# Mamoru KanekoUniversity of Tsukuba and Waseda University

Mamoru Kaneko

Doctor of Science

## About

129

Publications

20,141

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1,903

Citations

Citations since 2017

Introduction

My projects are:
(1) Epistemic logic and game theory
(2) Inductive game theory
(3) Social justice.
(1) is about interactions between logical inferences and decision/prediction making. Also, it treats false beliefs. (2) is relations between individual experiences and beliefs, in particular, emergence of beliefs from experiences is focussed. This includes partiality and incorrectness of individual basic beliefs. Based on (1) and (2), world social justice is considered.

Additional affiliations

April 2013 - present

June 1992 - March 2013

August 1989 - June 1994

Education

April 1972 - March 1974

March 1968 - March 1972

## Publications

Publications (129)

The earth has been getting smaller and narrower with the expansion of human activities. Now, it is an urgent task for social scientists to explore and study new socio-economic thoughts for this small and narrow earth. This article provides a normative theory and a descriptive theory for the present and future earth. The former is to provide, viewin...

Inductive game theory has been developed to explore the origin of beliefs of a person from his accumulated experiences of a game situation. It has been restricted to a person's view of the structure not including another person's thoughts. In this paper, we explore the experiential origin of one's view of the other's beliefs about the game situatio...

We reformulate expected utility theory, from the viewpoint of bounded rationality, by introducing probability grids and a cognitive bound; we restrict permissible probabilities only to decimal (ℓ-ary in general) fractions of finite depths up to a given cognitive bound. We distinguish between measurements of utilities from pure alternatives and thei...

We develop a series of small infinitary epistemic logics to study deductive inference involving intra/inter-personal beliefs/knowledge such as common knowledge, common beliefs, and infinite regress of beliefs. Specifically, propositional epistemic logics GL(L_{α}) are presented for ordinal α up to some given ordinal so that GL(L₀) is finitary KDⁿ w...

The world has been getting smaller and narrower with the expansion of human activities. Now, exploring and studying new socioeconomic thoughts for this small and narrow world is an urgent task for social scientists. This article provides a normative theory and a descriptive theory for the present and future of the world. The normative theory helps...

We analyze the St.Petersburg paradox from the perspective of a real social context. We formulate a market for a coin-tossing gamble between a banker with a finite budget and people with cognitive bounds on probabilities. The budget for the banker alone removes the paradox in the original form, as argued by Shapley. However, the standard expected re...

This volume is a posthumous collection of selected papers of Kenjiro Nakamura, a brilliant social scientist who died in 1979 at the age of 32. Most of the papers in the book were published in 1978, 1979 and 1980
(PDF) Game theory and social choice : Kenjiro Nakamura, Edited by Mitsuo Suzuki, Tokyo: Keiso Shobo, 1981, pp. 240, Y 5000.. Available f...

Quasi-linear utility functions are widely used in economics and game theory
as convenient tools. Quasi-linearity ignores income effects on individual
evaluations of alternative choices; indeed, it is captured by a condition of
no-income effects on such evaluations. However, income effects are
non-negligible relative to agents' economic activities i...

We develop an equilibrium-econometric analysis in the context of rental housing markets with indivisibilities. The theory provides some bridge between a (com-petitive) market equilibrium theory and a statistical/econometric analysis. First, we develop this theory: The listing service of apartments, which we call the hous-ing magazine, provides the...

We conduct an experimental study on behavior and cognition in various 2×2 games with/without role-switching from the perspective of inductive game theory (IGT). Here, subjects have no prior knowledge about payoffs and can only learn them by playing the game. Without role-switching, subjects can, and many do, successfully learn their own payoffs. To...

We study the process, called the IEDI process, of iterated elimination of (strictly) dominated strategies and inessential players for finite strategic games. Such elimination may reduce the size of a game considerably, for example, from a game with a large number of players to one with a few players. We extend two existing results to our context; t...

We present a logic called the epistemic infinite-regress logic EIR for players. It extends the epistemic logic KD , by incorporating the operators expressing infinite regresses. Here, an infinite regress arises from the interdependent thinking of a player about the other's thinking and vice versa. If we add Axiom T (truthfulness) for the beli...

We study the possibility of prediction/decision making in a finite 2—person game with pure strategies, following the Nash(-Johansen) noncooperative solution theory. We adopt the epistemic logic KD 2 as the base logic to capture individual decision making from the view-point of logical inference. Since some infinite regresses naturally arise in this...

The theories of Nash noncooperative solutions and of rationalizability intend to describe the same target problem of ex ante individual decision making, but they are distinctively different. We consider what their essential difference is by giving a unified approach and parallel derivations of their resulting outcomes. Our results show that the onl...

