Updated on 2022/01/28

写真a

 
YOKOTE, Koji
 
Affiliation
Affiliated organization, Waseda Institute for Advanced Study
Job title
Assistant Professor(without tenure)

Concurrent Post

  • Faculty of Political Science and Economics   Graduate School of Economics

Degree

  • 早稲田大学   博士(経済学)

 

Papers

  • Redistribution to the less productive: parallel characterizations of the egalitarian Shapley and consensus values

    Koji Yokote, Takumi Kongo, Yukihiko Funaki

    Theory and Decision   91 ( 1 ) 81 - 98  2021.07  [Refereed]

    Authorship:Lead author

    DOI

  • Consistency of the doctor-optimal equilibrium price vector in job-matching markets

    Koji Yokote

    Journal of Economic Theory    2021  [Refereed]

    Authorship:Lead author, Corresponding author

  • On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints

    Koji Yokote

    Journal of Mechanism and Institution Design   5 ( 1 ) 37 - 77  2020.12  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    When a government intervenes in markets by setting a target amount of goods/services traded, its tax/subsidy policy is optimal if it entices the market participants to obey the policy target while achieving the highest possible social welfare. For the model of job market interventions by Kojima et al. (2019), we establish the existence of optimal taxes/subsidies as well as their characterization. Our methodological contribution is to introduce a discrete version of Karush-Kuhn-Tucker's saddle-point theorem based on the techniques in discrete convex analysis. We have two main results: we (i) characterize the optimal taxes/subsidies and the corresponding equilibrium salaries as the minimizers of a Lagrange function, and (ii) prove that the function satisfies a notion of discrete convexity (called L#-convexity). These results together with others imply that an optimal tax/subsidy level exists and can be calculated via a computationally efficient algorithm.

    DOI

  • The discrete separation theorem and price adjustment directions in markets with heterogeneous commodities

    Koji Yokote

    Discrete Applied Mathematics   275   134 - 143  2020.03  [Refereed]

    DOI

  • Weakly differentially monotonic solutions for cooperative games

    Koji Yokote

    International Journal of Game Theory   48 ( 3 ) 979 - 997  2019.09  [Refereed]

  • Relationally equal treatment of equals and affine combinations of values for TU games.

    Koji Yokote, Takumi Kongo, Yukihiko Funaki

    Social Choice and Welfare   53 ( 2 ) 197 - 212  2019.08  [Refereed]

    DOI

  • The balanced contributions property for equal contributors

    Koji Yokote, Takumi Kongo, Yukihiko Funaki

    Games and Economic Behavior   108   113 - 124  2018.03  [Refereed]

     View Summary

    We introduce a new axiom, which we term the balanced contributions property for equal contributors. This axiom is defined by restricting the requirement of the balanced contributions property (Myerson, 1980) to two players whose contributions to the grand coalition are the same. We prove that this axiom, together with efficiency and weak covariance, characterizes a new class of solutions, termed the r-egalitarian Shapley values. This class subsumes many variants of the Shapley value, e.g., the egalitarian Shapley values and the discounted Shapley values. Our characterization provides a new axiomatic foundation for analyzing variants of the Shapley value in a unified manner.

    DOI

  • Coincidence of the Shapley value with other solutions satisfying covariance

    Koji Yokote, Yukihiko Funaki, Yoshio Kamijo

    MATHEMATICAL SOCIAL SCIENCES   89   1 - 9  2017.09  [Refereed]

     View Summary

    We identify the necessary and sufficient condition under which the Shapley value coincides with the prenucleolus for general TU games. For 0-normalized 3-person games, the coincidence holds if and only if the game is symmetric or satisfies the PS property (Kar et al., 2009). We also identify the necessary and sufficient coincidence condition in the following allocation problems: the airport games (Littlechild and Owen, 1973), the bidder collusion games (Graham et al., 1990) and the polluted river games (Ni and Wang, 2007). The coincidence between the Shapley value and the CIS and ENSC values is discussed as well. (C) 2017 Elsevier B.V. All rights reserved.

    DOI

  • Weighted values and the core in NTU games

    Koji Yokote

    INTERNATIONAL JOURNAL OF GAME THEORY   46 ( 3 ) 631 - 654  2017.08  [Refereed]

     View Summary

    Monderer et al. (Int J Game Theory 21(1):27-39, 1992) proved that the core is included in the set of the weighted Shapley values in TU games. The purpose of this paper is to extend this result to NTU games. We first show that the core is included in the closure of the positively weighted egalitarian solutions introduced by Kalai and Samet (Econometrica 53(2):307-327, 1985). Next, we show that the weighted version of the Shapley NTU value by Shapley (La Decision, aggregation et dynamique des ordres de preference, Editions du Centre National de la Recherche Scientifique, Paris, pp 251-263, 1969) does not always include the core. These results indicate that, in view of the relationship to the core, the egalitarian solution is a more desirable extension of the weighted Shapley value to NTU games. As a byproduct of our approach, we also clarify the relationship between the core and marginal contributions in NTU games. We show that, if the attainable payoff for the grand coalition is represented as a closed-half space, then any element of the core is attainable as the expected value of marginal contributions.

