114 research outputs found
Algebraic duality theorems for infinite LP problems
In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players
Common priors for generalized type spaces
The notion of common prior is well-understood and widely-used in the incomplete information games literature. For ordinary type spaces the common prior is de�fined. Pint�er and Udvari (2011) introduce the notion of generalized type space. Generalized type spaces are models for various bonded rationality issues, for �nite belief hierarchies, unawareness among others.
In this paper we de�ne the notion of common prior for generalized types spaces. Our results are as follows: the generalization (1) suggests a new form of common prior for ordinary type spaces, (2) shows some quantum game theoretic results (Brandenburger and La Mura, 2011) in new light
On the completeness of the universal knowledge-belief space
Meier (2008) shows that the universal knowledge-belief space exists. However, besides the universality there is an other important property might be imposed on knowledge-belief spaces, inherited also from type spaces, the completeness. In this paper we introduce the notion of complete knowledge-belief space, and demonstrate that the universal knowledge-belief space is not complete, that is, some subjective beliefs (probability measures) on the universal knowledge-belief space are not knowledge-belief types
Type space on a purely measurable parameter space
Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Hars´anyi suggested the concept of the type space. Later Mertens & Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space. The topological assumptions were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist. We construct a universal type space, which employs purely a measurable parameter space structure
Invariance under type morphisms: the bayesian Nash equilibrium
Ely and Peski (2006) and Friedenberg and Meier (2010) provide examples when changing the type space behind a game, taking a "bigger" type space, induces changes of Bayesian Nash Equilibria, in other words, the Bayesian Nash Equilibrium is not invariant under type morphisms. In this paper we introduce the notion of strong type morphism. Strong type morphisms are stronger than ordinary and conditional type morphisms (Ely and Peski, 2006), and we show that Bayesian Nash Equilibria are not invariant under strong type morphisms either. We present our results in a very simple, finite setting, and conclude that there is no chance to get reasonable assumptions for Bayesian Nash Equilibria to be invariant under any kind of reasonable type morphisms
A Note on Common Prior
Harsányi introduced the concept of type space in an intuitive way. Later Heifetz and Samet formalized it. Harsányi used conditional probabilities to model the beliefs of the players, Heifetz and Samet avoided using conditional probabilities formally. We show that in both cases the concept of transition probability can reproduce the models, moreover, the transition probability approach fits to both Harsányi's intuition and the formalization of Heifetz and Samet. As a consequence, our results suggest that the concept of common prior is not appropriate to determine the players' beliefs. Two examples are also given.Beliefs, Conditional probability, Common Prior
Common priors for generalized type spaces
The notion of common prior is well-understood and widely-used in the incomplete information games literature. For ordinary type spaces the common prior is defined. Pinter and Udvari (2011) introduce the notion of generalized type space. Generalized type spaces are models for various bonded rationality issues, for finite belief hierarchies, unawareness among others. In this paper we define the notion of common prior for generalized types spaces. Our results are as follows: the generalization (1) suggests a new form of common prior for ordinary type spaces, (2) shows some quantum game theoretic results (Brandenburger and La Mura, 2011) in new light.Type spaces; Generalized type spaces; Common prior; Harsányi Doctrine; Quantum games
On the impossibility of fair risk allocation
Measuring and allocating risk properly are crucial for performance evaluation and internal capital allocation of portfolios held by banks, insurance companies, investment funds and other entities subject to financial risk. We show that by using a coherent measure of risk it is impossible to allocate risk satisfying the natural requirements of (Solution) Core Compatibility, Equal Treatment Property and Strong Monotonicity. To obtain the result we characterize the Shapley value on the class of totally balanced games and also on the class of exact games
Cooperation in an HMMS-type supply chain: A management application of cooperative game theory = KooperáciĂł egy HMMS-tĂpusĂş ellátási láncban: A kooperatĂv játĂ©kelmĂ©let egy menedzsment alkalmazása
We apply cooperative game theory concepts to analyze a Holt-Modigliani-Muth-Simon (HMMS) supply chain. The bullwhip effect in a two-stage supply chain (supplier-manufacturer) in the framework of the HMMS-model with quadratic cost functions is considered. It is assumed that both firms minimize their relevant costs, and two cases are examined: the supplier and the manufacturer minimize their relevant costs in a decentralized and in a centralized (cooperative) way. The question of how to share the savings of the decreased bullwhip effect in the centralized (cooperative) model is answered by the weighted Shapley value, by a transferable utility cooperative game theory tool, where the weights are for the exogenously given “bargaining powers” of the participants of the supply chain. = A cikkben a kooperatĂv játĂ©kelmĂ©let fogalmait alkalmazzuk egy Holt-Mogigliani-Muth-Simon-tĂpusĂş ellátási lánc esetĂ©ben. Az ostorcsapás-hatás elemeit egy beszállĂtĂł-termelĹ‘ ellátási láncban ragadjuk meg egy kvadratikus kĂ©szletezĂ©si Ă©s termelĂ©si költsĂ©g mellett. FeltĂ©telezzĂĽk, hogy mindkĂ©t vállalat minimalizálja a releváns költsĂ©geit. KĂ©t működĂ©si rendszert hasonlĂtunk össze: egy hierarchikus döntĂ©shozatali rendszert, amikor elĹ‘ször a termelĹ‘, majd a beszállĂtĂł optimalizálja helyzetĂ©t, majd egy centralizált (kooperatĂv) modellt, amikor a vállalatok az egyĂĽttes költsĂ©gĂĽket minimalizálják. A kĂ©rdĂ©s Ăşgy merĂĽl fel, hogy a csökkentett ostorcsapás-hatás esetĂ©n hogyan osszák meg a rĂ©szvevĹ‘k ebben a transzferálhatĂł hasznosságĂş kooperatĂv játĂ©kban a költsĂ©g megtakarĂtást, exogĂ©n mĂłdon adott tárgyalási pozĂciĂł mellett
Young's axiomatization of the Shapley value - a new proof
We give a new proof of Young's characterization of the Shapley value. Moreover, as applications of the new proof, we show that Young's axiomatization of the Shapley value is valid on various well-known subclasses of TU games
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