Information Transmission and Core Convergence in Quasilinear Economies

We study core convergence in interim quasilinear economies with asymmetric information, concentrating on core notions in which information is transmitted endogenously within coalitions and the incentive constraints are relevant. Specifically, we shall focus on the credible core and randomized mediated core concepts. We consider independent replicas of the basic economy: independent copies of the economy in which each individual’s utility only depends on the information of the individuals who belong to the same copy. We provide an example in which core convergence does not obtain for the Dutta-Vohra credible core and for Myerson’s randomized mediated core. On the other hand, we establish a positive convergence result for a refinement of Myerson’s core for which information disseminates across coalitions within a given random blocking mechanism. Under some conditions, this core converges to the set of incentive compatible ex-post Walrasian allocations.Core Convergence; Information Transmission; Coalitional Voting; Mechanisms; Mediation; Rational Expectations Equilibrium

Information transmission and core convergence in quasilinear economies

We study core convergence in interim quasilinear economies with asymmetric information, concentrating on core notions in which information is transmitted endogenously within coalitions and the incentive constraints are relevant. Specifically, we shall focus on the credible core and randomized mediated core concepts. We consider independent replicas of the basic economy: independent copies of the economy in which each individual's utility only depends on the information of the individuals who belong to the same copy. We provide an example in which core convergence does not obtain for the Dutta-Vohra credible core and for Myerson's randomized mediated core. On the other hand, we establish a positive convergence result for a refinement of Myerson's core for which information disseminates across coalitions within a given random blocking mechanism. Under some conditions, this core converges to the set of incentive compatible ex-post Walrasian allocations.core convergence; information transmission; coalitional voting mechanisms; mediation; rational expectations equilibrium

Equilibrium blocking in large quasilinear economies

We study information transmission in large interim quasilinear economies using the theory of the core. We concentrate on the core with respect to equilibrium blocking, a core notion in which information is transmitted endogenously within coalitions, as blocking can be understood as an equilibrium of a communication mechanism used by players in coalitions. We consider independent, ex-post and signal-based replicas of the basic economy. For each, we offer an array of negative and positive convergence results as a function of the complexity of the mechanisms used by coalitions. We identify conditions under which asymmetric information remains as an externality and non-market outcomes stay in the core, as well as those for the core to converge to the set of incentive compatible ex-post Walrasian allocations. Further, all the results are robust to the relaxation of the incentive constraints, and hence suggest a process through which information may get incorporated into a fully revealing equilibrium price function.core w.r.t. equilibrium blocking; core convergence; independent replicas; ex-post replicas; signal-based replicas; information transmission; communication mechanisms; mediation; rational expectations

Equilibrium Blocking in Large Quasilinear Economies

We study information transmission in large interim quasilinear economies using the theory of the core. We concentrate on the core with respect to equilibrium blocking, a core notion in which information is transmitted endogenously within coalitions, as blocking can be understood as an equilibrium of a communication mechanism used by players in coalitions. We consider independent, ex-post and signal-based replicas of the basic economy. For each, we offer an array of negative and positive convergence results as a function of the complexity of the mechanisms used by coalitions. We identify conditions under which asymmetric information remains as an externality and non-market outcomes stay in the core, as well as those for the core to converge to the set of incentive compatible ex-post Walrasian allocations. Further, all the results are robust to the relaxation of the incentive constraints, and hence suggest a process through which information may get incorporated into a fully revealing equilibrium price function.Core w.r.t. Equilibrium Blocking; Core Convergence; Independent Replicas; Ex-Post Replicas; Signal-Based Replicas; Information Transmission; Communication Mechanisms; Mediation; Rational Expectations Equilibrium

On the Core of a Cost Allocation Problem Under Asymmetric Information

We study a cost allocation problem under asymmetric information, and show that the ex ante incentive compatible core is non-empty. We also obtain a non-emptiness result for the incentive compatible coarse core, which is one concept of an interim core. (original abstract

Information Transmission and Core Convergence in Quasilinear Economies ∗

Abstract. We study core convergence in interim quasilinear economies with asymmetric information, concentrating on core notions in which information is transmitted endogenously within coalitions and the incentive constraints are relevant. Specifically, we shall focus on the credible core and randomized mediated core concepts. We consider independent replicas of the basic economy: independent copies of the economy in which each individual’s utility only depends on the information of the individuals who belong to the same copy. We provide an example in which core convergence does not obtain for the Dutta-Vohra credible core and for Myerson’s randomized mediated core. On the other hand, we establish a positive convergence result for a refinement of Myerson’s core for which information disseminates across coalitions within a given random blocking mechanism. Under some conditions, this core converges to the set of incentive compatible ex-post Walrasian allocations

New approaches to cooperative game theory: Core and value

In this dissertation, I investigate the core with asymmetric information (Chapters 2 and 3) and the Shapely value with externalities (Chapter 4). In Chapter 2 (jointly with Professor Roberto Serrano), we investigate to what extent the core convergence results hold for core notions with asymmetric information. We concentrate on the core with respect to equilibrium blocking, a core notion in which information is transmitted endogenously within coalitions, as blocking can be understood as an equilibrium of a communication mechanism used by players in coalitions. We identify conditions under which asymmetric information remains as an externality and non-market outcomes stay in the core, as well as those for the core to converge to the set of incentive compatible ex-post Walrasian allocations. In Chapter 3, I investigate the non-emptiness of the incentive compatible coarse core. I show that the incentive compatible coarse core is non-empty in quasilinear economies, if agents are informationally small and the strict core in each state is non-empty. This result means that in quasilinear economies, the non-emptiness result in Vohra (1999) is robust to the relaxation of non-exclusive information. In Chapter 4, I analyze a situation where several players entail cooperation in the presence of externalities by using games in partition function form. I concentrate on the axioms of anonymity, monotonicity, and weak dummy on a restriction operator, which is defined in Dutta, Ehlers and Kar (2008) for the potential approach. I connect the Shapley value of the associated characteristic function constructed from a restriction operator with values of games in partition function form proposed in previous literature