A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements
In an economic or social situation where agents have to group in order to achieve common goals, how can we calculate the coalitional rents of the agents arising from the coalition formation? Once we have formalized the situation via a TU-game and a network describing the economic structure, we can apply different allocation rules to assign the coalitional rents to the agents. We specifically analyze situations where parties with a specific vote distribution in a parliament have to build agreements in order to reach some required quorum. In this situation, we want to measure the (relative) distribution of power. We analyze the allocation rules called Position value (Meessen (1988) and Borm et al. (1992)) and graph-chi-value (Casajus (2009)). Applying the generalized framework (Gomez et al. (2008)), a framework where coalitions are not established yet, we fi nd that the graph-chi-value does not differ for networks referring to the same coalition while the Position value takes into account the specific role of an agent within the network, i.e. the communication path. We define and characterize a new outside option sensitive value, the Kappa-value, which takes into account both outside options and the role of an agent within the network.
A probabilistic position value
In this article, we generalize the position value, defined by Meessen (Master’s thesis, 1988) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations (Gómez et al. in European Journal of Operational Research 190:539–556, 2008). We provide two characterizations of this new allocation rule. Following in Slikker’s (International Journal of Game Theory 33:505–514, 2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link contributions. Then we generalize the notion of link potential, defined by Slikker (International Game Theory Review 7:473–489, 2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule.
Effect of Aeration and Agitation Regimes on Lipase Production by Newly Isolated Rhodotorula mucilaginosa–MTCC 8737 in Stirred Tank Reactor Using Molasses as Sole Production Medium
The influence of media and process parameters (aeration and agitation) on fermentation broth rheology and biomass formation has been studied in 1.5-l stirred tank reactor for lipase production using Rhodotorula mucilaginosa MTCC 8737. Molasses, as sole production medium, is used for lipase production by varying aeration (1, 2, and 3 vvm) and agitation speeds (100, 200, and 300 rpm). Maximum lipase activity of 72 U/ml was obtained during 96 h of fermentation at 2 vvm, 200 rpm, pH 7, and 25 ± 2°C temperature. Lipase production kinetics with respect to dry cell weight of biomass showed YP/S of 25.71 U/mg, specific product formation of 10.9 U/mg DC, and YX/S 2.35 mg/mg. Maximum lipase activity (MC 2) of 56 U/ml was observed at 1% molasses, and a further increase in the molasses concentration of (%) 1.5 and 2 inhibited the product formation of lipase with 15 and 8.5 U/ml, respectively. The production kinetics of molasses media showed YP/X was 14 U/mg DC, YP/S 16 U/mg, and YX/S 1.14 mg/mg during 96 h of bioreactor operation. The kLa values for all batches (MC 1–MC 4) at 96 h of fermentation were 32, 28, 21, and 19/h, and the |oxygen transfer rate were 54.4, 56, 35.7, and 17.29 mg/l h, respectively. Increase in molasses concentration resulted in decreased lipase activity by increase in viscosity of the fermentation broth.