ECOLOGICAL GAME

<⇒Real Game>

Abstract

We intoroduce an interactive simulation game that links ecological and economic systems and considers important ecological laws and social systems.
This page is presented in two parts. Section 1 presents a sample ecological game, and section 2 provides the strategy of this game and offers policy advice.

Contents

1. Formulation of the game
1.1 Basic flow of the game
1.2 Actions
1.3 The function of the external world and poor circulation
1.4 Physical capital and points-melds table
1.5 Production and energy
1.6 Cards
1.7 Resource depletion and whistle
1.8 War
1.9 Contracts
1.10 Ethical principles and laws
2. The strategy of the game
2.1 The strategy for starvation and war
2.2 Ethical principles and redistribution
2.3 Poor circulation and Environmental issues
2.4 Strategy for whistle and recycling
2.5 Value theory
2.6 Innovation
2.7 Unemployment
2.8 Discussion and conclusions
⇒References

1. Formulation of the game

In section 1, we construct a game that appropriately simulates interactions between the human and environmental components of our world. When an event A in the real world corresponds to an event B in the game, B represents A. We attempt to construct a game consistent with ecological laws, economic principles, and social systems.

1.1 Basic flow of the game

The game, as in Mahjong, is played by four players with the aid of a dealer. Players sit at their respective positions at the table. The game is played with sets of tiles, cards, and chips. Players have a row of tiles (wall) in front of them on the table. Each player draws tiles from his own wall in turn and discards tiles in the center of the table. Each player completes a legal hand (meld) using some tiles and acquires points, which correspond to a points-melds table.

1.1.1 Objective of the game
The objective of the game is to achieve (1), (2), and (3), listed below, simultaneously.
(1) Avoid dying of starvation
(2) Avoid dying in a war
(3) Select A or B
A: Maximize points
B: Meet needs
In the real world, some people engage in ever increasing purchasing and consumption of material possessions, while others are satisfied with meeting their needs rather than their wants. The former and latter are primarily represented by player types A (growth-oriented players) and B (steadiness-oriented players), respectively. The game is not a race to acquire the most points.

1.1.2 Tiles
The following two colors represent two categories of matter or atoms: green and black. Green tiles represent organic matter. In particular, the green tiles represent the matter that constantly cycles through the ecosystem. There are many varieties of green tiles, including C tiles, H tiles, and N tiles. These tiles primarily represent carbon, hydrogen, and nitrogen, respectively. Each player can only discard melds that consist of green tiles (Green melds). After several turns, the dealer shuffles the discarded green melds and returns them to a player’s wall. Bread, a green meld, is formed using two C tiles and represents food. Black tiles represent inorganic and non-circulating matter. There are many varieties of black tiles, including Fe tiles, Cu tiles, Au tiles, etc. Players may not discard melds that consist of only black tiles (Black melds). Mixed melds consist of both green and black tiles.

1.1.3 Cards and chips
Cards represent human capital, such as collective knowledge, skills, culture, etc. Each player can obtain cards from the dealer but cannot acquire points directly from the cards. The cards help players. The chips represent money, which is the accepted medium of exchange.

1.2 Actions

Each player, in turn, engages in an action to attain an objective. Some bread is necessary to take action. When a player possesses less than five units of bread, the game is over as the player is dying of starvation. When a player has at least five units of bread, he or she discards five units and then takes action. There are 7 types of action.

Action 1: Draw green tiles
The player draws green tiles or melds from the wall. Players have imperfect information about which tiles or melds are contained in the wall. This action represents harvesting rice, catching fish, extracting petroleum, etc.

Action 2: Draw black tiles
The player draws black tiles or melds from the wall. Players have imperfect information about which tiles or melds are contained in the wall. This action primarily represents the mining of metal.

Action 3: Exchange
The player negotiates with the other players to trade tiles, melds, chips, or cards. Completing a trade requires the coincidence of wants and combinations such as tiles for chips, tiles for tiles, chips for cards, etc.. Other than when a special coalition exists, players may trade with the highest bidder. If the negotiation fails, the action fails and the discarded bread is wasted. The number of discarded units of bread depends on what is traded, and as such, it represents transaction costs, such as transport costs, etc. Each negotiation attempt is 1 minute long (the negotiation time). Only during this time can players exchange information about the tiles each player possesses, wants, etc. After 1 minute, no further conversation may take place. This negotiation time represents the time required to exchange information.

