In game theory, in order to properly use mixed strategies, equalizing strategies or the Nash arbitration method, we require cardinal payoffs. We present an alternative method to the possible tedious lottery method of ...In game theory, in order to properly use mixed strategies, equalizing strategies or the Nash arbitration method, we require cardinal payoffs. We present an alternative method to the possible tedious lottery method of von Neumann and Morgenstern to change ordinal values into cardinal values using the analytical hierarchy process. We suggest using Saaty’s pairwise comparison with combined strategies as criteria for players involved in a repetitive game. We present and illustrate a methodology for moving from ordinal payoffs to cardinal payoffs. We summarize the impact on how the solutions are achieved.展开更多
Problems associated with energy distribution, consumption and management are undoubtedly some of the most significant problems that energy utilities face globally. For instance, when development takes place, the deman...Problems associated with energy distribution, consumption and management are undoubtedly some of the most significant problems that energy utilities face globally. For instance, when development takes place, the demand for electrical power and in particular domestic electrical energy also increases. Thus improvement of energy distribution policies becomes important for utilities and energy decision making agencies. The authors had earlier [1] [2] provided a mixed strategy 2-player game model for a residential energy consumption profile for winter and summer seasons of the year using a dual-occupancy high-rise (11-storey) building located within the Polytechnic of Namibia, Windhoek. The optimum energy values and the corresponding probabilities obtained from the model extend the usual simple statistical analyses of minimum and maximum energy values and their associated percentages. The time-block and the week-day strategies depict critical probabilistic values worth considering for decision purposes, especially, the necessity and justification for a dual tariff regime for the residential and workplace residents of the building as against the existing institutional uniform energy tariff policy. However, this paper presents extended results of post-optimality analyses for the winter and summer seasons, and thus provides the optimal range of energy values over which the energy consumption can change without changing the optimal tariff estimate parameters obtained from the mixed strategy of critical energy game values. The post-optimality analyses also provide extended information on the mixed strategy of non-optimal week-day solutions obtained from the game model, hence validating one of the essential roles of sensitivity analysis, namely, investigation of sub-optimal solutions. From application point of view, the post-optimality model provides a useful tool for Utilities, especially for identifying flexibility range of optimal break-even energy values for consumers, such as in the informal settlements where metering is rather a challenge to determine varied or non-uniform tariffs.展开更多
文摘In game theory, in order to properly use mixed strategies, equalizing strategies or the Nash arbitration method, we require cardinal payoffs. We present an alternative method to the possible tedious lottery method of von Neumann and Morgenstern to change ordinal values into cardinal values using the analytical hierarchy process. We suggest using Saaty’s pairwise comparison with combined strategies as criteria for players involved in a repetitive game. We present and illustrate a methodology for moving from ordinal payoffs to cardinal payoffs. We summarize the impact on how the solutions are achieved.
文摘Problems associated with energy distribution, consumption and management are undoubtedly some of the most significant problems that energy utilities face globally. For instance, when development takes place, the demand for electrical power and in particular domestic electrical energy also increases. Thus improvement of energy distribution policies becomes important for utilities and energy decision making agencies. The authors had earlier [1] [2] provided a mixed strategy 2-player game model for a residential energy consumption profile for winter and summer seasons of the year using a dual-occupancy high-rise (11-storey) building located within the Polytechnic of Namibia, Windhoek. The optimum energy values and the corresponding probabilities obtained from the model extend the usual simple statistical analyses of minimum and maximum energy values and their associated percentages. The time-block and the week-day strategies depict critical probabilistic values worth considering for decision purposes, especially, the necessity and justification for a dual tariff regime for the residential and workplace residents of the building as against the existing institutional uniform energy tariff policy. However, this paper presents extended results of post-optimality analyses for the winter and summer seasons, and thus provides the optimal range of energy values over which the energy consumption can change without changing the optimal tariff estimate parameters obtained from the mixed strategy of critical energy game values. The post-optimality analyses also provide extended information on the mixed strategy of non-optimal week-day solutions obtained from the game model, hence validating one of the essential roles of sensitivity analysis, namely, investigation of sub-optimal solutions. From application point of view, the post-optimality model provides a useful tool for Utilities, especially for identifying flexibility range of optimal break-even energy values for consumers, such as in the informal settlements where metering is rather a challenge to determine varied or non-uniform tariffs.
