A Game Theoretic Approach to Cooperation with Pairwise Cost Reduction

WP_Query Object ( [query] => Array ( [post_type] => publicaciones [meta_key] => _wpcf_belongs_tesis_id [meta_value] => 4059 ) [query_vars] => Array ( [post_type] => publicaciones [meta_key] => _wpcf_belongs_tesis_id [meta_value] => 4059 [error] => [m] => [p] => 0 [post_parent] => [subpost] => [subpost_id] => [attachment] => [attachment_id] => 0 [name] => [pagename] => [page_id] => 0 [second] => [minute] => [hour] => [day] => 0 [monthnum] => 0 [year] => 0 [w] => 0 [category_name] => [tag] => [cat] => [tag_id] => [author] => [author_name] => [feed] => [tb] => [paged] => 0 [preview] => [s] => [sentence] => [title] => [fields] => [menu_order] => [embed] => [category__in] => Array ( ) [category__not_in] => Array ( ) [category__and] => Array ( ) [post__in] => Array ( ) [post__not_in] => Array ( ) [post_name__in] => Array ( ) [tag__in] => Array ( ) [tag__not_in] => Array ( ) [tag__and] => Array ( ) [tag_slug__in] => Array ( ) [tag_slug__and] => Array ( ) [post_parent__in] => Array ( ) [post_parent__not_in] => Array ( ) [author__in] => Array ( ) [author__not_in] => Array ( ) [ignore_sticky_posts] => [suppress_filters] => [cache_results] => 1 [update_post_term_cache] => 1 [lazy_load_term_meta] => 1 [update_post_meta_cache] => 1 [posts_per_page] => 10 [nopaging] => [comments_per_page] => 50 [no_found_rows] => [order] => DESC ) [tax_query] => WP_Tax_Query Object ( [queries] => Array ( ) [relation] => AND [table_aliases:protected] => Array ( ) [queried_terms] => Array ( ) [primary_table] => wp_posts [primary_id_column] => ID ) [meta_query] => WP_Meta_Query Object ( [queries] => Array ( [0] => Array ( [key] => _wpcf_belongs_tesis_id [value] => 4059 ) [relation] => OR ) [relation] => AND [meta_table] => wp_postmeta [meta_id_column] => post_id [primary_table] => wp_posts [primary_id_column] => ID [table_aliases:protected] => Array ( [0] => wp_postmeta ) [clauses:protected] => Array ( [wp_postmeta] => Array ( [key] => _wpcf_belongs_tesis_id [value] => 4059 [compare] => = [compare_key] => = [alias] => wp_postmeta [cast] => CHAR ) ) [has_or_relation:protected] => ) [date_query] => [request] => SELECT SQL_CALC_FOUND_ROWS wp_posts.ID FROM wp_posts INNER JOIN wp_postmeta ON ( wp_posts.ID = wp_postmeta.post_id ) WHERE 1=1 AND ( ( wp_postmeta.meta_key = '_wpcf_belongs_tesis_id' AND wp_postmeta.meta_value = '4059' ) ) AND ((wp_posts.post_type = 'publicaciones' AND (wp_posts.post_status = 'publish'))) GROUP BY wp_posts.ID ORDER BY wp_posts.post_date DESC LIMIT 0, 10 [posts] => Array ( [0] => WP_Post Object ( [ID] => 4062 [post_author] => 19 [post_date] => 2025-03-06 12:01:42 [post_date_gmt] => 2025-03-06 11:01:42 [post_content] => Abstract There are multiple situations in which bilateral interaction between agents results in considerable cost reductions. The cost reduction that an agent obtains depends on the effort made by other agents. We model this situation as a bi-form game with two states. In the first stage, agents decide how much effort to exert. We model this first stage as a non-cooperative game, in which these efforts will reduce the cost of their partners in the second stage. This second stage is modeled as a cooperative game in which agents reduce each other’s costs as a result of cooperation, so that the total reduction in the cost of each agent in a coalition is the sum of the reductions generated by the rest of the members of that coalition. The proposed cost allocation for the cooperative game in the second stage determines the payoff function of the non-cooperative game in the first stage. Based on this model, we explore the costs, benefits, and challenges associated with setting up a pairwise effort situation. We identify a family of cost allocations with weighted pairwise reductions which are always feasible in the cooperative game and contain the Shapley value. We also identify the cost allocation with weighted pairwise reductions that generate an efficient