Action 4: Produce
The player completes melds consisting of combinations of tiles, tiles and melds, or melds. The number of discarded units of bread is primarily determined by what the player produces. This action represents the producing of goods by combining materials.

Action 5: Consume
The player converts melds into points. No points are acquired until melds are consumed. When green melds are consumed, they are discarded and placed in the center of the table. When black melds are consumed, they remain in the player’s hand as spent black melds. When mixed melds are consumed, green tiles are discarded, while the black tiles remain in the player’s hand as spent black melds. The units of bread required is determined by what the player consumes. This represents actions such as eating food, watching television, listening to music, etc.

Action 6: Decompose
The player decomposes spent black melds into normal black tiles. Complete melds cannot be created from spent black melds. However, decomposition allows the reuse of the decomposed black tiles. The number of units of bread required is determined by what the player decomposes. These actions represent separating trash, recycling, disposing of sewage, etc.

Action 7: Research and education
The player can attempt to obtain cards from the dealer; however, whether the player obtains cards depends on luck. This action represents the research and education activities of universities and firms.

For example, Action 1 requires 2 units of bread, and Action 2 requires 3 units of bread. When a player takes Action 1 and Action 2, 5 units of bread are discarded. Each player selects actions so that the required units of bread do not exceed five.

1.3 The function of the external world and poor circulation

The wall, discard pile, and dealer (collectively called the external world) represent the natural world.
The first function of the external world is to complete melds. That is, the external world functions as a producer. Therefore, the dealer completes green melds and places them in a player's wall. This action represents the benefits that nature bestows upon people (natural foods, fur, etc.). The dealer does not affect black tiles. A unit of bread is the green meld that is completed only by the dealer. At the beginning of the game, some green melds are already present in the wall. These melds can be categorized into two types. The first is melds that are present in the wall at the beginning of the game, and thus, they are not produced after the game has commenced (non-renewable green melds). For example, oil and coal are non-renewable green melds. The second type is melds that are present in the wall at the beginning of the game and are subsequently produced and returned to the wall (renewable green melds). For example, bread, wood, and fur are renewable green melds.
The second function of the external world is to break down discarded green melds (that is, the external world functions as a decomposer). This represents the decomposition of organic matter by bacteria, fungi, etc. However, there is an upper limit to this function, and when the sum of discarded green tiles and melds exceeds this limit, all players suffer from the damage. The extent of the damage depends on the type and number of tiles and melds discarded. When players retain the spent black melds, which are not decomposed for a long time, all players are subject to damage. The extent of the damage depends on the type and number of melds and the length of time the spent black melds are retained. Only the dealer possesses complete information about limit value and the extent of damage. Renewable green melds that are returned to the wall decrease in number (that is, there is poor circulation). In other words, poor circulation decreases the ability of the external world to function as a producer. This represents environmental damage, such as algal bloom, global warming, acid rain, etc. In the real world, poor circulation sometimes increases the ability of the external world to function as a producer, but we ignore this problem for now. Green tiles are exchanged between players and the external world. Once black tiles are drawn, they will never return to the external world. This rule represents the circulation of organic matter and non-circulation of inorganic matter.

1.4 Physical capital and points-melds table

When players produce a chair (available green melds), they collect two C tiles, two H tiles, and discard five units of bread to take Action 4. In this case, the two C tiles, two H tiles, and five units of bread are the ingredients of the chair. There are 3 types of melds. The first is melds for points. A chair is one such meld. The second is melds for ingredients. The player completes new melds consisting of combinations of this type of meld. The third is melds for physical capital. Players cannot acquire points from physical capital, which aids a player’s action. Rather, physical capital is categorized into the following types according to its effects:

Physical capital 1-1:
Such capital can decrease the number of discarded units of bread required for Action 1. A plow is a type of physical capital 1-1. For example, people apply a plow to increase the efficiency of farm work so the farmer can use spare time for other actions.

Physical capital 1-2:
Such capital can increase the quantity of the green tiles and melds that the dealer places in the wall. That is, this type of capital can increase the external world’s function as a producer, which implies that the upper limit of green tiles and melds that players can obtain in rounds increases. For example, people apply fertilizers to increase crop yields, etc.

Physical capital 1-3:
Such capital, which can increase the external world’s function as a decomposer, represents garbage disposal facilities, etc.

