GAME COMPLETE ANALYSIS OF BERTRAND DUOPOLY
In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfi in [3], [6], [8] and [9]) and al-ready employed by himself and others in [4], [5], [7]) to the classic Bertrand Duopoly (1883), classic oligopolistic market in which there are two enterprises producing the same commodity and selling it in the same market. In this classic model, in a competitive background, the two enterprises employ as possible strategies the unit prices of their product, contrary to the Cournot duopoly, in which the enterprises decide to use the quantities of the commodity produced as strategies. The main solutions proposed in literature for this kind of duopoly (as in the case of Cournot duopoly) are the Nash equilibrium and the Collusive Optimum, without any subsequent critical exam about these two kinds of solutions. The absence of any critical quantitative analysis is due to the relevant lack of knowledge regarding the set of all possible outcomes of this strategic interaction. On the contrary, by considering the Bertrand Duopoly as a differentiable game (games with differentiable payoff functions) and studying it by the new topological methodologies introduced by D. Carfi, we obtain an exhaustive and complete vision of the entire payoff space of the Bertrand game (this also in asymmetric cases with the help of computers) and this total view allows us to analyze critically the classic solutions and to find other ways of action to select Pareto strategies. In order to illustrate the application of this topological methodology to the considered infinite game, several compromise pricing-decisions are considered, and we show how the complete study gives a real extremely extended comprehension of the classic model.
Optimal boundaries for decisions
In this paper we state and prove some new results about the optimal boundaries. These boundaries (also called Pareto boundaries or efficiency boundaries or maximal/minimal boundaries) are of increasing importance in the applications to Decision Theory and Economics. First of all the Pareto boundaries are the first and most important generalization of the optima of decision constraints. On the other hand, if f is a real functional (utility function) defined on a non empty set X (of choices or economic strategies) and K is a part of X, the determination of the optimal boundaries of the part K, with respect to some preference relation ≤ of X for which the function f is strictly increasing, allows to reduce the optimization problem of finding the minimum of the functional f upon the part K to the problem of finding the minimum of f upon the minimal boundary of K. We note that the minimal boundary of K is, in general, greatly smaller than the initial decision constraint K. An economic application to the Cournot duopoly is presented.
The lights that failed: European international history, 1919-1933
PART I: THE RECONSTRUCTION OF EUROPE, 1918-1929 1. The Hall of Mirrors: Peacemaking in the West 2. Distant Frontiers: Peacemaking in the East 3. Revolution from the Left: The Soviet Union and the Post-War Settlement 4. The Primacy of Economics: Reconstruction in Western Europe, 1919-1924 5. The Primacy of Nationalism: Reconstruction in Eastern and Central Europe 6. Revolution from the Right: Italy, 1919-25 7. The Geneva Dream: The League of Nations and Post-War Internationalism 8. New Dawn? Stabilisation in Western Europe after Locarno 9. Faltering Reconstruction: Cracks in the Locarno Facade 10. Troubled Waters: Uncertainties in Italy, Eastern Europe and the Soviet Union 11. Faltering Internationalism: Disarmament and Security after Locarno Conclusion: Europe Reconstructed? PART II: THE HINGE YEARS, 1930-1933 12. The Diplomacy of the Depression: Economics and Foreign Policy 13. Beyond Europe: The Manchurian Crisis 14. The Poisoned Chalice: The Pursuit of Disarmament Conclusion: The Hinge Years Appendices Select Bibliography