Partitioning Sequencing Situations and Games

The research that studies the interaction between sequencing situations and cooperative games, that started with the paper of Curiel et al. (1989), has become an established line of research. This paper introduces a new model in this field: partitioning sequencing situations and games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. Next, we define cooperative games that arise from these partitioning sequencing situations. It is shown that these games are convex. Moreover, we present a game independent expression for the Shapley value. Finally, it is shown that the partitioning equal gain splitting rule can be used to generate a core allocation and can be viewed as the average of two specific marginal vectors.Sequencing situations;sequencing games

A Game Theoretic Approach to Analyse Cooperation between Rural Households in Northern Nigeria

Much research focuses on development of new agricultural technologies to reduce poverty levels of the large population of smallholder farms in Sub Saharan Africa. In this paper we argue that smallholders can also increase their production in a different way, namely by using their resources more efficiently through cooperation. This is obtained by grouping their (heterogeneous) resources and making joint decisions based on the aggregate resources. Afterwards, the gains of the joint production are divided, such that each farmer remains independent. This type of cooperation is modeled using linear programming and cooperative game theory. While linear programming establishes insight in optimal farm plans for farmers that cooperate, game theory is used to generate fair divisions of the extra gain that is established by cooperation. The model is applied to a village in Northern Nigeria. Households are clustered based on socio-economic parameters, and we explore cooperation. The optimal farm plan of the cooperative (i.e., farmers cooperate) contains more crops with high market and nutritional value, such as cowpea and sugarcane. We show that the gross margin of the cooperative is 12% higher than the sum of the individual gross margins. To divide these gains, we consider four established solution concepts from game theory that divide these extra gains: the Owen value, Shapley value, compromise value and nucleolus. An interesting result is that all farmers gain from cooperation and that the four solution concepts give similar results. Finally, we show how the provision of micro-credit can be used to stimulate cooperation in practice, benefiting the least-endowed farmers as well.Linear Programming;Agriculture;Household models;Cooperative Game Theory;Nigeria

Partitioning Sequencing Situations and Games

The research that studies the interaction between sequencing situations and cooperative games, that started with the paper of Curiel et al. (1989), has become an established line of research. This paper introduces a new model in this field: partitioning sequencing situations and games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. Next, we define cooperative games that arise from these partitioning sequencing situations. It is shown that these games are convex. Moreover, we present a game independent expression for the Shapley value. Finally, it is shown that the partitioning equal gain splitting rule can be used to generate a core allocation and can be viewed as the average of two specific marginal vectors.

A Game Theoretic Approach to Analyse Cooperation between Rural Households in Northern Nigeria

To improve the livelihood of the poor in Sub-Saharan Africa (SSA) much attention has been paid to the development of new agricultural technologies. We hypothesize that farmers can also improve their livelihood through cooperation. Partial cooperation, in which knowledge is shared or bargaining power improved, is relatively common in SSA, while cooperation where all resources are fully shared, which we address, has rarely been investigated. An important pre-requisite to establish such cooperation, is the need for a fair division rule for the gains of the cooperation. This paper combines linear programming and cooperative game theory to model the effects of cooperation of (individual) households on income and farm plans. Linear programming establishes insight in the optimal farm plans in cooperation, and cooperative game theory is used to generate fair division rules. The model is applied to a village in Northern Nigeria. Households are clustered based on socio-economic parameters, and we explore cooperation between clusters. Cooperation leads to increased income and results in changes in farm plans, because more efficient use of resources leads to more intensified agriculture (labour intensive – high value crops).Cooperations, Linear Programming, Nigeria, Livelihood, Agricultural and Food Policy, Community/Rural/Urban Development, Consumer/Household Economics, Environmental Economics and Policy, Food Consumption/Nutrition/Food Safety, Food Security and Poverty, International Relations/Trade, Marketing, Productivity Analysis, Research and Development/Tech Change/Emerging Technologies,

Why Methods for Optimization Problems with Time-Consuming Function Evaluations and Integer Variables Should Use Global Approximation Models

This paper advocates the use of methods based on global approximation models for optimization problems with time-consuming function evaluations and integer variables.We show that methods based on local approximations may lead to the integer rounding of the optimal solution of the continuous problem, and even to worse solutions.Then we discuss a method based on global approximations.Test results show that such a method performs well, both for theoretical and practical examples, without suffering the disadvantages of methods based on local approximations.approximation models;black-box optimization;integer optimization

A Game Theoretic Approach to Analyse Cooperation between Rural Households in Northern Nigeria

