{"title":"Manu Will Unfold The Rubik’s Manifold: 42 Easy Steps To Solving The Cube","authors":"Manu Kashyap, R. Kashyap","doi":"10.2139/ssrn.3880841","DOIUrl":"https://doi.org/10.2139/ssrn.3880841","url":null,"abstract":"We have provided a simple step by step guide to solving the Rubik’s cube. We have aimed for this document to be completely self contained and yet easy to follow. We have described all the required notation and terminology in a clear manner. We have tried to provide all the steps in sufficient detail though we have strived to keep it as straightforward as possible. The number of steps is 42, which suggests that there is more to solving the cube than meets the eye and perhaps, the cube holds many more puzzles about unraveling the mystery of the cosmos. 42, or The Answer to the Ultimate Question of Life, The Universe, and Everything.","PeriodicalId":347673,"journal":{"name":"DecisionSciRN: Solution Concepts (Sub-Topic)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116819018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discovery Process in Normal-Form Games with Unawareness: Cognitive Stability and Closedness under Rational Behavior","authors":"Yoshihiko Tada","doi":"10.2139/ssrn.3781717","DOIUrl":"https://doi.org/10.2139/ssrn.3781717","url":null,"abstract":"This study examines how each player chooses her/his optimal action in \"normal-form games with unawareness\" by applying a \"discovery process\" to them. We show that if each player implements a best response to the opponents' immediately preceding plays, then any discovery process converges to a set closed under rational behavior (CURB) on the realizable action set. Moreover, in the objective game in any initial normal-form game with unawareness, when every CURB set on the realizable action set is mutually known, every discovery process converges to a discovered game possessing a cognitively stable generalized Nash equilibrium. It is not necessary that each player must be aware of the opponents' utilities in our results.","PeriodicalId":347673,"journal":{"name":"DecisionSciRN: Solution Concepts (Sub-Topic)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121778462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Recursive Nash-in-Nash Bargaining Solution","authors":"Xiaowei Yu, K. Waehrer","doi":"10.2139/ssrn.3319517","DOIUrl":"https://doi.org/10.2139/ssrn.3319517","url":null,"abstract":"The standard Nash-in-Nash solution is commonly applied in a number of policy applications. However, this bargaining framework does not capture renegotiation on off-equilibrium paths or contingent contracts and as a result in some situations the predictions of standard Nash-in-Nash are counter-intuitive. Thus, we propose a new bargaining solution for interdependent bilateral negotiations, which we call the recursive Nash-in-Nash bargaining solution. The main difference between this bargaining framework and the standard Nash-in-Nash is in the treatment of the disagreement point, which we assume is the bargaining payoffs given that all other negotiations happen with recognition of this disagreement rather than the equilibrium outcomes. We show that under some assumptions, the recursive Nash-in-Nash bargaining solution is the same as the Shapley value or the more general Myerson value for the corresponding cooperative game. This equivalence allows the recursive Nash-in-Nash solution to be calculated relatively easily for policy applications.","PeriodicalId":347673,"journal":{"name":"DecisionSciRN: Solution Concepts (Sub-Topic)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126880243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}