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Symmetrization of the Classical “Attack-defense” Model
Pavel Yuryevich Kabankov,
Alexander Gennadevich Perevozchikov,
Valery Yuryevich Reshetov,
Igor Evgenievich Yanochkin
Issue:
Volume 8, Issue 1, February 2020
Pages:
1-10
Received:
7 December 2019
Accepted:
18 December 2019
Published:
7 January 2020
Abstract: The article considers Germeyer’s “doubled” classic “attack-defense” game, which is symmetrical for the participants in the sense that in one game each participant is an “attack” party and in the other game each participant is a “defense” party. This corresponds to the logic of bilateral active-passive operations, when the parties simultaneously conduct defensive-offensive operations against each other. The mathematical expectation of the number of destroyed enemy means is taken as criteria for the effectiveness of the parties, which should be maximized implicitly. Thus, both sides are placed in a “defense” position. Under otherwise equal conditions, the parties strive to minimize shares aimed at defense, guided by a strategy of reasonable sufficiency of defense. The authors study Pareto-dominated equilibria depending on the initial ratio of the parties forces and, in particular, the extreme points of Pareto sets. Formulas are obtained for such equilibria depending on the parties’ balance of forces, which allows us to build a dynamic expansion of the model in the future. The main research method is the parametrization of Nash’s equilibria. The parameterization of the equilibria shows that they fill the two-dimensional subregion of a unit square with a boundary. Therefore, for its narrowing, it makes sense to distinguish from it the Pareto-non-dominated part of the boundary and its extreme points. The latter provide an opportunity to assess the maximum share of the strike means of the parties, which they can afford to allocate without prejudice to the defense. It is shown that these fractions represent piecewise continuous functions of the initial ratio of the parties’ forces and explicit expressions for them are obtained. A numerical example of the construction of the Pareto-non-dominated part of the boundary and its extreme points is given.
Abstract: The article considers Germeyer’s “doubled” classic “attack-defense” game, which is symmetrical for the participants in the sense that in one game each participant is an “attack” party and in the other game each participant is a “defense” party. This corresponds to the logic of bilateral active-passive operations, when the parties simultaneously con...
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Spatial Comparison and Quality Check of Farmer-recorded Daily Rainfall Data; A Case of Nyakach and Soin-sigowett, Kenya
Mawora Thomas Mwakudisa,
Edgar Ouko Otumba,
Joyce Akinyi Otieno
Issue:
Volume 8, Issue 1, February 2020
Pages:
11-18
Received:
11 December 2019
Accepted:
2 January 2020
Published:
9 January 2020
Abstract: Small scale farming is currently still heavily dependent on rainfall in developing nations. With the challenge of climate change, many innovations are proposed to help the farmers mitigate and adapt. The use of historical data provides a starting point in development of decision support tools for them. However, most climate data are not local, but far from the farmers. Thus, the challenge of representability of the data is questioned. In order to use the decision support tools with farmers at Nyakach and Soin-Sigowett, Kenya, historical data was used from a synoptic station 20 km away. The locals felt it was not representative enough, hence the need to look for more local data. In 2014, a CCAFS project empowered 100 farmers from the region with low cost rain gauges to collect and record their own data for use in decision support tools. In this paper, we look at the quality of the data comparing it to the KMS data. Line graphs were used to compare the total seasonal rain for more than 30 years with the farmers perception. In addition, pairwise t-tests have been used to compare difference in farmers recorded rain to the value at the synoptic station. Data from volunteer stations have also been used to confirm the validity of the spatial difference in the data. The results showed that quality of the farmers data is adequate for use. Further, data from farmers deviated from the main synoptic station half of the time. The results clearly show that there is need to allow locals collect their own data to help capture the spatial differences in climate. The farmers recorded data was good quality hence can be used in decision support tools to help them adapt to possible climate change.
