Stability and Diversity in Collective Adaptation

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by information flux between agents, giving a novel view of collective adaptation.Comment: 22 pages, 23 figures; updated references, corrected typos, changed conten

Effect of Uncertainty about Others' Rationality in Experimental Asset Markets: An Experimental Analysis

We investigate the extent to which price deviations from fundamental values in an experimental asset market are due to the uncertainty of subjects regarding others' rationality. We do so by comparing the price forecasts submitted by subjects in two market environments: (a) all six traders are human subjects (6H), and (b) one human subject interacts with five profit-maximizing computer traders who assume all the traders are also maximizing profit (1H5C). The subjects are told explicitly about the behavioral assumption of the computer traders (in both 6H and 1H5C) as well as which environment they are in. Results from our experiments show that there is no significant difference between the distributions of the initial deviations of the forecast prices from the fundamental values in the two markets. However, as subjects learn by observing the realized prices, the magnitude of deviations becomes significantly smaller in 1H5C than in 6H markets. We also conduct additional experiments where subjects who have experienced the 1H5C market interact with five inexperienced subjects. The price forecasts initially submitted by the experienced subjects follow the fundamental value despite the fact that the subjects are explicitly told that the five other traders in the market are inexperienced subjects. These findings do not support the hypothesis that uncertainty about others' rationality plays a major role in causing substantial deviation of forecast prices from the fundamental values in these asset market experiments

Learning Games

This paper proposes a model of learning about a game. Players initially have littleknowledge about the game. Through playing the identical game repeatedly, eachplayer not only learns which action to choose but also constructs his personal viewon the game. The model is studied using a hybrid payoff matrix of the prisoner’sdilemma and coordination games. Results of computer simulations show (1) when allthe players are slow in learning the game, they have only a partial understanding ofthe game, but may enjoy higher payoffs than the cases with full or no understandingof the game; (2) when one of the players is quick in learning the game, he obtains ahigher payoff than the others. However, all of them can receive lower payoffs than thecase where all the players are slow learners

10.7 研究テーマ

研究テーマ秋山英三［慶應義塾大学理工学部］＊所属は当時のものを記

Evolution of Reciprocal Cooperation in the Avatamsaka Game

The Avatamsaka game is investigated both analytically and using computer simulations. The Avatamsaka game is a dependent game in which each agent’s payoff depends completely not on her own decision but on the other players’. Consequently, any combination of mixed strategies is a Nash equilibrium.Analysis and evolutionary simulations show that the socially optimal state becomes evolutionarily stable by a Pavlovian strategy in the repeated Avatamsaka game, and also in any kind of dependent game. The mechanism of the evolutionary process is investigated from the viewpoint of the agent’s memory and mutation of strategies.Book Series：Lecture Notes in Economics and Mathematical SystemsThis Book：The Complex Networks of Economic InteractionsEssays in Agent-Based Economics and Econophysic

Inductive Game Theory: A Simulation Study of Learning a Social Situation

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 (13). So far, IGT has been studied chiefly in theoretical manners, while some other papers targete

Chaotic itinerancy on Bertrand competition model with many firms

The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of (n − d) curvilinear coordinatesparametrizingthe manifold of configurations satisfying the constraints, and to compute the Lagrangian generating the unconstrained dynamics in these (n − d) configuration coordinates. Starting from this Lagrangian an unconstrained Hamiltonian H(q,p) on 2(n−d) dimensional phase space can then typically be defined in the standard way via a Legendre transform. Furthermore, if the system is in contact with a heat bath, the associated Langevin and Fokker-Planck equations can be introduced. Provided that an appropriate fluctuation-dissipation condition is satisfied, there will be a canonical equilibrium distribution of the Gibbs form exp(−βH) with respect to the flat measure dqdp in these 2(n − d) dimensional curvilinear phase space coordinates. The existence of (n − d) coordinates satisfying the constraints is often guaranteed locally by an implicit function theorem. Nevertheless in many examples these coordinates cannot be constructed in any tractable form, even locally, so that other approaches are of interest. In ambient space formulations the dynamics are defined in the full original n-dimensional configuration space, and associated 2n-dimensional phase space, with some version of Lagrange multipliers introduced so that the 2(n − d) dimensional sub-manifold of phase space implied by the holonomic constraints and their time derivative, is invariant under the dynamics. In this article we review ambient space formulations, and explain that for constrained dynamics there is in fact considerable freedom in how a Hamiltonian form of the dynamics can be constructed. We then discuss and contrast the Langevin and Fokker-Planck equations and their equilibrium distributions for the different forms of ambient space dynamics