Physical capital 2:
Such capital can decrease the number of units of bread required for Action 2. Equipment such as mining machines for iron-ore mining, etc. constitute this type of capital. By using mining machines, the amount of time required for work can be reduced by half. That is, one person can do the work of two.

Physical capital 3-1:
Such capital can decrease the number of units of bread required for Action 3 and includes trucks that transports goods, etc.

Physical capital 3-2:
Such capital can extend the negotiation time available for Action 3, and as such, it represents the reduction in time required to convey important information via technologies, such as the telephone, etc.

Physical capital 4:
Such capital decreases the number of units of bread required for Action 4.Tools, such as a saw, that allow people to produce chairs more easily represent this type of capital etc.

Physical capital 5:
Such capital can decrease the number of units of bread required for Action 5 and is represented by tools, such as forks and knives, which allow people to eat food more easily.

Physical capital 6:
Such capital can decrease the number of units of bread required for Action 6 and includes tools, such as screwdrivers, that allow people to assemble and disassemble items more efficiently.

Physical capital 7:
Such capital can decrease the number of units of bread required for Action 7 or improves the probability of obtaining cards from the dealer. This type of capital includes the enhanced human capital produced by schools and research facilities.

Produced melds lose effectiveness after a certain number of rounds (that is, they possess expiration dates). After the expiration date, green melds are discarded and black melds automatically become spent black melds. Each player strategically consumes or exchanges melds for points before the expiration date. Melds for ingredients and physical capital can also be used or exchanged before the expiration date. Chips do not expire. Acquiring points represents the satisfaction of their desires. The number of points acquired from consuming a meld for points depends on the points-melds table, which varies for each player. This variation reflects that the value of goods varies by individual. The points-melds tables, which are dealt at the beginning of the game, define the points that correspond to a meld. Additionally, the value of the table changes depending on the round and the situation with which a player is confronted. For example, when a player consumes a chair, X points are acquired. However, when he or she consumes 3 chairs, fewer than 3X points are acquired (according to the law of diminishing marginal utility). As more chairs are consumed, the value of the chairs approaches zero and no points are acquired as the need for chairs has been met. If needs are repeatedly met, all of the values of the melds approach zero. While steadiness-oriented players aim to achieve this situation, the situation can never persist because after completing additional rounds, the point values will increase again. Completing successive rounds represents the passage of time. It is also possible that, for example, clothes, which were valued at 15 points during the 5 previous rounds, are now valued at 10 points, thus representing a change in fashions. Players strategically value tiles, melds, chips, and cards that are kept on hand. Players also find value in the wall and in trusting relationships with other players that cannot be kept on hand. Consuming melds for points meets short-term demands (needs), while other valuable resources meet long-term demands. Because these valuable resources can change into points as a long-term strategy, the desire of growth-oriented players for these resources is infinite, even when needs are met.

1.5 Production and energy

When players take Action 4, they must play by following certain rules. The number produced by subtracting 1 from the total number of tiles in a meld is the “bond number” of that meld. For example, when a player arranges the chair, which consists of four tiles in a row, the number of gaps between tiles is 3. In other words, the bond number of the chair is 3. The bond number of bread is 1. As the ingredients of a chair are two C tiles, two H tiles, and five units of bread, the total bond number of the ingredients is 5.

Rule: The bond number of the melds (3) is less than the bond number of the total bond number of the ingredients (5).

If a player possesses physical capital, such as a saw, the number of units of bread required to produce a chair decreases from 5 to 4. This rule cannot be violated regardless of the physical capital and cards that players possess. The bond number represents the Gibbs free energy stored in matter, a rule that represents the decrease in Gibbs free energy in closed, isothermal, and isobaric systems, that is, the second law of thermodynamics. In other words, a player cannot usually increase the bond number in isolation. However, if players possess natural energy power plants or batteries (types of physical capital), they can increase the bond number without the external world. When a player produces a natural energy power plant, the player must place it beside the wall. The player then produces ten batteries and places them beside the natural energy power plant. As a result, the ten batteries are linked and the bond number increases by 9 as the batteries are charging. The natural energy power plant is produced by the players, and the battery charging is produced by the external world. A natural energy power plant represents solar panels, wind plants, hydropower plants, etc. There are three ways to increase the bond number:
(1) Mine green melds, which are produced by the external world
(2) Obtain bound melds by exchanging with other players
(3) Charge batteries
Because oil (a non-renewable green meld) consists of 11 bound green tiles, its bond number is ten. Because oil has a large bond number, the players treat it as being important on strategic grounds.

