Chapter 4 A Game Theory Coopetitive Perspective for Sustainability of Global Feeding:

Agreements Among Vegan and Non-Vegan Food Firms

David Carfì
University of California – Riverside, USA
Alessia Donato
University of Messina, Italy
Dania Panuccio
University of Messina, Italy

ABSTRACT

Throughout this study, the authors propose possible agreements among different food producers, in order to develop a new better conceived diet for the future generations, by using a coopetitive approach and game theory. Specifically, the authors shall consider food producers and sellers of vegan (respectively, vegetarian) and non-vegan (or non-vegetarian) food. The coopetitive approach used by the authors provides a mathematical game theory model, which could help producers of vegan food a simpler entry in the market and free significant publicity. Meanwhile, the model could allow producers of non-vegetarian food a smooth transaction to vegetarian and vegan production. In particular, authors propose an agreement setting among McDonald's and Muscle of Wheat, because they think that Muscle of Wheat cannot enter a global market without the help of a large food producer already in the market. The game theory model represents an asymmetric R&D alliance between McDonald's and Muscle of Wheat.

INTRODUCTION

General Perspective and Objectives

In this chapter, the authors study a game theory model for the sustainability of food production. Specifically, we construct a coopetitive model suggesting general possible alliances among vegan and non-vegan food producers. It is now well known that the meat production has begun non-sustainable, from several points of view. Moreover, the meat consumption reveals linked with heart strokes, cancers, diabetes and several other diseases. Indeed, affluent citizens in middle-income and low-income countries are adopting similar high-meat diets and experiencing increased rates of those chronic diseases. The industrial agricultural system (nowadays, the predominant form of agriculture in the USA and increasingly world-wide) - required for the meat and dairy production - determines consequences for public health, owing to:

• Its extensive use of fertilizers and pesticides;
• Strongly unsustainable use of resources (such as water and fertile soil);
• High environmental pollution.

Moreover, in industrial animal production, we emphasize the strong public health concerns for feed formulations, including animal tissues, arsenic and antibiotics. We underline also the strong concerns for the induced laborer health risks - coming from such unsustainable work - and also for the consequent related health hazards regarding the communities living close to the meat production factories.

A Game Theory Approach

We shall consider possible agreements among different food producers, in order to develop a new better conceived diet for the future generations, by using a coopetitive approach and game theory. Our coopetitive approach provides a mathematical game theory model, which could help producers of vegan food a simpler entry in the market and free significant publicity. Meanwhile, our model could allow producers of non-vegetarian food a smooth transaction to vegetarian and vegan production.

Economic Perspective

Everywhere, during the last years, the industry is taking increasingly more note of the evident circumstance that vegetarians and vegans worlds represent a very attractive economic target. Nowadays, indeed, the major brands of the food industry are trying to create more space for themselves in a food market increasingly less niche and continuously widening.

Vegan Consumption in Europe

In Europe, the “average” consumer shows an increasing interest for alternative foods with respect to meat and dairy products: it is evident the gradual growth in sales of products based on soy, almonds, coconuts, legumes, seeds, beans and other noble vegetables - coming from, also, a thorough marketing campaign which in recent years has extolled the virtues of the legumes health benefits (see Seclì, 2007).

BACKGROUND

Literature Reviews on Food Production

In this section we present, by citing some relevant sentences, some of the literature we used for the construction of our ideas about the sustainability of food production.

Problems with Meat Production

In an article of 2005 written by Walker, Rhubart-Berg, McKenzie, Kelling, and Lawrence, we read: “We live in a world of contradictions, where one billion people are overweight or obese and another one billion lack adequate food resources, despite the fact that current world food production could feed the 6.3 billion people on Earth (now 7.5 billion people), if distributed equitably and based on a diet with only moderate amounts of animal products Animal products, however, are the primary source of saturated fat responsible for higher risk of cardiovascular disease, diabetes mellitus and some cancers. Meat itself is also associated with increased risk of some cancers. An important public health challenge is to provide adequate amounts of protein and essential nutrients without also causing over-consumption of saturated fat” (see Walker et al., 2005).

