論理と確率の推論を「心の中のゲーム」としてモデル化する

抄録

This study presents a model of human reasoning as a collection of micro-level in-
ternal agents, and applies it especially to two problems: the four-card selection task
(selecting cards to verify a conditional sentence) and the problem of three prisoners
(a problem to estimate probability when an outcome proves impossible). In both the
problems real people tend to report an intuitive answer which differs from one that is
considered mathematically correct. In the presented approach, game theory is used to
explain human reasoning, and connected to the frame systems and the society of mind
proposed by Marvin Minsky. As it is assumed in a standard non-cooperative game the-
ory, the internal agents do not have a language to communicate with other than game
play. Also, it is assumed that the intelligence of agents is restricted only in terms of
improving one’s expected payoff. At any step of reasoning, each agent microscopically
responds (i.e., collecting labels) to a given collective action of other agents. The infor-
mation response model, the best responses in standard game theory, is parametrized
by the payoffs of a bimatrix game, so as to predict the observed patterns typically cho-
sen/answered by real people at an equilibrium point of the game. Human reasoning is
modeled as a path from the first (i.e., default) equilibrium point to the final equilibrium
point. Moves between the two equilibrium points are represented using Lloyd Shap-
ley’s labeling system and interpreted as Minsky’s frame system (or K-lines). It can be
concluded that the proposed modeling can summarize and improve previous research
on both the four-card selection task and the problem of three prisoners, which seems
to have been inaccurately modeled in the literature.