Intertemporal resource allocation and intergenerational equity: compatibility of efficiency and equity

研究成果の概要 (和文) : 異時点間資源配分の理論研究として、(1)最適経済成長経路の特徴付け、(2)異時点間選好の効用関数表現、(3)衡平分割問題の解法、という3つの観点から研究を行った。代表的消費者が時間選好率が消費経路に依存する再帰的効用関数を持つ場合に、収穫逓増をともなう経済で最適成長経路が存在するための条件を求め、最適成長経路の支持価格による特徴付けを行った。衡平分割問題において、効率性と衡平性を同時に満たす解の存在を示した。研究成果の概要 (英文) : I have investigated the following three theoretical aspects of intertemporal resource allocations : (1) a characterization of optimal paths for economic growth ; (2) representation of intertemporal preferences by utility functions ; (3) solutions to fair division problems. I have proved the existence of optimal path for economies with increasing returns in which a representative agent possesses a recursive utility function that endogenizes time preference for consumption paths. In the fair division problem, I have demonstrated the existence of solutions which satisfy both efficiency and fairness

Macroeconomic Policy Analysis using utility function with non-constant discount factor

研究成果の概要 (和文) : 割引因子が一定でないマクロモデルを用いて、財政政策と金融政策の分析を行った。特に、逐次的効用関数と呼ばれる、割引因子が効用もしくは消費や実物貨幣残高といったマクロ変数の関数に商店を当てた。いくつかの論文を書き上げ、国際学会でプレゼンテーションを実施し、国際査読付き雑誌に投稿し、いくつかはすでに出版された。また、研究代表者は、この成果を含めた論文集「選好と国際マクロ経済学」法政大学出版局、2012を編集した。この本は2012年3月に法政大学出版局から出版された。研究成果の概要 (英文) : We conduct a public/fiscal policy analysis using macroeconomic models with non-constant discount factors. In particular, we focused on recursive utility models, in which the discount factor is a function of utility or some aggregate macroeconomic variables including consumption and real balances. We wrote some research papers to give presentations at international academic conferences and to submit to international refereed journals. Some of them have been already published. In addition, Kenji Miyazaki edited a Japanese book including our research papers. This book, titled \u27Preference and International Macroeconomics,\u27was published in March, 2012

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems

Mean field optimization problems: stability results and Lagrangian discretization

We formulate and investigate a mean field optimization (MFO) problem over a set of probability distributions $\mu$ with a prescribed marginal $m$. The cost function depends on an aggregate term, which is the expectation of $\mu$ with respect to a contribution function. This problem is of particular interest in the context of Lagrangian potential mean field games (MFGs) and their discretization. We provide a first-order optimality condition and prove strong duality. We investigate stability properties of the MFO problem with respect to the prescribed marginal, from both primal and dual perspectives. In our stability analysis, we propose a method for recovering an approximate solution to an MFO problem with the help of an approximate solution to an MFO with a different marginal $m$, typically an empirical distribution. We combine this method with the stochastic Frank-Wolfe algorithm of a previous publication of ours to derive a complete resolution method

Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities

This paper studies the existence of Pareto optimal, envy-free allocations of a heterogeneous, divisible commodity for a finite number of individuals. We model the commodity as a measurable space and make no convexity assumptions on the preferences of individuals. We show that if the utility function of each individual is uniformly continuous and strictly monotonic with respect to set inclusion, and if the partition matrix range of the utility functions is closed, a Pareto optimal envy-free partition exists. This result follows from the existence of Pareto optimal envy-free allocations in an extended version of the original allocation problem. © 2013 Springer-Verlag Berlin Heidelberg

