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A sequential variation of the Arrow—Debreu abstract economy is developed to closely capture the timing of moves of the Walrasian general equilibrium model. Instead of inducing a pseudo- game, the extensive form game of our sequential variation is well defined. It is shown that when information is symmetric, Walrasian equilibrium allocations are equivalent to subgame-perfect equilibrium allocations. When information is asymmetric, rational expectations equilibrium allocations are shown to be equivalent to perfect Bayesian equilibrium allocations. These results are useful for understanding and characterizing Walrasian and rational expectations equilibrium allocations.

We consider a network game based on matching pennies with two types of agents, conformists and rebels. Conformists prefer to match the action taken by the majority of her neighbors while rebels like to match the minority. We investigate the simultaneous best response dynamic focusing on the lengths of limit cycles (LLC for short). We show that \\[\\hbox {LLC}=1\\] or 2 when all agents are of the same type, and \\[\\hbox {LLC}=4\\] when there is no conformist-rebel edge and no two even-degreed agents (if any) are neighboring each other. Moreover, \\[\\hbox {LLC}=1\\] for almost all type configurations when the network is a line or a ring, which implies that a pure strategy Nash equilibrium is reached from any initial action profile. However, \\[\\hbox {LLC}=4\\] for about one half of the type configurations with star networks.

Competitive implications of cross-holdings have been extensively analyzed in the literature. Incentives for engaging cross-holdings and welfare effects were however rarely studied. Although a similar logic as with the merger paradox holds for Cournot oligopolies with homogeneous products and symmetric technologies, we show that there are profit incentives for firms to engage cross-holdings with asymmetric technologies. Furthermore, we show that social welfare could be enhanced with cross-holdings even though the market becomes more concentrated. We also discuss the robustness of both the submodularity of the Cournot model with respect to the presence of cross-holdings and our results with respect to product differentiation.

The chaotic motions were shown by the vibrations of a bulk permanent magnet (PM) supported by a cylindrical high-Tc superconductor (HTSC) under external disturbance in very early experiments. There are few theoretical studies on the nonlinear behaviors of the HTSC levitation system as the complex interaction between the HTSC and PM. In this paper, we developed a numerical program to analyze the nonlinear vibrations of the levitated PM coupled with the electromagnetic force, taking into account the heat diffusion on HTSC. When the levitation system displayed chaotic oscillations by vertical excitation, the electromagnetic and thermal characteristics of the HTSC will change. The dynamic responses are shown by comparing the calculation results in which the thermal effects are taken into account and not. The numerical results display the displacements of PM, magnetic levitation forces, the acceleration, and the maximum Lyapunov exponent. The results show that the thermal effect will influence the stability of the levitation system.

A network approach is proposed to analyze the formation of cross-holdings and anti-competitive implications. Our approach is motivated by the bilateral ar- rangement of passive ownership between Microsoft and Apple in 1997. We provide a complete characterization of pairwise stable cross-holdings for a model of Cournot oligopoly with a homogeneous product. Our results strengthen the competitive impli- cations of endogenous cross-holdings in Cournot oligopoly found in the literature.

We analyze the evolution of fashion based on a network game model. Each agent in this model is a conformist or a rebel. A conformist prefers to take the action most common among her neighboring agents, whereas a rebel prefers the opposite. When there is only one type of agents, the model possesses an exact potential function, implying that fashion cycles are unlikely to emerge in a homogeneous population. The homophily index, a measure of segregation in networks with multiple types of nodes, is shown to play a key role in the emergence of fashion cycles. Our main finding is that a lower homophily index, in general, promotes the emergence of fashion cycles. We establish this result through a potential analysis, a partial potential analysis, and a stability analysis of a system of ordinary differential equations that is approximated from a stochastic best response dynamic. Numerical simulations based on a variety of networks confirm that the approximate analysis is reliable. The e-companion is available at https://doi.org/10.1287/opre.2018.1744 .

This paper analyzes the role of price as a signal of the quality of amonopoly firm’s new product. The quality of the goods is drawn from a continuum and is unknown to consumers. We establish a unique separating equilibrium using equilibrium characterization results for signaling games. The equilibrium price monotonically increases with quality levels and exceeds the complete-information monopoly price for all quality levels but the lowest one. However, the upward distortion decreases as the proportion of pre-informed consumers increases. These results extend both the signaling role of price and characteristics of the separating equilibrium as established in Bagwell and Riordan (1991).

We introduce log-convexity for bargaining problems. With the requirement of some basic regularity conditions, log-convexity is shown to be necessary and sufficient for Nash's axioms to determine a unique single-valued bargaining solution up to choices of bargaining powers. Specifically, we show that the single-valued (asymmetric) Nash solution is the unique solution under Nash's axioms without that of symmetry on the class of regular and log-convex bargaining problems, but this is not true on any larger class. We apply our results to bargaining problems arising from duopoly and the theory of the firm. These problems turn out to be log-convex but not convex under familiar conditions. We compare the Nash solution for log-convex bargaining problems with some of its extensions in the literature.

We analyze welfare effect of information acquisition for a model of competitive financial markets with diverse information and rational expectations. We show that in the fully revealing rational expectations equilibrium, each agent's gain from trade in ex ante utility decreases as more agents become informed. An implication of the result is that market efficiency and ex ante Pareto optimality are not compatible in competitive financial markets with diverse information and rational expectations. Our result can be viewed as complementary to the Grossman paradox, which shows that market efficiency and individuals' incentives to acquire information are not compatible. This paper is the first step in a projected exploration of welfare effect of information acquisition in models with diverse information.

The enlargement of the general-equilibrium structure to allow for default subject to penalties results in a construction of a simple mechanism for selecting a unique competitive equilibrium. We consider economies for which a common credit money can be applied to uniquely select each of the competitive equilibria with suitable default penalties. We identify two classes of such economies.