Abstract
In this overview of the study conducted, allocation rules in cooperative games are examined. The paper collects some possible and impossible results of merging into a single player or splitting into a smaller unit in corporative games. The cooperative games come with side payment.
Introduction
A cooperative game with side payments is a basis of conflict. The game involves a definite number of players and the worth of each player in each team (Herings & Habis, 2006). The problems arise when analysts try to determine the player set and each of their value. Since each player is entitled to a valuation, most players in the game decide to merge or split into smaller components to streamline operations or increase profits.
Players in corporative games may include a group of people such as a nation or a labour union. The players can be induced to merge to form a single player or split into smaller units. The decision to either split or merge is driven by market factors and is usually dictated by the allocation rules that are set in place. The merging of players to form cartels has been proven to bring profitability to the individual operations, and splitting has been known to help streamline business operations. These actions can, however, set back the overall game. Mergers in an oligopoly can lead to the creation of monopolies which eventually have a harmful effect on the industry (Knudsen & Østerdal, 2012). The study will look at the variables of the games and determine if there are allocation rules that reduce the effects of the actions of mergers and split-offs.
This paper seeks to analyze the possible and impossible results that can come from manipulation of the allocation rules. The aim of the study is to establish whether an allocation rule can be immune to the effects of a merger between players. Another measure of this study is to create the possible results of an allocation rule being immune to the consequences of a split-off. Empirical data on monotonic convex games show that there exist allocation rules that are resistant to mergers, but none exists that are robust against split-offs.
Methodology
Various relations are tested with the variables going through monotonic, additive, balanced, convex and super balanced states. The various scenarios are denoted in algebraic formulae to represent the various allocation rules and the influences of allocation rules on them. The data derived from these formulae establish a basis for the results of the study.
Data
The data used included results of formulae that apply various allocation measures on the variables. The data collected in the survey is completely hypothetical and requires no physical data collection method. The results of the formulae are used to establish a pattern of the most likely real-life scenario that can occur.
Results
Impossibilities
The results concluded that in strictly monotonic convex games, no game is random. In monotonic convex games, no rule is anonymous and immune to the effect of splitting. Impossibility is in the class of monotonic totally balanced games no core selection is immune to the effects of a spilt or a merge.
Possibilities
In strictly monotonic convex games, a core selection is immune to a split while the Fujishige-Dutta-Ray rule is immune to a merger.
Final Remarks
Conclusion
The study was on a topic of interest with multitudes of applications in the real business world. A study of the complexities of allocation rules in cooperate games can be used to counter the threats of creations of monopolies (Lasisi, 2013). This action will serve to secure the market keeping competition in all industry (Maestripieri, 2012). The writers should also be applauded for the use of a methodology that does not require a lot of data collection.
The report, however, has several shortcomings. The first failure of this study is the lack of proper literature review and a theoretical framework. These factors make the study too weak to have any major impact on the industry. The second mistake is the language used in the write-up. The language is too technical for the lay reader to understand. This jargon automatically limits the number of readers of the study, decreasing its potential impact.
References
Herings, P. J., & Habis, H. (2006). Stochastic Bankruptcy Games. SSRN Electronic Journal. doi:10.2139/ssrn.1961141
Knudsen, P. H., & Østerdal, L. P. (2012). Merging and splitting in cooperative games: some (im)possibility results. International Journal of Game Theory, 41(4), 763-774. doi:10.1007/s00182-012-0337-7
Lasisi, R. O. (2013). Experimental Analysis of the Effects of Manipulations in Weighted Voting Games.
Maestripieri, D. (2012). Games primates play: An undercover investigation of the evolution and economics of human relationships. New York, NY: Basic Books.
