Functional dynamics

Kataoka, Naoto; Kaneko, Kunihiko

doi:10.1016/s0167-2789(00)00203-7

Cited by 14 publications

(11 citation statements)

References 7 publications

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“…Equation (15) represents the functional dynamics [34][35][36], where the change in time depends on the function rather than the dynamic systems of state variables of a finite dimension (for example, in dynamicalsystems game [37]). Hence, we need to solve the dynamics of infinite dimensions.…”

Section: Functional Dynamics Of Strategiesmentioning

confidence: 99%

Functional dynamic by intention recognition in iterated games

Fujimoto

Kaneko

2019

New J. Phys.

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Intention recognition is an important characteristic of intelligent agents. In their interactions with others, they try to read others' intentions and make an image of others to choose their actions accordingly. While the way in which players choose their actions depending on such intentions has been investigated in game theory, how dynamic changes in intentions by mutually reading others' intentions are incorporated into game theory has not been explored. We present a novel formulation of game theory in which players read others' intentions and change their own through an iterated game. Here, intention is given as a function of the other's action and the own action to be taken accordingly as the dependent variable, while the mutual recognition of intention is represented as the functional dynamics. It is shown that a player suffers no disadvantage when he/she recognizes the other's intention, whereas the functional dynamics reach equilibria in which both players' intentions are optimized. These cover a classical Nash and Stackelberg equilibria but we extend them in this study: Novel equilibria exist depending on the degree of mutual recognition. Moreover, the degree to which each player recognizes the other can also differ. This formulation is applied to resource competition, duopoly, and prisoner's dilemma games. For example, in the resource competition game with player-dependent capacity on gaining the resource, the superior player's recognition leads to the exploitation of the other, while the inferior player's recognition leads to cooperation through which both players' payoffs increase.

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Section: Functional Dynamics Of Strategiesmentioning

confidence: 99%

Functional dynamic by intention recognition in iterated games

Fujimoto

Kaneko

2019

New J. Phys.

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“…Theorem 4.1 A quadratic extension graph consists of a single cluster, whose distinct blocks have distinct discriminants. If char(K) = 2, then the block-graph is a complete graph, and the set of mappings F b , defined in (13), form a group of permutations of blocks, isomorphic to the multiplicative group of K 2 . The isomorphism associates b 2 ∈ (K * ) 2 to the permutation sending the block Θ to F b/2 (Θ).…”

Section: Graphsmentioning

confidence: 99%

“…Our interest in such systems is motivated by the desire of developing an algebraic variant of some abstract models of adaptive systems and chemical interactions, where functions were made to act on other functions via composition, within the framework of λ-calculus [9,10]. Subsequently, a similar concept was proposed as functional dynamics on coupled map lattices [12,13] using again the composition of smooth functions as interaction.…”

Section: Introductionmentioning

confidence: 99%

Self-interacting polynomials

Vivaldi

2007

Preprint

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We introduce a class of dynamical systems of algebraic origin, consisting of selfinteracting irreducible polynomials over a field. A polynomial f is made to act on a polynomial g by mapping the roots of g. This action identifies a new polynomial h, as the minimal polynomial of the displaced roots. By allowing several polynomials to act on one another, we obtain a self-interacting system with a rich dynamics, which affords a fresh viewpoint on some algebraic dynamical constructs. We identify the basic invariant sets, and study in some detail the case of quadratic polynomials. We perform some experiments on self-interacting polynomials over finite fields.

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“…Several models have been proposed to study the dynamic change of functions [3][4][5][6][7][8][9]. Sato and Ikegami [3] introduced switching map systems, in which maps to govern the evolution of the systems are dynamically switched with other maps in the system.…”

Section: Introductionmentioning

confidence: 99%

“…Sato and Ikegami [3] introduced switching map systems, in which maps to govern the evolution of the systems are dynamically switched with other maps in the system. Kataoka and Kaneko [4][5][6] investigated the evolution of a one-dimensional function f n defined by f n+1 = (1 − )f n + f n • f n . Studying dynamics in which functions vary in time using metadynamics can be important when considering system evolution or learning.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and computation in functional shifts

Namikawa¹,

Hashimoto²

2004

Nonlinearity

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Abstract. We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift that is defined by a set of bi-infinite sequences of some functions on a set of symbols. To analyze the complexity of functional shifts, we measure them in terms of topological entropy, and locate their languages in the Chomsky hierarchy. Through this study, we argue that considering functional shifts from the viewpoints of both dynamics and computation give us opposite results about the complexity of systems. We also describe a new class of shift spaces whose languages are not recursively enumerable. §

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Functional dynamics

Cited by 14 publications

References 7 publications

Functional dynamic by intention recognition in iterated games

Functional dynamic by intention recognition in iterated games

Self-interacting polynomials

Dynamics and computation in functional shifts

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