On the Future Parameter

In Japanese companies, most of decisions at first seem to be illogical according to game and decision theories; however, they are in fact logically led by the high future parameter. In a non-zero sum environment, typified by the prisoner’s dilemma game, there is no convincing equilibrium or stability. Axelrod’s study on the evolution of cooperation states that players who survive are the ones who choose future cooperation over immediate benefits or revenge for past defection. In the repeated game of the prisoner’s dilemma, the future parameter is defined as the probability of playing the next move. The future parameter is not simply a theoretical number; a high future parameter gives meaning to the actual behavior of organization members on the shop floor and those in the office. It forms the basis of the day-to-day experiences of Japanese company employees, giving them something from which they can derive a sense of achievement, something for them to feel worthwhile doing, and something to live for.


Introduction
When people make decisions, whether consciously or subconsciously, the decisions are made according to some rule or principle.Let us call this the decision principle.There are various kinds of decision principles in decision theory that are derived from game theory, for example, Wald's maximin principle, the maximax principle, Hurwicz's optimism-pessimism index principle, and Savage's minimax regret principle, etc. (French, 1986;Takahashi, 1993).A random choice of alternatives is also one of the typical decision principles (Takahashi, 1997a).
The minimax theorem proves that in a zero-sum two-person game, as long as one player chooses a strategy according to Wald's maximin principle, the same principle should be the optimal decision principle for the other player as well.However, in a non-zero-sum two-person game, despite the existence of the Nash equilibrium, even if both players choose their strategy in accordance with maximin principle, they will not reach the Nash equilibrium point.On the contrary, an attempt to explain the Nash equilibrium solely by economic rationality has been unsuccessful (Kandori, 1997).Rather than explaining the economic rationality of the equilibrium, it is better to analyze path dependency when multiple equilibria exist.
It has been said that the Japanese have no decision principles; however, this is highly doubtful-the Japanese have decision principles.If their behaviors were not guided by decision principles, people and companies of Japan would not be able to predict each other's actions, and any kind of social life would become impossible; however, this is not the case.Indeed, their actions are being led by some kind of principle.The decision principle commonly observed in many Japanese companies appears to be different from typical decision principles in game and decision theories.
Generally, a person's choice of strategy depends on the decision principle he or she adopts.When two people use different decision principles, it is difficult for a player to imagine or understand what kind of decision principle the opponent is using, particularly when the opponent's choice upsets the player's expectations.Therefore, it appears to non-Japanese people that the Japanese have no decision principle.However, they do have decision principles, although different from well-known typical principles.So then, what types of decision principles lead the Japanese people's actions?This paper proposes a hypothesis to answer this question.

