Optimal Dimension of Transition Probability Matrices for Markov Chain Bootstrapping

� While the large portion of the literature on Markov chain (possibly of order higher than one) bootstrap methods has focused on the correct estimation of the transition probabilities, little or no attention has been devoted to the problem of estimating the dimension of the transition probability matrix. Indeed, it is usual to assume that the Markov chain has a one-step memory property and that the state space could not to be clustered, and coincides with the distinct observed values. In this paper we question the opportunity of such a standard approach. In particular we advance a method to jointly estimate the order of the Markov chain and identify a suitable clustering of the states. Indeed in several real life applications the "memory" of many processes extends well over the last observation; in those cases a correct representation of past trajectories requires a significantly richer set than the state space. On the contrary it can sometimes happen that some distinct values do not correspond to really "different states of a process; this is a common conclusion whenever, for example, a process assuming two distinct values in t is not affected in its distribution in t+1. Such a situation would suggest to reduce the dimension of the transition probability matrix. Our methods are based on solving two optimization problems. More specifically we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping: preserving the similarity between the observed and the bootstrap series and reducing the probabilities of getting a perfect replication of the original sample. A brief axiomatic discussion is developed to define the desirable properties for such optimal criteria. Two numerical examples are presented to illustrate the method. �order of Markov chains,similarity of time series,transition probability matrices,multiplicity of time series,partition of states of Markov chains,Markov chains,bootstrap methods

Trading Blocs and Foreign Direct Investment: Endogenous Coalition Structure

I examine the relationship between trading blocs and Foreign Direct Investment (FDI). Firms in the model serve foreign markets either by exporting or by setting up plants abroad, which is FDI. I find that countries forming a bloc could attract FDI from non-member countries. However, I show by using a coalition formation game that this FDI-attracting bloc cannot be an equilibrium outcome when multilateralism (i.e., the free trade world) is an option for countries. This result is mainly related to the adverse welfare effects of the tariff-jumping FDItrading blocs, multinational corporations, FDI, coalition formation game

A Taxonomy of Myopic Stability Concepts for Hedonic Games

We present a taxonomy of myopic stability concepts for hedonic games in terms of deviations, and discuss the status of the existence problems of stable coalition tructures. In particular, we show that contractual strictly core stable coalition tructures always exist, and provide su¢ cient conditions for the existence of con- ractually Nash stable and weak individually stable coalition structures on the class of separable games.Coalition formation, Hedonic games, Separability, Taxonomy

The construction of choice. A computational voting model.

Social choice models usually assume that choice is among exogenously given and non decomposable alternatives. Often, on the contrary, choice is among objects that are constructed by individuals or institutions as complex bundles made of many interdependent components. In this paper we present a model of object construction in majority voting and show that, in general, by appropriate changes of such bundles, different social outcomes may be obtained, depending upon initial conditions and agenda, intransitive cycles and median voter dominance may be made appear or disappear, and that, finally, decidability may be ensured by increasing manipulability or viceversa.Voting, Social choice, Agenda power, Power, Voting paradox, Median voter

Non-bossy social classification

We consider the problem of how societies should be partitioned into classes if individuals express their views about who should be put with whom in the same class. A non-bossy social aggregator depends only on those cells of the individual partitions the society members classify themselves in. This fact allows us to concentrate on a corresponding 'opinion graph' for each profile of views. By means of natural sovereignty, liberalism, and equal treatment requirements, we characterize the non-bossy aggregators generating partitions in which the social classes are refinements of the weakly connected components of the opinion graph. --social aggregation,group identity,liberalism, non-bossiness

Contractually stable networks

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, whre the network specifies the natyure of the relationship each individual has with his coalition members and with individuals outside his coalition. To predict the coalitional networks that are going to emerge at equiibrium we propose the concept of contractual stability which requires that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. We show that there always exists a contractually stable coalitional network under the simple majority decision rule and the component-wise egalitarian or majoritarian allocation rules. Moreover, requiring the consent of group members may help to reconcile stability and efficiencyNetworks; coaliation structures; contractual stability; allocation rules

Contractually stable networks

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network speciÖes the nature of the relationship each individual has with his coalition members and with individuals outside his coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concept of contractual stability which requires that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. We show that there always exists a contractually stable coalitional network under the simple majority decision rule and the component-wise egalitarian or majoritarian allocation rules. Moreover, requiring the consent of group members may help to reconcile stability and e¢ ciency.Networks ; Coalition Structures ; Contractual Stability ; Allocation Rules Networks ; Strong efficiency

Contractually Stable Networks

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each individual has with his coalition members and with individuals outside his coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concept of contractual stability which requires that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. We show that there always exists a contractually stable coalitional network under the simple majority decision rule and the component-wise egalitarian or majoritarian allocation rules. Moreover, requiring the consent of group members may help to reconcile stability and efficiency.Networks, Coalition Structures, Contractual Stability, Allocation Rules

Formation of Collective Decision-Making Units: Stability and a Solution

We study how individuals divide themselves into coalitions and choose a public alternative for each coalition. When preferences have consecutive support and coalition feasible sets are positively population- responsive, the proposed consecutive benevolence solution generates allocations belonging to the coalition structure core and that are also Tiebout equilibria. However, when each coalition follows a single-valued collective decision rule, the coalition structure core may be empty. Our results show that if individual preferences are, in a sense, similar and if members can be as well off when a coalition enlarges, then a stable formation of collective decision-making units can be guaranteed. A predetermined decision rule makes coalitions less stable.