Fuzzy Coalitions and Solutions of Cooperative Games: Beyond the Market Solutions

研究成果の概要 (和文) : 伝統的な市場ゲームでは，プレイヤーは初期保有量のすべてを参加する提携に拠出することを同意した上で実現した提携利得がプレイヤーに配分されるが，ファジィ提携ではプレイヤーは必ずしも初期保有量のすべてを提供する必要はなく，その一部を自由に提供することで提携へのコミットメントの度合いを決定することができる．同質的分割可能財が存在する交換経済においては，ファジイ・コア配分が競争均衡配分に一致することが先行研究で示されている．ファジイ提携を考慮しない場合，市場メカニズムで実現できないコア配分が一般的に存在するが，交渉解の一つであるファジイ・コア配分は市場メカニズムによって実現することができることを示した．研究成果の概要 (英文) : In traditional market games, coalitional payoffs are allocated to each player contingent upon the agreement that players contribute every initial endowment to the coalitions they are participating. On the contrary, in fuzzy market games, players do not necessarily have to contribute every initial endowment to the coalitions and they are free to decide their degree of commitment by contributing partially their initial endowment to the coalitions. It is well known in the literature that in economies with homogeneous divisible commodities fuzzy core allocations coincide with competitive equilibrium allocations. Without fuzzy coalitions, in general there is a core allocation that cannot be realized through the market mechanism. Nevertheless, in this research, I demonstrated that fuzzy core allocations can be attained by the market mechanism

Essays on Games of Strategic Substitutes with Incomplete Information

This dissertation consists of three individual chapters. The first chapter applies lattice theoretic techniques in order to establish fundamental properties of Bayesian games of strategic substitutes (GSS) when the underlying type space is ordered either in increasing or decreasing first-order stochastic dominance. Existence and uniqueness of equilibria is considered, as well as the question of when such equilibria can be guaranteed to be monotone in type, a property which is used to guarantee monotone comparative statics. The second chapter uses the techniques of the first and combines them with the existing results for strategic complements (GSC) in order to extend the literature on global games under both GSC and GSS. In particular, the model of Carlsson and Van Damme (1993) is extended from 22 games to GSS or GSC involving a finite amount of players, each having a finite action space. Furthermore, the possibility that groups of players receive the same signal is allowed for, a condition which is new to the literature. It is shown that under this condition, the power of the model to resolve the issue of multiplicity is unambiguously increased. The third chapter considers stability of mixed strategy Nash equilibria in GSS. Chapter 1 analyzes Bayesian games of strategic substitutes under general conditions. In particular, when beliefs are order either increasingly or decreasingly by first order stochastic dominance, the existence and uniqueness, monotonicity, and comparative statics in this broad class of games are addressed. Unlike their supermodular counterpart, where the effect of an increase in type augments the strategic effect between own strategy and opponent’s strategy, submodularity produces competing effects when considering optimal responses. Using adaptive dynamics, conditions are given under which such games can be guaranteed to exhibit Bayesian Nash equilibria, and it is shown that in many applications these equilibria will be a profile of monotone strategies. Comparative statics of parametrized games is also analyzed using results from submodular games which are extended to incorporate incomplete information. Several examples are provided. The framework of Chapter 1 is applied to global games in Chapter 2. Global games methods are aimed at resolving issues of multiplicity of equilibria and coordination failure that arise in game theoretic models by relaxing common knowledge assumptions about an underlying parameter. These methods have recently received a lot of attention when the underlying complete information game is a GSC. Little has been done in this direction concerning GSS, however. This chapter complements the existing literature in both cases by extending the global games method developed by Carlsson and Van Damme (1993) to multiple player, multiple action GSS and GSC, using a p-dominance condition as the selection criterion. This approach helps circumvent recent criticisms to global games by relaxing some possibly unnatural assumptions on payoffs and parameters necessary to conduct analysis under current methods. The second part of this chapter generalizes the model by allowing groups of players to receive homogenous signals, which, under certain conditions, strengthens the model’s power of predictability. Chapter 3 analyzes the learning and stability of mixed strategy Nash equilibria in GSS, complementing recent work done in the case of GSC. Mixed strategies in GSS are of particular interest because it is well known that such games need not exhibit pure strategy Nash equilibria. First, a bound on the strategy space which indicate where randomizing behavior may occur in equilibrium is established. Second, it is shows that mixed strategy Nash equilibria are generally unstable under a wide variety of learning rules