equilibrium effort level. [post_title] => Efficient effort equilibrium in cooperation with pairwise cost reduction [post_excerpt] => [post_status] => publish [comment_status] => closed [ping_status] => closed [post_password] => [post_name] => efficient-effort-equilibrium-in-cooperation-with-pairwise-cost-reduction [to_ping] => [pinged] => [post_modified] => 2025-03-06 12:01:51 [post_modified_gmt] => 2025-03-06 11:01:51 [post_content_filtered] => [post_parent] => 0 [guid] => http://doctoradodecide.com/?post_type=publicaciones&p=4062 [menu_order] => 0 [post_type] => publicaciones [post_mime_type] => [comment_count] => 0 [filter] => raw ) [1] => WP_Post Object ( [ID] => 4060 [post_author] => 19 [post_date] => 2025-03-06 11:57:44 [post_date_gmt] => 2025-03-06 10:57:44 [post_content] => Abstract Corporation tax games were introduced by Meca and Varela-Peña (2018) as an application of linear cost games (see Meca and Sosic, 2014) to a corporate tax reduction system. The authors considered a model of cooperation in corporate tax systems with one benefactor and several beneficiaries. In this chapter, we present a new model of cooperation in corporate tax systems with several beneficiaries and multiple dual benefactors: multiple corporation tax games. Benefactors are dual in the sense they reduce the costs of both beneficiaries and other benefactors. We can say that they are benefactors and beneficiaries. They are also irreplaceable benefactors because all the members of a coalition may see their cost increase if one of them leaves the group. We prove the grand coalition is stable in the sense of the core of multiple corporation tax games. Then, we propose the Shapley value as an easily computable core-allocation that benefits all agents and, in particular, compensates the benefactors for their dual and irreplaceable role. [post_title] => The Shapley Value of Corporation Tax Games with Dual Benefactors [post_excerpt] => [post_status] => publish [comment_status] => closed [ping_status] => closed [post_password] => [post_name] => the-shapley-value-of-corporation-tax-games-with-dual-benefactors [to_ping] => [pinged] => [post_modified] => 2025-03-06 11:58:14 [post_modified_gmt] => 2025-03-06 10:58:14 [post_content_filtered] => [post_parent] => 0 [guid] => http://doctoradodecide.com/?post_type=publicaciones&p=4060 [menu_order] => 0 [post_type] => publicaciones [post_mime_type] => [comment_count] => 0 [filter] => raw ) ) [post_count] => 2 [current_post] => -1 [in_the_loop] => [post] => WP_Post Object ( [ID] => 4062 [post_author] => 19 [post_date] => 2025-03-06 12:01:42 [post_date_gmt] => 2025-03-06 11:01:42 [post_content] => Abstract There are multiple situations in which bilateral interaction between agents results in considerable cost reductions. The cost reduction that an agent obtains depends on the effort made by other agents. We model this situation as a bi-form game with two states. In the first stage, agents decide how much effort to exert. We model this first stage as a non-cooperative game, in which these efforts will reduce the cost of their partners in the second stage. This second stage is modeled as a cooperative game in which agents reduce each other’s costs as a result of cooperation, so that the total reduction in the cost of each agent in a coalition is the sum of the reductions generated by the rest of the members of that coalition. The proposed cost allocation for the cooperative game in the second stage determines the payoff function of the non-cooperative game in the first stage. Based on this model, we explore the costs, benefits, and challenges associated with setting up a pairwise effort situation. We identify a family of cost allocations with weighted pairwise reductions which are always feasible in the cooperative game and contain the Shapley value. We also identify the cost allocation with weighted pairwise reductions that generate an efficient equilibrium effort level. 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