Prisoner's Dilemma
There exists a non-zero-sum two-person game having an unconvinced "equilibrium".A particularly well-known example is the prisoner's dilemma.By associating "not confessing" to "cooperation" and "confessing" to "defection," the prisoner's dilemma game is often generalized in the following cooperation/defection game (Axelrod, 1984, pp. 7-8).(c) Regardless of the opponent's choice, defection yields a higher payoff than cooperation.However, if both players have defected, both get lower payoffs than if both had cooperated.
The dilemma here is (c).In other words, two players (two prisoners in the classic version of prisoner's dilemma) faced the dilemma where despite mutual cooperation having more benefit than mutual defection, if both players yield to the temptation to sell out their opponent in a one-sided defection, the result will end in mutual defection.
If the prisoner's dilemma game is played a known finite number of times, theoretically, the game will never end in cooperation (Axelrod, 1984;Luce & Raiffa, 1957).This is because as long as the number of moves is known and finite, on the last move, the game will result in mutual defection since there is no future; this is the same as playing the game once.On the next-to-last move, both players defect since they can expect mutual defection on the last move.Such a line of reasoning, that is backward induction from the last move, implies that the first move also ends in mutual defection.
What a foolish state this is if both players really lost in an equilibrium of mutual defection.In fact, the author is not the only one who thinks this.This tapped many psychologists' desire to study the topic further.Twenty years since the first research results were announced (Scodal, Minas, Ratoosh, & Lipetz, 1959), more than 1,000 academic writings have been publicized (Pruitt & Kimmel, 1977).Through experimentation, we now understand that the prisoner's dilemma game does not always end in mutual defection.
For example, Rapoport and Chammah (1965) paired up 70 pairs of male students from the University of Michigan as research subjects to play the prisoner's dilemma games 300 times in succession.The results showed that "cooperation" appeared quite frequently.The study paid particular attention to the last 25 moves out of 300 for each pair; the number of "CC lock-ins" was 53%.Their criterion of a "CC lock-in" is 23 or more CC responses out of the last 25, where a CC response is the situation in which both players choose "cooperation" (C).Fifty-three percent of the games ended in a stable state of mutual cooperation.Axelrod (1980a) tested a round-robin league match, in other words a computer tournament, between computer programs.Fourteen programs, provided by 14 professional game theorists, and a 15th program RANDOM, which randomly cooperates and defects with equal probability, were entered into a round-robin competition.Each program was paired with each other and itself.The winner was a program TIT FOR TAT.In this case, TIT FOR TAT was to begin with "cooperation" on the first move and thereafter copy the opponent's previous move.Axelrod (1980b) planned a second computer tournament and gave the entrants a detailed analysis of the first tournament.For this second tournament, 62 players from six countries participated, including players from the first tournament.In the first tournament, a game consisted of 200 moves; however, in the second tournament, no one knew exactly when the last move would come, and everyone knew that the probability of continuing on to the next move after each move (represented as discount parameter w) was 0.99654.That is, the expected median length of a game was set at 200 moves.Again, TIT FOT TAT won in the second tournament.Axelrod (1980b) examines the result of the simulation of hypothetical future rounds (i.e., generations) of this tournament.It is assumed that the share of a given program in a round i+1 will be proportional to the program's tournament score in the previous round i.The results showed that after 50 generations the bottom third of programs had almost disappeared.Most of the middle-ranking third had started to decline, while the top-ranking third were growing.Programs that exploited opponents through skillful defection made good progress for a while, but got terminated once the programs they preyed upon were all gone.TIT FOR TAT continued to win throughout the entire 1000 generations of the simulation, occupying the highest share ranking and showing the greatest rate of share increase until the end.

Evolution of Cooperation
Since no new programs were added into the simulation as the generations progressed, strictly speaking, this simulation can be classified as an ecological simulation.By contrast, analyses of evolutionary situations that allow for mutation use the concept of collective stability based on the evolutionarily stable strategy (ESS) (Maynard Smith, 1982).Assume a group of individuals using a certain program and a single mutant individual using a different program.If the mutant individual can gain a higher score than the other individuals in the group, the mutant individual is said to invade the native individuals.A program is said to be collectively stable if no other program is able to invade it.Axelrod (1981) proves that the ALL D program (which always selects "defection" regardless of the opponent's choice) is always collectively stable.In other words, even by employing the concept of collective stability instead of equilibrium, unfortunately collective stability was also achieved through mutual defection.In this respect, equilibrium and collective stability are very much the same.However, whenever TIT FOR TAT invaded a group of ALL D for the same payoff matrix and w used in the computer tournament, the group would return to being solely ALL D if the TIT FOR TAT ratio was lower than 0.17%, but all individuals of the group would use TIT FOR TAT if the ratio was higher than 0.17% (Shimizu, 1996).In other words, even though ALL D is theoretically collectively stable, this is true only if the ALL D ratio is higher than 99.83%.Otherwise, the invasion of TIT FOR TAT cannot be prevented.It is doubtful to exaggerate the actual significance of this kind of "stability."In fact, if w is large enough, TIT FOR TAT can be proven to be collectively stable.1

Future-Oriented System
It is necessary to question whether equilibrium and collective stability are truly fascinating and convincing ideas and concepts.Axelrod's (1984) analysis of the first computer tournament is highly suggestive on that point.High scoring programs share two propensities.Surprisingly, only one propensity was separating the high scoring and low scoring programs, as explained below.