We explore the inductively derived views obtained by players with partial temporal (short-term) memories. A player derives
his personal view of the objective game situation from his accumulated (long-term) memories, and then uses it for decision
making. A salient feature that distinguishes this paper from others on inductive game theory is partiali...

This is the second symposium of the same title “Logic and Economics” in this journal and has four papers studying the issues expressed in the subtitle. In this introduction, the guest editor first describes a general perspective for this symposium and then explains each paper from this perspective. Finally, a few remarks are given.

Inductive game theory (IGT) aims to explore sources of beliefs of a person in his individual
experiences from behaving in a social situation. It has various steps, each of which already
involves a lot of different aspects. A scenario for IGT was spelled out in Kaneko-Kline [15].
So far, IGT has been studied chiefly in theoretical manners, while som...

Game Theory, 83-128, (2010), ed. Huang Qiming. Sciyo.com. This is based on the publications in Journal of Mathematical Economics 44, (2008), 1332--1363, and the same journal: 46, (2010), 620-622.

These two dialogues are between two professional people on a new field called ‘epistemic logic and inductive game theory’. At the time of the first dialogue, one speaker is already a specialist and has been working in this field for a long time. The other is a game theorist, who is both younger and a novice in the field. Dialogue I takes place in J...

This paper undertakes a simulation study of a player’s learning about the structure of a game situation. In a simple 1-person example called Mike’s Bike Commuting, we simulate the process by which Mike experiences and accumulates memories about the game structure. It is the basic requirement that to keep an experience as a long-term memory, Mike ne...

This paper presents a measure of inference in classical and intuitionistic logics in the Gentzen-style sequent calculus. The definition of the measure takes two steps: First, we measure the width of a given proof. Then the measure of inference assigns, to a given sequent, the minimum value of the widths of its possible proofs. It counts the indispe...

This paper provides an analysis of discrimination and prejudices from the perspective of inductive game theory. We extend the festival game, originally given by Kaneko–Matsui, to include new constraints on the observability of ethnic identities and on accessible locations for players. We characterize the Nash equilibrium set, which reveals a differ...

This corrigendum corrects a mistake in Theorem 8.1.(a) of the authors’ paper [ibid. 44, No. 12, 1332–1363 (2008; Zbl 1156.91012)].

The aim of this paper is to present the new theory called "inductive game theory". A paper, published by one of the present authors with A. Matsui, discussed some part of inductive game theory in a specific game. Here, we present a more entire picture of the theory moving from the individual raw experiences, through the inductive derivation of a vi...

We introduce a new mathematical representation of an extensive game situation, called an information protocol, without using the hypothetical underlying structure of nodes and branches. Its necessity has been emerging in our study of inductive game theory. It has two main differences from a standard extensive game: one is the use of information pie...

We present certain duality results on comparative statics on competitive rent vectors in the rental housing market model. In the model, apartments as indivisible goods are classified into a finite number of categories, and are traded for one composite commodity. Our concern is about certain general properties of the behavior of rents with parameter...

This book consists of five acts and two interludes, which are all written as dialogues between three main characters and other supporting characters. Each act discusses the epistemological, institutional and methodological foundations of game theory and economics, while using various stories and examples. A featured aspect of those discussions is t...

This book consists of five acts and two interludes, which are all written as dialogues between three main characters and other supporting characters. Each act discusses the epistemological, institutional and methodological foundations of game theory and economics, while using various stories and examples. A featured aspect of those discussions is t...

Utility theories for the denitions of cooperative games and associated solution concepts are discussed. A game with side payments needs the assumptions of transferable utility and side payments. We discuss the axioms for the transferable utility assumption and also the role of side payments for various solution concepts. We also discuss games witho...

Kaneko-Suzuki developed epistemic logics of shallow depths with multiple players for investigations of game theoretical problems. By shallow depth, we mean that nested occurrences of belief operators of players in formulae are restricted, typically to be of finite depths, by a given epistemic structure. In this paper, we develop various methods of...

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships...

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as xed-point t ype extensions and innnitary ones, have been proposed. Although we h a ve n o w a good list of such proposed extensions, the relationships among these extensions are still unclear. The pur-pose of this paper is to draw a map...

Individual decision making is based on predictions about other players' choices as well as on valuations of reactions to predictions. In this sense, a player has a prediction-decision criterion for decision making. We develop a theory of prediction-decision criteria, which enables us to capture new phenomena on individual decision making in games....

This paper is written as an introduction to epistemic logics and their game theoretic applications. It starts with both semantics and syntax of classical logic, and goes to the Hilbert-style proof-theory and Kripke-style model theory of epistemic logics. In these theories, we discuss individual decision making in some simple game examples. In parti...

