Double Exponential Instability of Triangular Arbitrage Systems

If financial markets displayed the informational efficiency postulated in the efficient markets hypothesis (EMH), arbitrage operations would be self-extinguishing. The present paper considers arbitrage sequences in foreign exchange (FX) markets, in which trading platforms and information are fragmented. In Kozyakin et al. (2010) and Cross et al. (2012) it was shown that sequences of triangular arbitrage operations in FX markets containing 4 currencies and trader-arbitrageurs tend to display periodicity or grow exponentially rather than being self-extinguishing. This paper extends the analysis to 5 or higher-order currency worlds. The key findings are that in a 5-currency world arbitrage sequences may also follow an exponential law as well as display periodicity, but that in higher-order currency worlds a double exponential law may additionally apply. There is an "inheritance of instability" in the higher-order currency worlds. Profitable arbitrage operations are thus endemic rather that displaying the self-extinguishing properties implied by the EMH.Comment: 22 pages, 22 bibliography references, expanded Introduction and Conclusion, added bibliohraphy reference

Generalization of the Born rule

A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a correlation between the positions of a particle at two different times. Under reasonable conditions for the wave function, this correlation implies that the particles follow quasi-classical trajectories. It is also shown that the Born rule is equivalent to a particular case of the new principle. These features allow the principle to provide a unified explanation of the results of the statistical experiments and of the quasi-classical macroscopic evolution. There is a strong analogy between the new quantum principle and a probabilistic principle which is necessary to derive empirical predictions from the mathematical formalism of probability theory. This principle is referred to by some authors as Cournot's principle, while other authors use the equivalent notion of typicality. In this paper probability theory and quantum mechanics are formulated in such a way as to explicitly include the two principles and to emphasize the very similar conceptual structure of the two theories.Comment: 29 pages, 3 figures. To appear in Physical Review A, a section added and some minor improvement

Stackelberg Independence

The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. I show that under the standard assumptions, leaders' actions are informative about market conditions and independent of lead-ers' beliefs about the arrivals of followers. However, this Stackelberg independence property relies on all standard assumptions being satisfied. It fails to hold whenever the demand function is non-linear, marginal cost is not constant, goods are differentiated, firms are non-identical, or there are any externalities. I show that small deviations from the linear demand assumption may make the leaders' choices completely uninformative

Complementary Patents and Market Structure

Many high technology goods are based on standards that require several essential patents owned by different IP holders. This gives rise to a complements and a double mark-up problem. We compare the welfare effects of two different business strategies dealing with these problems. Vertical integration of an IP holder and a downstream producer solves the double mark-up problem between these firms. Nevertheless, it may raise royalty rates and reduce output as compared to non-integration. Horizontal integration of IP holders solves the complements problem but not the double mark-up problem. Vertical integration discourages entry and reduces innovation incentives, while horizontal integration always benefits from entry and innovatio

Uniqueness of Nash equilibria in quantum Cournot duopoly game

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and, (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.Comment: 7 pages, 2 figure

Bailouts in a common market: a strategic approach

Governments in the EU grant Rescue and Restructure Subsidies to bail out ailing firms. In an international asymmetric Cournot duopoly we study effects of such subsidies on market structure and welfare. We adopt a common market setting, where consumers from the two countries form one market. We show that the subsidy is positive also when it fails to prevent the exit. The reason is a strategic effect, which forces the more efficient firm to make additional cost-reducing effort. When the exit is prevented, allocative and productive efficiencies are lower and the only gaining player is the rescued firm

Modeling Airline Frequency Competition for Airport Congestion Mitigation

Demand often exceeds capacity at congested airports. Airline frequency competition is partially responsible for the growing demand for airport resources. We propose a game-theoretic model for airline frequency competition under slot constraints. The model is solved to obtain a Nash equilibrium using a successive optimizations approach, wherein individual optimizations are performed using a dynamic programming-based technique. The model predictions are validated against actual frequency data, with the results indicating a close fit to reality. We use the model to evaluate different strategic slot allocation schemes from the perspectives of the airlines and the passengers. The most significant result of this research shows that a small reduction in the total number of allocated slots translates into a substantial reduction in flight and passenger delays and also a considerable improvement in airlines' profits