1.6 Cards

Obtaining cards represents innovation. When a player exchanges cards, the player can exchange copied cards (not the original cards) to the trading partner. This ability represents the spread of technologies and ideas as these do not physically move. Cards have no expiration dates. Therefore, once a player obtains cards, they remain in force. Cards are divided into categories according to their effects.

Card 1-1:
This card can decrease the number of units of bread required for Action 1. For example, with knowledge of where mushrooms often grow, it is easier to seek mushrooms.

Card 1-2:
This card can increase the quantity of the green tiles and melds the dealer places into the wall. For example, knowledge of the most effective season to sow seeds can increase crop yields.

Card 1-3:
This card can increase the ability of the external world to function as a decomposer. For example, knowledge of where garbage should be buried can increase the decomposition rate.

Card 2:
This card can decrease the number of units of bread required for Action 2. For example, knowledge of iron ore mining increases the efficiency of such mining.

Card 3-1:
This card can decrease the number of units of bread required for Action 3. For example, knowledge of optimal transportation routes can decrease transport time.

Card 3-2:
This card can extend the negotiation time available for Action 3. For example, if this technology is the Internet, such time can be extended.

Card 4-1:
This card can decrease the number of units of bread required for Action 4. For example, it represents a method of assembling a chair more efficiently.

Card 4-2:
This card can decrease the required ingredients, except for bread. For example, a plow is produced from three Fe tiles, one Cu tile, and two C tiles at the beginning of the game; however, with the card, a plow can be produced from two Fe tiles, one Cu tile, and two C tiles. Moreover, as the effects of the plow do not change, it represents methods of reducing material costs without causing deterioration in functions.

Card 4-3:
This card can make it possible to produce new melds. For example, each player cannot produce a truck (a type of physical capital) at the beginning of the game; however, when a player obtains a truck card (a creation card) by Action 7, that player can produce a truck any time after the next round. This represents the invention of the automobile. The number of melds that a player can produce coincides with the number of the creation cards the player obtains. Players possess some creation cards at the beginning of the game.

Card 5:
This card can decrease the number of units of bread required for Action 5. For example, this can represent the knowledge required to produce a fan.

Card 6:
This card can decrease the number of units of bread required for Action 6. This represents the knowledge of disassembly procedures.

Card 7:
This card can decrease the number of units of bread required for Action 7, or it can improve the probability of obtaining cards from the dealer. This represents educational advances.

1.7 Resource depletion and whistle

The state of the wall is now explained in detail. The green tiles, green melds, and black tiles are stacked separately. Some tiles and melds are directly visible to players, while the rest are hidden below an opaque sheet. When a player sees bread in the wall, the player can draw bread for Action 1. Players may not draw tiles and melds below the sheet. As the player draws, the dealer gradually removes the sheet and reveals additional details about the wall. As non-renewable green melds and black tiles are exhausted after some rounds, players try to predict the time of the depletion, though they do not know the period. After some rounds, the dealer can blow a whistle. The whistle is the harbinger of depletion and signals to the players that the remaining non-renewable green melds and black tiles are scarce. This represents the situation that resources will be exhausted and that predicting the depletion period is difficult. The green tiles and renewable green melds continue to be returned to walls after the whistle.

1.8 War

Each player can begin a war by discarding bread and designating a player with whom to fight. Winning or losing the war is decided by the number of weapons (a meld) in the players’ hands. When the difference in the number of weapons is greater than ten times, the player with many weapons steals the tiles and cards of the player with few weapons. The game is then over for the player with fewer weapons (that is, the player died in the war). When the difference in the number of weapons is not more than ten times, nothing happens. Weapons are calculated by the meld for war, which has a large bond number. Accordingly, each player must use many resources to produce a weapon.

1.9 Contracts

Players can create a unique rule by negotiating with each other. The negotiation time is the time for Action 3. This unique rule is a contract, which represents a law, promise, etc. Players can contract between two or more players. To rescind a contract unilaterally, players must consider the risk of breaching the contract. Herein, to reduce the complexity of the game, we assume that players cannot rescind a contract unilaterally.