Much research focuses on development of new agricultural technologies to reduce poverty levels of the large population of smallholder farms in Sub Saharan Africa. In this paper we argue that smallholders can also increase their production in a different way, namely by using their resources more efficiently through cooperation. This is obtained by grouping their (heterogeneous) resources and making joint decisions based on the aggregate resources. Afterwards, the gains of the joint production are divided, such that each farmer remains independent. This type of cooperation is modeled using linear programming and cooperative game theory. While linear programming establishes insight in optimal farm plans for farmers that cooperate, game theory is used to generate fair divisions of the extra gain that is established by cooperation. The model is applied to a village in Northern Nigeria. Households are clustered based on socio-economic parameters, and we explore cooperation. The optimal farm plan of the cooperative (i.e., farmers cooperate) contains more crops with high market and nutritional value, such as cowpea and sugarcane. We show that the gross margin of the cooperative is 12% higher than the sum of the individual gross margins. To divide these gains, we consider four established solution concepts from game theory that divide these extra gains: the Owen value, Shapley value, compromise value and nucleolus. An interesting result is that all farmers gain from cooperation and that the four solution concepts give similar results. Finally, we show how the provision of micro-credit can be used to stimulate cooperation in practice, benefiting the least-endowed farmers as well.

Why Methods for Optimization Problems with Time-Consuming Function Evaluations and Integer Variables Should Use Global Approximation Models

This paper advocates the use of methods based on global approximation models for optimization problems with time-consuming function evaluations and integer variables.We show that methods based on local approximations may lead to the integer rounding of the optimal solution of the continuous problem, and even to worse solutions.Then we discuss a method based on global approximations.Test results show that such a method performs well, both for theoretical and practical examples, without suffering the disadvantages of methods based on local approximations.

Partitioning sequencing situations and games

The interaction between sequencing situations and cooperative games starting from the paper of Curiel et al. [Curiel, I., Pederzoli, G., Tijs S., 1989. Sequencing games. European Journal of Operational Research 40, 344-351], has become an established line of research within the theory of operation research games. The current paper introduces a new model in this field: partitioning sequencing situations and associated games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. We define cooperative games corresponding to partitioning sequencing situations and show that these games are convex. Moreover, we present a game independent expression for the Shapley value of these games. Finally, it is shown that the partitioning equal gain splitting rule leads to a core allocation which is the average of two specific marginal vectors

A quantitative framework to analyse cooperation between rural households

Different types of cooperative agreements between smallholders continue to play an important role in rural areas in developing countries. While some empirical studies examine the conditions catalysing the successful formation of cooperatives, quantifications of the net benefits, i.e., difference between revenues and costs, of cooperation and how farmers divide these net benefits are scarce. Therefore, we develop a quantitative framework to analyse and allocate net benefits in a cooperative production agreement. The framework allows for cooperative exchange of several types of resources and the production of multiple products. Linear programming provides insight into optimal production levels, both for individual and cooperating farmers, and gives optimal revenue levels. A transaction cost function is used to account for costs of cooperation, such as meeting costs, moral hazard and free ridership of labour use and the risks of farmers defaulting from the agreement. Transaction costs are likely to increase with the number of households participating, the total cropping area and the heterogeneity of resources of the cooperating farmers. Therefore, we introduce a measure of heterogeneity in the resources for each cooperative. Finally, cooperative game theory is used to generate fair divisions of the net benefits in a cooperative. This framework may be used to give additional explanations to the findings in empirical studies on cooperatives. We illustrate this with an empirical example from northern Nigeria. It is found that cooperation between farmers sharing complementary resources gives the highest revenues. Next, we illustrate the effects of two different transaction cost functions. For reasonable assumptions on these functions, cooperation remains economically attractive. Nevertheless, larger and more diverse coalitions are not always the most beneficial, while the returns in some small coalitions are negative, possibly impeding the formation of cooperatives in some location

A quantitative framework to analyse cooperation between rural households

Different types of cooperative agreements between smallholders continue to play an important role in rural areas in developing countries. While some empirical studies examine the conditions catalysing the successful formation of cooperatives, quantifications of the net benefits, i.e., difference between revenues and costs, of cooperation and how farmers divide these net benefits are scarce. Therefore, we develop a quantitative framework to analyse and allocate net benefits in a cooperative production agreement. The framework allows for cooperative exchange of several types of resources and the production of multiple products. Linear programming provides insight into optimal production levels, both for individual and cooperating farmers, and gives optimal revenue levels. A transaction cost function is used to account for costs of cooperation, such as meeting costs, moral hazard and free ridership of labour use and the risks of farmers defaulting from the agreement. Transaction costs are likely to increase with the number of households participating, the total cropping area and the heterogeneity of resources of the cooperating farmers. Therefore, we introduce a measure of heterogeneity in the resources for each cooperative. Finally, cooperative game theory is used to generate fair divisions of the net benefits in a cooperative. This framework may be used to give additional explanations to the findings in empirical studies on cooperatives. We illustrate this with an empirical example from northern Nigeria. It is found that cooperation between farmers sharing complementary resources gives the highest revenues. Next, we illustrate the effects of two different transaction cost functions. For reasonable assumptions on these functions, cooperation remains economically attractive. Nevertheless, larger and more diverse coalitions are not always the most beneficial, while the returns in some small coalitions are negative, possibly impeding the formation of cooperatives in some locations.Linear programming Agriculture Household models Cooperative game theory Transaction costs