Abstract: Small scale farming is currently still heavily dependent on rainfall in developing nations. With the challenge of climate change, many innovations are proposed to help the farmers mitigate and adapt. The use of historical data provides a starting point in development of decision support tools for them. However, most climate data are not local, but ...
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The Association Between Cancer Incidence, HIV Prevalence, and Gross Domestic Product in Uganda
Kelvin Roland Mubiru,
Hellen Namawejje,
Leonard Atuhaire
Issue:
Volume 8, Issue 1, February 2020
Pages:
19-26
Received:
25 January 2020
Accepted:
10 February 2020
Published:
14 February 2020
Abstract: This research examines the association of cancer incidence, HIV prevalence and gross domestic product in Uganda. The study utilised secondary data were Cancer data was obtained from the Kampala Cancer Registry, Uganda. Gross domestic product data from IMF’s World Economic Outlook and AIDS data from UNAIDS 2017 report. Multivariate time series analysis method was used covering a period from 1993 -2014. The research findings indicate that the Non-AIDS defining cancers, that is, stomach (p=0.000), eye (p=0.000), liver (p=0.000) and prostate (p=0.000) had a long run positive significant relationship with HIV prevalence while colon (p=0.002), lung (p=0.00) and breast (p=0.004) had a negative significant relationship with HIV prevalence. Also breast (p=0.00) and prostate (p=0.001) had a positive significant relationship with Gross domestic product while cancer of the lung (p=0.000) had a negative significant relationship with gross domestic product in Uganda. AIDS defining cancers such as Non-Hodgkin cancer (p=0.001) had a long run positive significant relationship with HIV prevalence while cervical (p=0.000) had a negative significant relationship with HIV prevalence. Cervical cancer (p=0.014) had a positive significant relationship with Gross domestic product in Uganda. The study recommends government to enhance policies that reduce HIV since it was observed that HIV had a significant relationship with cancer.
Abstract: This research examines the association of cancer incidence, HIV prevalence and gross domestic product in Uganda. The study utilised secondary data were Cancer data was obtained from the Kampala Cancer Registry, Uganda. Gross domestic product data from IMF’s World Economic Outlook and AIDS data from UNAIDS 2017 report. Multivariate time series analy...
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Distribution Effect on the Efficiency of Some Classes of Population Variance Estimators Using Information of an Auxiliary Variable Under Simple Random Sampling
Etaga Harrison Oghenekevwe,
Etaga Cecilia Njideka,
Osuoha Chizoba Sylvia
Issue:
Volume 8, Issue 1, February 2020
Pages:
27-34
Received:
29 January 2020
Accepted:
12 February 2020
Published:
20 February 2020
Abstract: In many sampling situations, researchers come across variety of data. These data are largely affected by the parent distribution. There are characteristics which some data share based on the parent distribution. These characteristics define their distribution as well as their behavior. The use of auxiliary variable in estimating a study variable has been on the increase. Auxiliary variable has been used in estimating population means as well as variances. The variance is very sensitive to distribution. Thus, estimating the variance using auxiliary variable might lead to some unexpected results. Hence the need to check the effect of the distribution of the performances of some selected classes of variance estimators. Twelve estimators were selected for comparison. Eight distributions were considered using simulation study. The selected distributions are: Normal, Chi-square, Uniform, Gamma, Exponential, Poisson, Geometric and Binomial. A population size of 330 was used while sample size of 30 was considered using simple random sample without replacement. The estimators were compared using Bias, and Mean Square Error. The performances of the estimators vary in some distributions. The gamma and exponential distributions showed wide variability. The performances of the estimators based on Bias is the same as that based on Mean Square Error. The Mean Square Errors were ranked. The best estimator is t1 followed be t10 and t12. The results showed that the estimators are not distribution free.
Abstract: In many sampling situations, researchers come across variety of data. These data are largely affected by the parent distribution. There are characteristics which some data share based on the parent distribution. These characteristics define their distribution as well as their behavior. The use of auxiliary variable in estimating a study variable ha...
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