1.10 Ethical principles and laws

Before beginning the game, all players discuss the desirable state of the table and create consensus, which is known as the ethical principle. The ethical principle primarily represents a constitution, natural law, ethics, religion, etc. For example, if avoid dying of starvation is established as an ethical principle, the game will advance by assisting one another. If progress of individual freedom is established as an ethical principle, the game will advance through self-responsibility. When players discuss the ethical principle, they do not know the conditions of the environment (tiles, cards, chips in hands, walls) that will be received. This situation represents the original position as elaborated by John Rawls. Therefore, the content of the ethical principle may be risk-averse or risk-attractive. Nonetheless, players must establish an ethical principle to achieve the objective of the game.
Next, all players must discuss the specific measures required to achieve an ethical principle and then make a contract with each other. This special contract is called a law, which represents the embodiment of spirit of the constituent by enacting a positive law. For example, if avoid dying of starvation is established as an ethical principle, the players need a law that specifies when, whom, and how to support players. If progress of individual freedom is established as an ethical principle, the players may require a minimum risk-averse law or no laws at all. The direction and number of laws will vary depending on the ethical principle selected and the players. Accordingly, the behavioral patterns of players vary depending on the laws. Players can also discuss the possibility/impossibility and manner of changing ethical principles and laws.

The preceding discussion represents the formulation of an ecological game. While many aspects of this game remain undefined, we can develop a strategy for the defined aspects. We contend that this level of accuracy is appropriate.

2. The strategy of the game

The rules of the game constructed in section 1 represent important ecological laws and social systems. In section 2, we consider the strategic choices that players will be most inclined to make. There are action strategies, contract strategies, ethical principal strategies, etc. Strategies vary between growth-oriented players and steadiness-oriented players.

2.1 The strategy for starvation and war

During early stages of the game, both growth-oriented players and steadiness-oriented players likely behave similarly. The foremost priorities are to avoid dying of starvation and dying in a war. To that end, players decide on an action, negotiate a contract, and establish an ethical principle. To avoid dying of starvation, players must prevent a shortage of bread. To avoid dying in a war, players must either acquire many weapons or agree on a peace contract. As the game progresses, strategies begin to vary between growth-oriented players and steadiness-oriented players. Players should consider creation cards. Growth-oriented players continue to acquire creation cards, create new needs, and acquire points. Conversely, once steadiness-oriented players meet all needs, they have no intention of obtaining creation cards and creating new needs. However, players who have a considerable amount of physical capital and many cards do have an advantage over a player without such capital with respect to obtaining weapons. Therefore, when steadiness-oriented players are at risk for war, they focus on acquiring creation cards. In other words, steadiness-oriented players are also oriented toward growth to avoid dying in a war.

2.2 Ethical principles and redistribution

There are two principles upon which every player likely agrees. The game is equal, and certain efforts are rewarded. There are two ways to realize an equal game. One is equality of opportunity and the other is equality of outcome. It is difficult to achieve absolute equality of opportunity at the beginning of the game because the wall is an immovable object and players cannot predict the dealer’s actions. Therefore, players may intend to redistribute valuable resources to achieve equality of outcome. Herein, the redistribution strategy with respect to the when, whom, and how to support players is detailed. As the game progresses, the average number of acquired points in a round usually increases (growth) because players often receive or obtain physical capital and cards. The growth of the player usually results in even further growth of the player, and thus, the gap between and among players widens. The more the players redistribute their capital and their cards, the more equality is promoted. However, the incentive to expend effort is decreased. A player cannot view other players’ values on the points-melds table. Therefore, a player can only infer others’ values on the table from the maximum number of chips that a player is willing to pay to obtain a resource (willingness to pay). We call a player’s willingness to pay for all of the acquired resources in a round, the utility in a round. It is difficult to estimate the exact value of utility. We call the total of all players’ utility in a round the total utility of a round. Both chips and utility are represented in the same unit. Redistribution may raise total utility in the present round, while distorting players’ incentives. Therefore, this redistribution may lower the total utility in future rounds. When players discuss the ethical principle, they may face this trade-off. All of the goods have market prices at which they are currently trading for chips in the market. All of the tiles and melds that are drawn or produced in a round by all players are converted into market prices (GDP in the round).
Generally, a rise in the GDP raises total utility and increases poor circulation. Generally, redistribution raises total utility in the present round without a change in the GDP in the present round. This redistribution also distorts players’ incentives with a decrease in the GDP in future rounds. The descending order of long-term value is as follows: cards; melds for physical capital; melds for ingredients, tiles, breads; and melds for points. Chips have both long-term and short-term values. Generally, valuable resources are redistributed from winning players to losing players.
Three examples of ethical principle are as follows: utilitarianism, liberalism, and libertarianism. However, these principles do not necessarily represent the political philosophy that bears the same name in the real world. To establish an ethical principle is similar to obtaining social insurance aimed at protecting people against the risk of adverse events. Without any social insurance, the game represents a chronically unequal society.

