58,898 research outputs found
From winning strategy to Nash equilibrium
Game theory is usually considered applied mathematics, but a few
game-theoretic results, such as Borel determinacy, were developed by
mathematicians for mathematics in a broad sense. These results usually state
determinacy, i.e. the existence of a winning strategy in games that involve two
players and two outcomes saying who wins. In a multi-outcome setting, the
notion of winning strategy is irrelevant yet usually replaced faithfully with
the notion of (pure) Nash equilibrium. This article shows that every
determinacy result over an arbitrary game structure, e.g. a tree, is
transferable into existence of multi-outcome (pure) Nash equilibrium over the
same game structure. The equilibrium-transfer theorem requires cardinal or
order-theoretic conditions on the strategy sets and the preferences,
respectively, whereas counter-examples show that every requirement is relevant,
albeit possibly improvable. When the outcomes are finitely many, the proof
provides an algorithm computing a Nash equilibrium without significant
complexity loss compared to the two-outcome case. As examples of application,
this article generalises Borel determinacy, positional determinacy of parity
games, and finite-memory determinacy of Muller games
Preference fusion and Condorcet's Paradox under uncertainty
Facing an unknown situation, a person may not be able to firmly elicit
his/her preferences over different alternatives, so he/she tends to express
uncertain preferences. Given a community of different persons expressing their
preferences over certain alternatives under uncertainty, to get a collective
representative opinion of the whole community, a preference fusion process is
required. The aim of this work is to propose a preference fusion method that
copes with uncertainty and escape from the Condorcet paradox. To model
preferences under uncertainty, we propose to develop a model of preferences
based on belief function theory that accurately describes and captures the
uncertainty associated with individual or collective preferences. This work
improves and extends the previous results. This work improves and extends the
contribution presented in a previous work. The benefits of our contribution are
twofold. On the one hand, we propose a qualitative and expressive preference
modeling strategy based on belief-function theory which scales better with the
number of sources. On the other hand, we propose an incremental distance-based
algorithm (using Jousselme distance) for the construction of the collective
preference order to avoid the Condorcet Paradox.Comment: International Conference on Information Fusion, Jul 2017, Xi'an,
Chin
Evaluating strategies for implementing industry 4.0: a hybrid expert oriented approach of B.W.M. and interval valued intuitionistic fuzzy T.O.D.I.M.
open access articleDeveloping and accepting industry 4.0 influences the industry structure and customer willingness. To a successful transition to industry 4.0, implementation strategies should be selected with a systematic and comprehensive view to responding to the changes flexibly. This research aims to identify and prioritise the strategies for implementing industry 4.0. For this purpose, at first, evaluation attributes of strategies and also strategies to put industry 4.0 in practice are recognised. Then, the attributes are weighted to the experts’ opinion by using the Best Worst Method (BWM). Subsequently, the strategies for implementing industry 4.0 in Fara-Sanat Company, as a case study, have been ranked based on the Interval Valued Intuitionistic Fuzzy (IVIF) of the TODIM method. The results indicated that the attributes of ‘Technology’, ‘Quality’, and ‘Operation’ have respectively the highest importance. Furthermore, the strategies for “new business models development’, ‘Improving information systems’ and ‘Human resource management’ received a higher rank. Eventually, some research and executive recommendations are provided. Having strategies for implementing industry 4.0 is a very important solution. Accordingly, multi-criteria decision-making (MCDM) methods are a useful tool for adopting and selecting appropriate strategies. In this research, a novel and hybrid combination of BWM-TODIM is presented under IVIF information
Liquidity preference and information
This paper explores the link between anticipated information and a preference for liquidity in investment choices. Given a subjective ordering of investment portfolios by their liquidity, we identify a sufficient condition under which the prospect of finer resolution of uncertainty creates a preference for more liquid positions. We then show how this condition might arise naturally in some standard classes of sequential decision problems
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