    DOI

  • Monotonicity implies linearity: characterizations of convex combinations of solutions to cooperative games

    Koji Yokote, Yukihiko Funaki

    SOCIAL CHOICE AND WELFARE   49 ( 1 ) 171 - 203  2017.06  [Refereed]

     View Summary

    The purpose of this study is to provide a comprehensive characterization of linear solutions to cooperative games by using monotonicity. A monotonicity axiom states an increase in certain parameters of a game as a hypothesis and states an increase in a player's payoff as a conclusion. We focus on various parameters of a game and introduce new axioms. Combined with previous results, we prove that efficiency, symmetry and a monotonicity axiom characterize (i) four linear solutions in the literature, namely, the Shapley value, the equal division value, the CIS value and the ENSC value, and (ii) a class of solutions obtained by taking a convex combination of the above solutions. Our methodological contribution is to provide a new linear algebraic approach for characterizing solutions by monotonicity. Using a new basis of the linear space of TU games, we identify a class of games in which a solution that satisfies monotonicity is linear. Our approach provides some intuition for why monotonicity implies linearity.

    DOI

  • Random reduction consistency of the Weber set, the core and the anti-core

    Yasushi Agatsuma, Yukihiko Funaki, Koji Yokote

    MATHEMATICAL METHODS OF OPERATIONS RESEARCH   85 ( 3 ) 389 - 405  2017.06  [Refereed]

     View Summary

    In this paper we introduce a new consistency condition and provide characterizations for several solution concepts in TU cooperative game theory. Our new consistency condition, which we call the random reduction consistency, requires the consistency of payoff vectors assigned by a solution concept when one of the players is removed with some probability. We show that the random reduction consistency and other standard properties characterize the Weber set, the convex hull of the marginal contribution vectors. Another salient feature of random reduction consistency is that, by slightly changing its definition, we can characterize the core and the anti-core in a parallel manner. Our result enables us to compare the difference between the three solution concepts from the viewpoint of consistency.

    DOI

  • The balanced contributions property for symmetric players

    Koji Yokote, Takumi Kongo

    OPERATIONS RESEARCH LETTERS   45 ( 3 ) 227 - 231  2017.05  [Refereed]

     View Summary

    This paper introduces a new relational axiom, the balanced contributions property for symmetric players, in TU cooperative games. It describes the fair treatment of symmetric players by restricting the requirement of the balanced contributions property to two symmetric players. Even under efficiency, our new axiom is logically independent of symmetry, which requires that symmetric players receive the same payoff. Nonetheless, in previous axiomatizations of an anonymous solution, replacing symmetry with our new axiom results in new axiomatizations of the solution. (C) 2017 Elsevier B.V. All rights reserved.

    DOI

  • Weak differential monotonicity, flat tax, and basic income

    Koji Yokote, Andre Casajus

    ECONOMICS LETTERS   151   100 - 103  2017.02  [Refereed]

     View Summary

    We suggest a weak version of differential monotonicity for redistribution rules: whenever the differential of two persons' income weakly increases, then their post-redistribution rewards essentially change in the same direction. Together with efficiency, non-negativity, and the average property, weak differential monotonicity characterizes redistribution via taxation at a fixed rate and equal distribution of the total tax revenue, i.e., a flat tax and a basic income. (C) 2016 Elsevier B.V. All rights reserved.

    DOI

  • Weak differential marginality and the Shapley value

    Andre Casajus, Koji Yokote

    JOURNAL OF ECONOMIC THEORY   167   274 - 284  2017.01  [Refereed]

     View Summary

    The principle of differential marginality for cooperative games states that the differential of two players' payoffs does not change when the differential of these players' marginal contributions to coalitions containing neither of them does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show that this characterization can be improved by using a substantially weaker property than differential marginality. Weak differential marginality requires two players' payoffs to change in the same direction when these players' marginal contributions to coalitions containing neither of them change by the same amount. (C) 2016 Elsevier Inc. All rights reserved.

    DOI

  • Core and competitive equilibria: An approach from discrete convex analysis

    Koji Yokote

    JOURNAL OF MATHEMATICAL ECONOMICS   66   1 - 13  2016.10  [Refereed]

     View Summary

    We extend the assignment market (Shapley and Shubik, 1972; Kaneko, 1976, 1982) by utilizing discrete convex analysis. We consider the market in which buyers and sellers trade indivisible commodities for money. Each buyer demands at most one unit of commodity. Each seller produces multiple units of several types of commodities. We make the quasi-linearity assumption on the sellers, but not on the buyers. We assume that the cost function of each seller is M-b-convex, which is a concept in discrete convex analysis. We prove that the core and the competitive equilibria exist and coincide in our market model. (C) 2016 Elsevier B.V. All rights reserved.