1. Utilitarianism is the ethical principle for which players aim to maximize total utility. Players may have to balance the gains from greater equality against the losses from distorted incentives. When the efforts of losing players are not rewarded, more redistribution may be needed. When losing players are lazy, less redistribution may be needed. When the efforts of winning players are not rewarded, redistributed resources may be changed to capital or items with long-term value. These changes in capital or items, however, must be negotiated and established by law. In this game, there is no way to measure the success and failure of the law.

2. Liberalism is the ethical principle whereby players aim for the maximization of the utility of the lowest utility player.

3. Libertarianism is the ethical principle whereby players aim for the absolute equality of opportunity. The wall is an immovable object, and the players cannot predict the dealer’s action. Therefore, players may establish laws that confer some tiles and chips on players who have a poor wall at the beginning of the game. Players intend to maximize incentives with minimum redistribution.

2.3 Poor circulation and Environmental issues

Let us consider a strategy for poor circulation. What ethical principle and laws are required? If players had substantial information about limit value and the damage caused by poor circulation, a perpetrator should compensate a victim for the damage. However, players do not know the detailed rules of poor circulation. Players usually find out about poor circulation by observing decreases in renewable green melds. Some cards provide information about limit value and the damage to a player (rule cards, these cards are not included in cards 1 to 7). Rule cards provide reliable information about the stochastically uncertain external world. Thus, when poor circulation is recognized, players likely adopt Action 7 to get rule cards as they intend to produce a compensation system. However, it is difficult to produce a compensation system when a rule card is not found.
When players produce a compensation system, players may question whether compensation is effective retroactively before finding the cause. Before finding the cause, once a player depends heavily on meld A, he or she likely denies any responsibility for A, causing players to likely lay blame on each other for the cause. Therefore, it is important that players produce a compensation system for A before someone depends heavily on A. To avoid dispute about poor circulation, the ethical principle may be changed, as below, in the beginning of the game. "Each player must take great responsibility for all of one's melds retroactively before finding the cause. Therefore, players record the number of retained spent black melds and discarded green tiles and melds for compensation."
The two types of poor circulation are violence and environmental issues. Violence is the poor circulation wherein the perpetrator, victim, and extent of damage are apparent. An environmental issue is the poor circulation wherein the perpetrator, victim, and extent of damage are not evident. While it is easy to produce a compensation system for violence, it is difficult as an environmental issue.

2.4 Strategy for whistle and recycling

Recycling is the strategy by which a player decomposes spent black melds and reuses decomposed black tiles. The following constitutes the recycling of a car (one of the melds for points). The car production factory (one of the melds for physical capital 4) and the car decomposition factory (one of melds for physical capital 6) are, respectively, necessary for car production and decomposition. We assume that, for simplicity, one car is produced and decomposed with the help of one car production factory and one car decomposition factory. With a car production factory, the ingredients of a car can be thirty Fe tiles, thirty oil (non-renewable green melds), ten fur (one of which is renewable green melds), and five units of bread. The ingredients of a car production factory are twenty Fe tiles, twenty oil, ten wood (one of which is renewable green melds), and four units of bread. The ingredients of a car decomposition factory are fifteen Fe tiles, fifteen oil, ten wood, and three units of bread. Should a player select the recycling strategy after the consumption of a car? If a car is decomposed, a player can recovery thirty Fe tiles in exchange for fifteen Fe tiles, fifteen oil, ten wood, and three units of bread. The player must weigh the costs against the benefits. Usually, there are three ways to obtain Fe tiles, and players select best way.
(1) Draw from the wall
(2) Exchange
(3) Recycle (decompose)
However, after the whistle and Fe depletion, players cannot select the way (1).