This is a dialogue between two professional people on the new field called "epistemic logics and game theory". One speaker is a specialist who has been working in this field for a long time, and the other is a game theorist who is quite new to the field and younger than the specialist. They start discussing the Konnyaku Mondô and find that it has m...

This paper presents a multi-modal epistemic logic GL EF of shallow depths. The logic GL EF is a fragment of the multi-modal logic KD n , and enables us to consider interpersonal inferential epistemic complexities. The subscripts E and F are called epistemic structures, which restrict interpersonal epistemic depths involved in formulae and proofs. W...

From the ex ante point of view, an axiomatization of decision making in a game with pure strategies is given, while considering its epistemic aspects in propositional game (epistemic) logic. Our axiomatization consists of four base axioms for predicted final decisions. One of them is an epistemic requirement, which together with the others leads to...

We show the faithful embedding of common knowledge logic CKL into game logic GL, that is, CKL is embedded into GL and GL is a conservative extension of the fragment obtained by this embedding. Then many results in GL are available in CKL, and vice versa. For example, an epistemic consideration of Nash equilibrium for a game with pure strategies in...

This paper proposes a new theory, which we call inductive game theory. In this theory, the individual player does not have a priori knowledge of the structure of the game that he plays repeatedly. Instead, he accumulates experiences induced by occasional random trials in the repeated play. A stationary state is required to be stable against intenti...

The aim of this paper is to present the new theory called "inductive game theory". A paper, published by one of the present authors with A. Matsui, discussed some part of inductive game theory in a specific game. Here, we present a more entire picture of the theory moving from the individual raw experiences, through the inductive derivation of a vi...

In game theory and economics, we often meet the concept of common knowledge. In literature, there are quite a few approaches to common knowledge. In this paper, we discuss the approach in the terms of epistemic logics, and consider several questions on the definability of common knowledge in such logics by means of axioms.1

This paper provides a Genzten style formulation of the game logic framework GLm (0 ≤ m ≤ ω), and proves the cut-elimination theorem for GLm. As its application, we prove the term existence theorem for GLω used in Part I.

From the ex ante point of view, we consider decision making in partially interactive games. In a partially interactive game, players may not be required to predict all the others’ decisions such as in Prisoner’s Dilemma. In some games, some players can ignore some other players’ decision making but need to predict decisions of some different ones....

We consider two models of n-person bargaining problems with the endogenous determination of disagreement points. In the first model, which is a direct extension of Nash's variable threat bargaining model, the disagreement point is determined as an equilibrium threat point. In the second model, the disagreement point is given as a Nash equilibrium o...

We prove the nonemptiness of the core of a continuum game without side payments where only small coalitions — ones bounded in absolute size of finite cardinality — are permitted. This result covers assignment games with a continuum of players and includes combinations of several assignment games, such as housing and automobile markets.

This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there i...

When perfect recall is not satisfied, the informational contents of mixed and behavior strategies differ and are more than what the information partition describes. First, we consider two kinds of additional information strategies may carry, and show that such information leads to the perfect recall refinement of a given information partition. This...

The Nash equilibrium concept has been playing a central role in game theory. Nevertheless, its meaning or interpretation has not been fully explicated. In this paper, we consider the epistemic foundation of Nash equilibrium from the viewpoint of the one-shot play interpretation. In this interpretation, each player makes his strategy choice before t...

We consider four examples of economies with widespread externalities. These examples illustrate various forms of interactions between externalities and markets. We suggest that some phenomena usually regarded as incompatible with general equilibrium theory are in fact results of interactions of widespread externalities and perfect competition and t...

We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that ar...

The economy of this paper has a continuum of producers who live from the infinite past to the infinite future and have linear production technologies. In each period, each producer brings a commodity bundle produced in the previous period to trading posts and gets a new commodity bundle, which will be used as inputs to the production of the present...

This note proves that the two person Nash bargaining theory with polyhedral bargaining regions needs only an ordered field (which always includes the rational number field) as its scalar field. The existence of the Nash bargaining solution is the main part of this result and the axiomatic characterization can be proved in the standard way with slig...

This paper provides a simple game-theoretic account of racial discrimination without assuming individual prejudices as a basic concept. We consider a recurrent situation of a festival game with merrymakers, and give a formulation of a stable convention. We show that stable conventions of one type involve discrimination against one group of players....

This paper attempts to explain the Nash equilibrium concept from the viewpoint of its one-shot play interpretation. We consider a final decision to be made by each player before the game is actually played. We formalize this game situation in terms of an infinitary first-order predicate logic. Then we give an axiom for final decisions-in the two-pe...

We develop a new model of a continuum economy with coalitions consisting of only finite numbers of agents. The core, called the f-core, is the set of allocations that are stable against improvement by finite coalitions and feasible by trade within finite coalitions. Even with widespread externalities—preferences depend on own consumptions and also...

