and consumer surplus is established. On the one hand, the type and the stability of the boundary equilibrium points and the stability conditions of the Nash equilibrium point are discussed in detail. On the other hand, the potential complex dynamics of the system is demonstrated by a set of 2D bifurcation diagrams. It is found that the bifurcation diagrams have beautiful fractal structures when the adjustment speed of production is taken as the bifurcation parameter. And it is verified that the area with scattered points in the 2D bifurcation diagrams is caused by the coexistence of multiple attractors. It is also found that there may be two, three or four coexisting attractors. It is even found the coexistence of Milnor attractor and other attractors. Moreover, the topological structure of the attracting basin and global dynamics of the system are investigated by the noninvertible map theory, using the critical curve and the transverse Lyapunov exponent. It is concluded that two different types of global bifurcations may occur. Because of the symmetry of the system, it can be concluded that the diagonal of the system is an invariant one-dimensional submanifold. And it is controlled by a one-dimensional map which is equivalent to the classical Logistic map. The bifurcation curve of the system on the adjustment speed and the weight of the consumer surplus is obtained based on the properties of the Logistic map. And the synchronization phenomenon along the invariant diagonal is discussed at the end of the paper.

We consider the strategic interaction between two firms competing for the opportunity to invest in a project with uncertain future values. Starting in complete markets, we provide a rigorous characterization of the strategies followed by each firm in continuous time in the context of a timing/coordination game. In particular, the roles of leader and follower emerge from the resulting symmetric, Markov, sub-game perfect equilibrium. Comparing the expected value obtained by each firm in this case with that obtained when the roles of leader and follower are predetermined, we are able to calculate the amount of money that a firm would be willing to spend in advance (either by paying a license or acquiring market power) to have the right to be the leader in a subsequent game — what we call the priority option. We extend these results to incomplete markets by using utility-indifference arguments.

This paper deals with duopoly models with vertical product differentiation. These are two-stage games. In the first stage, the quality game, the two firms choose their quality. In the second stage, the price game, they choose their prices. When the market is covered, the properties of this game are well known, even when the consumers are not uniformly distributed. When the market is uncovered the literature is not always clear about these models. In the present paper it is shown that the price game can be solved, when the consumers are distributed according to a distribution function with a log-concave density function.

We study the effects of endogenous cost formation in the classic Cournot oligopoly through an extended two-stage game. The competing Cournot firms produce low-cost but limited quantities of a single homogeneous product. For additional procurements, they may refer to a revenue-maximizing supplier who sets a wholesale price prior to their orders. We express this chain as a two-stage game and study its equilibrium under two different information levels: complete and incomplete information on the side of the supplier about the actual market demand. In the deterministic case, we derive the unique subgame-perfect Nash equilibrium for different values of the retailers’ capacity levels, supplier’s cost and market demand. To study the incomplete information case, we model demand uncertainty via a continuous probability distribution. Under mild assumptions, we characterize the supplier’s optimal pricing policy as a fixed point of a proper translation of his expectation about the orders that he will receive from the retailers. If this expectation is decreasing in his price, then such an optimal policy always exists and is unique. Based on this characterization, we are able to proceed with comparative statics and sensitivity analysis, both analytically and numerically. Incomplete information gives rise to market inefficiencies because the supplier may ask for a too high price. Increasing supplier’s cost results in increasing wholesale prices, decreasing orders from the retailers and hence decreasing consumer surplus. Increasing retailers’ production capacities results in decreasing wholesale prices and increasing consumer surplus. Finally, as the number of second-stage retailers increases, the supplier’s profit may initially rise but eventually drops.

Social pressures, in addition to the law, incite more and more firms to pursue multiple and separate objectives. This trend raises the following question: will the change in the number of objectives pursued by firms affect their strategic interactions? To address this issue we focus on a dynamic duopoly where each firm has two objectives: one of the firms’ objectives is financial and the other is environmental. Production is a polluting activity and the actual level of pollution depends on current and past emissions. We analyze both open-loop Nash and cooperative equilibria (these equilibria are also trivially feedback as the equilibrium strategies are constant). We show that contrary to the case where firms’ unique objective is the financial one, there are Nash equilibria where production is lower than in the cooperative equilibrium. This stems from the fact that in a Nash equilibrium firms do not coordinate the choice of the relative weight given to the environmental objective. We obtain the same conclusion when firms can mitigate pollution. In this case, we also show that there are Nash equilibria where the sum of the firms’ mitigation efforts is higher than its value in the cooperative equilibrium.

The so-called “Win-Continue, Lose-Reverse” (WCLR) rule is a simple iterative procedure that can be used to choose a value for any numeric variable (e.g., setting a price or a production level). The rule dictates that one should evaluate the effect on profits of the last adjustment made to the value (e.g., a price variation), and keep on changing the value in the same direction if the adjustment led to greater profits, or reverse the direction of change otherwise. Somewhat surprisingly, this simple rule has been shown to lead to collusive outcomes in Cournot oligopolies, even though its application requires no information about the other firms’ profits or choices. In this paper, we show that the convergence of the WCLR rule toward collusive outcomes can be very sensitive to small independent perturbations in the cost functions or in the income functions of the firms. These perturbations typically push the process toward the Nash equilibrium of the one-shot game. We also explore the behavior of WCLR against other strategies and demonstrate that WCLR is easily exploitable. We then conduct a similar analysis of the WCLR rule in a differentiated Bertrand model, where firms compete in prices.

Brand awareness is recognized to be an important determinant in shaping the success of durables [13, 16], yet it is very difficult to be quantified. This is exactly the main goal of this paper: propose a suitable model where brand awareness of two competing firms is modeled and, eventually, estimated. To this aim, we build a random utility model for a duopoly where each competitor is characterized by different pricing strategies and brand awareness. As a result, different levels of market shares will emerge at the equilibrium. As a case study, we calibrate the model with real data from the smartphone industry obtaining an estimate of the value of the brand awareness of two leading brands.

For decades, Boeing and Airbus have struggled for dominance in the large commercial aircraft market. In 2010 and 2011, the World Trade Organization ruled that each firm has received illegal subsidies from the governments of the United States and the European Union, which have enhanced their competitive positions. This paper considers the nature of these rulings and the future competitive environment in the global jetliner industry.

In this paper we consider a game modelling a market consisting of two firms with market power and a continuum of consumers. A specific feature of a market for toys is considered with each firm producing two kinds of distinguishable goods. The problem of finding a Nash equilibrium implies firms' optimal advertising and production plans over time, where the aggregate of demands of consumers may depend on firms' past decisions. Equilibria at this market may have strange properties, like oscillatory production and advertising strategies.