(A) Nice: The propensity of never being the first to defect
The eight highest scoring programs out of the fifteen were all nice.
None of the other seven programs were nice.There exists a gap in scores between the nice programs and the others.In other words, while testing, and sometimes exploiting, one's opponent brought temporary gain, it later led to a collapse of cooperation and resulted in lower scores than continued cooperation.By contrast, nice programs continued to cooperate as long as their opponent did not defect, resulting in a higher mean score.Furthermore, the response to the opponent's defection determined the overall mean score of each of the nice programs.The highest scoring nice programs also had the following second propensity.In other words, (A) and (B) suggest "not to make choice (A) for immediate benefits or choice (B) as revenge for past defection."Or, in order to survive, "one should choose cooperation (C) in the future."TIT FOR TAT is the simplest typical example of a program that steadily built up scores through cooperation and prospered by winning good results and advancing to the next generation.
However, under careful consideration, this concept seems too obvious and does not need simulation to prove it.When considering this outside of the framework of a cooperation/defection game, the concept becomes nothing more than a competition between the momentary system of living for the moment and seeking immediate fulfillment and pleasure, which is the principle of living only for the moment (seeking revenge could also be called pleasure) and the future-oriented system of thinking 10, 20, or more years ahead, enduring the present and saving for the future.Even if the momentary system has a period of short-term high scores, after several decades, only the future-oriented system will have survived.
Aesop's fable of "The Ant and the Grasshopper" describes this situation accurately.
Like the flitting grasshopper with the principle of living only for the moment, American institutional investors hold no interest in the long-term soundness and growth of individual companies, and they request for immediate shareholder returns without retaining any profits for company or for group growth.By contrast, Japanese companies having a strong orientation to future growth endure the current tough environment to make profit, and they are tight-fisted when it comes to paying salaries and dividends to shareholders.Even if they do not elaborate on the reinvestment, they retain the profits as internal reserves for investing into future expansion.Their patient and plodding perseverance will lead to future profits.In order to explain their behaviors, Takahashi (1996aTakahashi ( , 1996b) ) proposes a decision principle called the leaning on future principle.The leaning on future principle is a principle along which people choose a better future rather than act through present mercenary motives based on the past results.Axelrod (1984) calls the probability w of playing the next move the discount parameter.However, by multiplying the profit by w 10 or w 20 , even after 10 or 20 years, the distant-future profit will still be almost nil if w is any less than 1.In other words, the discount parameter way of thinking, which discounts the future, ignores distant-future profits even though there may be large profits in the distant future.

Future Parameter
Consequently, despite the name "long-term", in reality "long-term profit" is only determined by near-future profit.In order to take on a "project with little initial profit but that will gradually increase in profitability and make huge total profits in 10 or 20 years," w must be approximately equal to 1, or in other words, the future must not be discounted at all or discounted very little.
In fact, it has already been pointed out that Japanese companies hardly use the discount rate when making investment decisions.A survey of investment decision methods of 632 listed Japanese non-financial companies and 35 foreign companies in Japan taken between August and September 1992 showed that 63% of companies used methods involving payback periods and profitability indexes.
Only 17% of companies used discount rate methods, such as internal rate of return (IRR: a discount rate that makes the net present value (NPV) equal to zero) or NPV, when making investment decisions (Survey Report on Financial Activities of Companies, Japan Productivity Center, 1993).By contrast, a similar survey of 200 companies carried out in 1979 among Fortune top 1,000 companies in the United States showed that as many as 63% of companies used discount rate methods (Kim & Farragher, 1981).
Valuation methods using discount rates spread rapidly throughout the United States in the 1960s.Another survey (of 184 companies) showed that in 1959, only 19% of companies had adopted these methods, but by 1970 that figure had risen to 57% (Klammer, 1972).something to live for.For example, under the circumstances of high future parameter, future challenge and growth regardless of present difficulties is valued more highly than using probabilities to convert future profits to the present value and settle future accounts at present.
In fact, when explaining work motivation of Japanese companies, actual survey data can demonstrate better Deci's (1975) intrinsic motivation (Takahashi, 2002) in which challenges 2 are more significant than Vroom's (1964) (a) Each player must choose either "cooperation" (C) or "defection" (D).(b) Each player must make the choice without knowing what the opponent will do.

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B) Forgiveness: The propensity to cooperate in the moves after the opponent has defected Morally speaking, a player should always forgive and forget past defection without holding a grudge, and choose cooperation in the future.Otherwise, one instance of defection by the opponent would stir up an endless battle of retribution, and both players would spend a long time in an inescapable bog.
expectancy theory.Takahashi (1996b) collects papers recording examples of supplier systems in the automotive industry, collaborative research and development in the pharmaceutical industry, and cross-licensing in the semiconductor industry.Evolutionarily speaking for Japanese companies, from the viewpoint of long-term performance, future-oriented systems based on the leaning on future principle thrived while systems based on other decision principles declined.