Teruhisa Nakai

The construction of subjective games by motive distributions in n -person non-cooperative game

The purpose of this paper is to propose the model considering the subjective viewpoint of player in a n -person non-cooperative game. It is realized by taking in players subjective feeling for values as his motive distribution. Subjective games and subjective Nash equilibrium strategies are defined, and some examples of motive are shown. By using the subjective game, we can rationally explain various possibilities in selecting a strategy by a player.

A distinction among stable equilibria in a noncooperative game

Abstract As a result of a conflict analysis for noncooperative game we obtain a stable equilibrium point (SEP), but in the case of many SEPs these can’t become a suitable guidance for selecting a strategy. We represent a prediction of a motive for selecting a strategy by a motive distribution, calculate a probability of realization of each SEP and propose that a player should aim at a SEP having the maximum realization probability.

Fuzzy subjective game considering non-additive feelings of players

In the field of non-cooperative game Nakai [3] proposes a subjective game to explain the variety in a strategy selection by a player. But in constructing a subjective game by a motive distribution, the expected payoff is calculated additively. In actuality the degree of satisfaction for a player is generally very subjective and non-additive. Therefore this paper proposes a fuzzy subjective game in which we represent the non-additive feelings of a player by a fuzzy measure and evaluate the expected payoff by the fuzzy integral.

Inventory model for deteriorating items with returns and disposals

Abstract We consider an inventory model for deteriorating items in consideration for returns and disposals. At the end of each period the deteriorating items left unsold must be disposed of, but the new items left unsold can be returned to the supplier within limits and can be also disposed of without limit if necessary. The remains of new items are carried over to the next period as deteriorating items. The optimal inventory policies are obtained in two cases, that is, the demand for new items is independent of or dependent on one for deteriorating items.

Optimal inventory control for deteriorative goods considering delays of deliveries

Abstract We consider an inventory control model for goods with deteriorative qualities in consideration of delays of deliveries and disposals. On condition that an item with a shorter residual lifetime is sold earlier, we formulate this problem by a dynamic programming and obtain the analytic solution sequentially. Moreover, we propose a forward and backward algorithm to obtain the optimal policy concretely.

Verification of the subjective game by game experiments

In a non-cooperative game, to explain the variety in strategy selections by players, Nakai [11] presents the concept of subjective game, but its verification is not yet performed. We perform game experiments in various dilemma situations and obtain the result that the rate of coincidence of the action indicated by the subjective Nash equilibrium strategy with the actually selected action is more than 75%, especially, the rate in a prisoners dilemma game is 91.7%. Since it is known that the rate of coincidence of the Nash equilibrium strategy with the actual action in a prisoners dilemma game is 53%, the high explanation power of the subjective game has been verified.

Influences of social motives in an information operation game

In a repeated n–person nonzero–sum game with an incomplete information structure, taking into account social motives of players, we consider an information operation problem by an information-dominant player. We formulate this problem and derive the optimal subjective information operation and subjective Nash equilibrium strategies of all players.A numerical example is given to explain these concepts.

Fuzzy subjective conflict analysis

For an analysis of a noncooperative game we propose a fuzzy subjective conflict analysis which applies a conflict analysis to a fuzzy subjective game considering a subjective sense of value of a player and a fuzziness and nonadditivity of human judgments. Using this method we can explain the variety in selecting a strategy by a player and dispel the gap between the individual rationality and the social one.

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection

In the behavior analysis of a company we propose a method considering subjectivity of each company.We introduce some motives for strategy selection by a company and construct his subjective game by using his motive distribution. It is desirable that each company follows his Nash equilibrium strategy for his own subjective game.We apply this method to the Cournot oligopoly market model and obtain the subjective Nash equilibrium strategy for each player. Moreover by some numerical examples we examine the influence of the motive distribution on the equilibrium strategy.

A generalized Deegan-Packel index for multialternative voting games in case of nonhomogeneous voters

Abstract This paper proposes a generalized Deegan-Packel index which is applicable to multialternative voting systems considering voters are not always homogeneous. The Deegan-Packel index is proposed under assumption that all minimal winning coalitions (MWC) are formed with equal probability. We consider the case that each MWC is formed with a probability in inverse proportion to theα-th power of the Euclidean distance with respect to affinity among players and in inverse proportion to the β-th power of the number of players constituting it. We show an axioms system on which the new index is based. Finally we compare some power indices in case of the House of Councilors in Japan and show the new index is considerably superior to the others.