    DOI

  • A new basis and the Shapley value

    Koji Yokote, Yukihiko Funaki, Yoshio Kamijo

    MATHEMATICAL SOCIAL SCIENCES   80   21 - 24  2016.03  [Refereed]

     View Summary

    The purpose of this paper is to introduce a new basis of the set of all TU games. Shapley (1953) introduced the unanimity game in which cooperation of all players in a given coalition yields payoff. We introduce the commander game in which only one player in a given coalition yields payoff. The set of the commander games forms a basis and has two properties. First, when we express a game by a linear combination of the basis, the coefficients related to singletons coincide with the Shapley value. Second, the basis induces the null space of the Shapley value. (C) 2016 Elsevier B.V. All rights reserved.

    DOI

  • Weak addition invariance and axiomatization of the weighted Shapley value

    Koji Yokote

    INTERNATIONAL JOURNAL OF GAME THEORY   44 ( 2 ) 275 - 293  2015.05  [Refereed]

     View Summary

    In this paper, we give a new axiomatization of the weighted Shapley value. We investigate the asymmetric property of the value by focusing on the invariance of payoff after the change in the worths of singleton coalitions. We show that if the worths change by the same amount, then the Shapley value is invariant. On the other hand, if the worths change with multiplying by a positive weight, then the weighted Shapley value with the positive weight is invariant. Based on the invariance, we formulate a new axiom, -Weak Addition Invariance. We prove that the weighted Shapley value is the unique solution function which satisfies -Weak Addition Invariance and Dummy Player Property. In the proof, we introduce a new basis of the set of all games. The basis has two properties. First, when we express a game by a linear combination of the basis, coefficients coincide with the weighted Shapley value. Second, the basis induces the null space of the weighted Shapley value. By generalizing the new axiomatization, we also axiomatize the family of weighted Shapley values.

    DOI

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Research Projects

  • A theoretical analysis of markets with indivisible commodities: An approach from discrete mathematics

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists

    Project Year :

    2020.04
    -
    2022.03
     

Specific Research

  • A new characterization of substitutes/complements conditions in markets with indivisibilities

    2020  

     View Summary

    The purpose of this research is to reveal connections between mathematical concepts in economics and those in discrete mathematics. Traditionally, economists have analyzed economic models by using mathematical tools in a continuous setting, such as differential calculus. However, with the rise of computer technology, economists have begun to put an economic model in computer and then compute an equilibrium (a stationary state of economic activities) via some algorithm. When computing an equilibrium, we often utilize discrete mathematics rather than mathematical tools in a continuous setting. Hence, some recent studies intend to reveal the connections between economics and discrete mathematics. This research intends to make a new contribution to this line of research. On the economics side, I focused on the “substitutes condition” imposed on preferences. On the discrete mathematics side, I focused on “M-concavity”, a concept of discrete concavity in discrete mathematics. I proved the equivalence between these two concepts in a more refined manner than before. Although prior studies have proved this equivalence with assuming the continuity of prices, I proved that this assumption can be relaxed. This result clarifies the exact assumptions necessary to compute equilibrium prices in computationally efficient time.

  • 非分割財の分配方法の理論研究、及び現実の分配方法への応用

    2019  

     View Summary

     政府が公共施設(例:公立学校、保育所)に利用者を受け入れる場合、「受け入れ枠をどのように分配すれば良いのか」という問題が生じる。本研究では、受け入れ枠のような「非分割財」(即ち、細かく分けることができない財)を適切に分配する方法について、経済学・離散数学を用いて分析した。主に二つの研究を進めた。一つ目の研究では、労働マッチング市場に政府が介入する状況を考え、適切な税・補助金額を発見するアルゴリズムを提示した。この研究成果をまとめた論文は国際的な学術雑誌に受理された。二つ目の研究では、日本における保育所の分配問題を取り上げ、現行の制度の問題点と修正案を論じた。

  • ゲーム理論、離散凸解析を用いた望ましい分配方法の理論研究

    2017  

     View Summary

        The purpose of this research is to analyze allocation rules that describe how to distribute limited resources among agents. We explain two results obtained in this research.     First, we identify desirable allocation rules in the framework of cooperative games. The is a joint work with Professor Andre Casajus at HHL Leipzig Graduate School of Management.  We introduce a new axiom, termed weak differential monotonicity. This axiom requires monotonicity of the difference of final rewards between two specific players. We prove that this axiom characterizes the class of egalitarian Shapley values. I presented this result at East Asian Game Ttheory Conference 2017 held in Singapore.     Second, we apply discrete separation theorem to an auction model. Discrete convex analysis is a branch of mathematics that studies convexity in discrete settings. In an auction model, a non-equilibrium situation induces the discrepancy between aggregate demand and supply. Applying the discrete separation theorem to this situation, we obtain a new characterization of competitive price vectors. This result enables a unified understanding of existing auctions. I summarized this result in a working paper, which is accesible through Munich Personal Repec Archive.

 

Syllabus