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.
A framework of coopetitive games:applications to the Greek crisis
In the present work we propose an original analytical model of coopetitive game. We shall apply this analytical model of coopetition (based on normal form game theory) to the Greek crisis, while conceiving this game theory model at a macro level. We construct two realizations of such model, trying to represent possible realistic macro-economic scenarios of the Germany-Greek strategic interaction. We shall suggest - after a deep and complete study of the two samples - feasible transferable utility solutions in a properly coopetitive perspective for the divergent interests which drive the economic policies in the euro area.
A quality control model that uses PTV-rectal distances to predict the lowest achievable rectum dose, improves IMRT planning for patients with prostate cancer.
BACKGROUND AND PURPOSE
To predict the lowest achievable rectum D35 for quality assurance of IMRT plans of prostate cancer patients.


MATERIALS AND METHODS
For each of 24 patients from a database of 47 previously treated patients, the anatomy was compared to the anatomies of the other 46 to predict the minimal achievable rectum D35. The 24 patients were then replanned to obtain maximally reduced rectum D35. Next, the newly derived plans were added to the database to replace the original clinical plans, and new predictions of the lowest achievable rectum D35 were made.


RESULTS
After replanning, the rectum D35 reduced by 9.3 Gy±6.1 (average±1 SD; p<0.001) compared to the original plan. The first predictions of the rectum D35 were 4.8 Gy±4.2 (average±1 SD; p<0.001) too high when evaluated with the new plans. After updating the database, the replanned and newly predicted rectum D35 agreed within 0.1 Gy±2.8 (average±1 SD; p=0.89). The doses to the bladder, anus and femoral heads did not increase compared to the original plans.


CONCLUSIONS
For individual prostate patients, the lowest achievable rectum D35 in IMRT planning can be accurately predicted from dose distributions of previously treated patients by quantitative comparison of patient anatomies. These predictions can be used to quantitatively assess the quality of IMRT plans.