2.5 Value theory

In this game, value is defined as that which helps players achieve the objective of the game. Bread is often scarce during the early stage of the game. Therefore, the number of units of bread that players discard with actions is valuable. This number represents labor, and therefore, it determines price at that time. Accordingly, this represents the labor theory of value. When the bond number is scarce, it may become value and determine price. This represents the energy theory of value. However, the points-melds table makes a strong contribution to value. This represents the subjective theory of value. In poker games in the real world, there is no card that is valuable in every situation because the winner is determined by combinations of the cards. Similarly, in this game, there is no invariant unit of measure for value as labor as proposed by Adam Smith.

2.6 Innovation

There are three types of terms. Middle-term is the term in which each player’s points in a round are approximately stable. Short-term is the term in which the stochastic variation of players’ points in a round is apparent. Long-term is the term in which each player obtains some cards, etc. and grows to acquire more points (innovation). Innovations are as follows.
The first is to obtain cards (cards 1 to 7, rule cards).
The second is to obtain physical capital.
The third is to obtain new valuable information about players’ conditions during a negotiation time.
Innovations can be categorized into six types according to their results.

Innovation A: Decrease the number of units of bread required for action
Innovation B-1: Increase the external world’s function as a producer
Innovation B-2: Increase the external world’s function as a decomposer
Innovation C: Decrease the required ingredients, except for bread
Innovation D: Obtain new information about players’ conditions, or obtain rule cards
Innovation E: Obtain creation cards

Which innovation is the best strategy? Innovations may bring winners and losers. By law, winners may compensate losers. It is important to note that some players’ points may be reduced as a result of innovation. Even a player who develops innovations (innovator) may acquire fewer points because of a law, such as a redistribution system, compensation system, etc. Because an innovator should know about such a law, he or she may not try to develop innovations when he or she will lose (hold strategy). Trade protection in the real world is represented by one of the hold strategies. To avoid compensation, players most likely intend to develop a win-win innovation rather than a win-lose innovation. Innovations from A to E can be win-win or win-lose depending on players’ conditions. If an ethical principle that profits from an unequal distribution of information is unfair is established, Innovation D is always promoted. Regardless of the innovation developed by the players, the bond number rule as described previously cannot be violated. Accordingly, while the required ingredients, including bread, can be decreased by innovation A or C, there exists a lower limit. As for innovation B, there is an upper limit to the external world’s function as a producer and a decomposer. This represents the finite nature of an ecosystem. Conversely, there are no limits to the effect of innovations D and E. This game is a representation of the real world with almost infinite information and atomic arrangement. To avoid poor circulation, innovation B-2 and C are probably effective. However, innovation A and B-1 probably increase poor circulation.

2.7 Unemployment

In spite of enough bread, actions sometimes do not lead directly to points (a player has extra action). Furthermore, if the condition worsens, a player acquires no points (unemployment). Growth-oriented players always intend to avoid unemployment. When they face unemployment, they likely invest extra action in Action 7. Steadiness-oriented players do not always intend to avoid unemployment when all of the needs for melds have been met. Unemployment can be categorized into three types according to their cause.

Unemployment 1: Poor circulation or shortage of ingredients, except for bread, causes unemployment. Therefore, unemployment is caused by the smallness of the external world’s function as a producer and a decomposer. However, unemployment can be resolved by innovation B or C.
Unemployment 2: Failure of exchange causes unemployment. Therefore, a lack of information or failure of negotiation is the cause of unemployment. It can be resolved by innovation D.
Unemployment 3: Meeting all needs causes unemployment. It can be resolved by innovation E.

If liberalism is established as an ethical principle, players may intend to avoid unemployment by law because extra action tends to be concentrated on a specific player and the gap between winners and losers widens. At the beginning of the game, players may discuss what is considered an acceptable unemployment rate. To decrease chronic unemployment, decreasing extra action may be important. Players should not develop arbitrary innovation A. However, players should develop innovation B to E to resolve unemployment.

2.8 Discussion and conclusions

To avoid poor circulation and unemployment after the whistle, innovation B-2, C, D, and E are probably more strategic than A and B-1. This is a representation of policy advice in a sustainable world.
Many social systems and ecological rules in the real world are not represented in the game. If the point of equilibrium changes as a result of representing these systems and rules, they should be represented. In this game (the Micro game), players primarily represent individuals. Conversely, we can consider players as representatives of firms, nations, etc. (the Macro game). In the Macro game, in addition to Micro game equipment, players have little dolls (tokens), which represent the population of the nation. Action 8: Control population (the player controls the number of tokens) is added.
In the macro game, players can engage in a greater variety of strategies to deal with poor circulation. Details are our next work.

⇒References



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