When permissible coalitions in finite economies are constrained to be small relative to the player set, the continuum model with finite coalitions and its f-core are the limits of large finite economies and their ε-cores. We show convergence both of game-theoretic structures—relatively small coalitions in the finite economies converge to finite coa...

This paper applies the theory of the conventionally stable set to monopolistic and oligopolistic markets. A market model with a finite number of producers and a continuum of buyers is presented and then is formulated as a strategic game in which the producers' strategies are prices and the buyers' strategies are demands for commodities. It is shown...

This paper attempts to define a new solution concept for n-person noncooperative games. The idea of it is close to that of the von Neumann-Morgenstern stable set, more precisely, is based on their ‘standards of behavior’ interpretation of the stable set. This new approach enables us to consider new interesting problems of information. Further this...

In this paper we develop a new model of a cooperative game with a continuum of players. In our model, only finite coalitions - ones containing only finite numbers of players - are permitted to form. Outcomes of cooperative behavior are attainable by partitions of the players into finite coalitions: this is appropriate in view of our restrictions on...

This paper considers an exchange economy called a generalized assignment market, in which sellers and buyers trade one indivisible commodity possibly with product differentiation for a perfectly divisible commodity. The existence of a competitive equilibrium in this economy is proved using Kakutani's fixed point theorem. This existence theorem is a...

We explore the relation between information patterns and Nash equilibria in extensive games. By information we mean what players know about moves made by others, as well as by chance. For the most part we confine ourselves to pure strategies. But in Section 7 behavioral strategies are also examined. It turns out that they can be modeled as pure str...

This paper provides an axiomatic model based on an extraneous random device generating objective probabilities for the derivation of expected utilities and subjective probabilities. Four basic axioms fully determine a real-valued utility function and a finitely additive subjective probability measure. The restrictions of these axioms to lotteries d...

This paper provides a new formulation of the Nash social welfare function for a continuum of individuals. The new formulation removes redundant assumptions of Kaneko's original formulation and in particular shows that the continuity axiom on social orderings is unnecessary. The derivation of the Nash social welfare function is also much directer an...

This paper argues that interpersonal comparisons of utility levels are difficult in principle, and that interpersonal comparisons of utility differences can also be hardly defined based solely on individual choice behavior.

A model of a rental housing market in which houses are treated as indivisible commodities is presented. A recursive equation that determines a competitive equilibrium is provided, and it is argued that this competitive equilibrium is representative of the set of all competitive equilibria. Using this representative equilibrium, several propositions...

It is argued that although the pathological multiplicity of Nash equilibria of super games stated by the folk theorem can be removed by introducing limited observations into super games with a continuum of players, the consideration of super games in terms of the Nash equilibrium concept involves a more fundamental and conceptual difficulty.

Initially this paper considers an assignment game without side payments and proves the non- emptiness of the core of it. Next, a market model with invisible goods but without the transferable utility assumption is presented, and the non-emptiness of the core and the existence of a competitive equilibrium of the market model are shown, using the fir...

The purpose of this paper is to consider the problem of optimal income taxation in the domain of progressive (convex) income tax function. This paper proves the existence of an optimal tax function and that the optimal marginal and average tax rates tend asymptotically to 100 percent as income level becomes arbitrarily high.

A generalization of assignment games, called partitioning games, is introduced. Given a finite set N of players, there is an a priori given subset pi of coalitions of N and only coalitions in pi play an essential role. Necessary and sufficient conditions for the non-emptiness of the cores of all games with essential coalitions pi are developed. The...

This volume is a posthumous collection of selected papers of Kenjiro Nakamura, a brilliant social scientist who died in 1979 at the age of 32. Most of the papers in the book were published in 1978, 1979 and 1980.
Look at Linked Data
https://www.researchgate.net/publication/330717097_Game_Theory_and_Social_Choice1981_Nakamurapdf

In this paper we consider the Nash social welfare function for a society which is given as an arbitrary finite measure space. We show that the Nash social welfare function for the society is derived from certain rationality criteria.

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numeri...

## Projects

Projects (2)

We develop a theory of an equilibrium-econometric analysis of rental housing markets with indivisibilities. It provides a bridge between a (competitive) market equilibrium theory and a statistical/econometric analysis. The listing service of apartments provides the information to both economic agents and an econometric analyzer: each economic agent uses a small part of the data from the service for his economic behavior, and the analyzer uses them to estimate the market structure. It is argued that the latter may be done by assuming that the economic agents take the standard price-taking behavior. We apply our theory to the data in the rental housing markets in the Tokyo area, and examine the law of diminishing marginal utility for household. It holds strictly with respect to the consumption, less with commuting time-distance, and much less with the sizes of apartments