Costs of Non-Vegan Food Production

Consider the following data about the costs of meat production as reported by Fiala (2008): “Current production processes for meat products have been shown to have a significant impact on the environment, accounting for between 15% and 24% of current greenhouse gas emissions. Meat consumption has been increasing at a fantastic rate and is likely to continue to do so into the future” (see Fiala, 2008).

Moreover, in Nguyen, Hermansen, and Mogensen (n.d.), we read: “The environmental costs of meat are displayed as characterized results at different midpoint categories e.g. global warming, nature occupation, acidification, eutrophication, ecotoxicity, etc.

In decreasing order of importance, nature occupation has been found to be the main contributor to the costs (55%), followed by global warming (21%) and respiratory inorganics (18%).

A breakdown of the external costs into three damage categories shows that impacts on ecosystems obtain high importance with 80% contribution to the costs whereas impacts on human well-being and impacts on resource productivity carry relatively low importance with 15% and 5% contribution, respectively.

Approximately 75.4% of the environmental costs of pig meat production is related to feed production and the remaining is distributed among the other sub processes, “emissions from housing and manure storage”, “manure utilization for crop fertilization”, “feed transport and direct energy use” by 16.3%, 3.2%, 3.7% and 1.2% respectively.

As for the detailed information about on which part (or component) of the pig meat life cycle, the highest load of different environmental impacts occurs or the largest potential for improvements lies, Figure 1 summarizes the results of such analysis”.

For a deeper study you can read Nguyen et al. (n.d.).

Figure 1. Breakdown of contributing sub-processes and contributing impact categories

Source: Nguyen et al., n.d.

Meat and Sustainability: Data of the Consumption of Meat in the World

Recent data, however, show that in the US, with a population of 316 million in habitants, but also in other European countries, the consumption of animal products is decreasing: 6% between 2006 and 2010. Aided by the economic downturn, but even healthier lifestyles, responsible and sustainable - for example, is increasing in the number of vegetarians or vegans. Western countries are slightly changing their eating habits or keeping them less stable. Other countries see their meat consumption increase, i.e., very large and densely populated countries experiencing a period of strong economic growth. They are the BRICS countries (Brazil, Russia, India, China, South Africa) (see Figure 2).

Figure 2. Estimated consumption of meat for person in kilograms in 2010-12, and forecast in 2022

Source: Böll-Stiftung (2014, pp. 49)

What the W.H.O. Said on Meat

Epidemiological studies suggest that increases in the risk of several cancers are associated with high consumption of red meat or processed meat. These risks are very important for public health because many people worldwide eat meat and meat consumption is increasing in low- and middle - income countries (See Figure 3).

Figure 3. Worldwide Annual Meat Consumption per capita - Source: ChartsBin (2009)

A group of 22 international experts, from 10 countries, examined more than 800 different studies on cancer in humans, and summarized the data in a document of IARC, the International Agency for Research on Cancer. Red meat was classified as “Group 2A - probably carcinogenic to humans”, and processed meat was classified as “Group 1 - carcinogenic to humans”. Processed meat has been classified in the same category as causes of cancer such as tobacco smoking and asbestos (IARC Group 1, carcinogenic to humans i.e. there is sufficient evidence of carcinogenicity in humans from epidemiological studies). The IARC classifications describe the strength of the scientific evidence about an agent being a cause of cancer, rather than assessing the level of risk. An analysis of data from 10 studies estimated that every 50 gram portion of processed meat and every 100 gram portion of red meat, eaten daily, increases the risk of colorectal cancer by about 18% and 17% respectively, if the association of red meat and colorectal cancer were proven to be causal (see WHO, 2015).

Why is Meat and Dairy So Bad for The Environment?

On The Vegan Society (n.d.) we read: “The production of meat and other animal products places a heavy burden on the environment - from crops and water required to feed the animals, to the transport and other processes involved from farm to fork. The vast amount of grain feed required for meat production is a significant contributor to deforestation, habitat loss and species extinction. In Brazil alone, the equivalent of 5.6 million acres of land is used to grow soya beans for animals in Europe. This land contributes to developing world malnutrition by driving impoverished populations to grow cash crops for animal feed, rather than food for themselves. On the other hand, considerably lower quantities of crops and water are required to sustain a vegan diet, making the switch to veganism one of the easiest, most enjoyable and most effective ways to reduce our impact on the environment” (see The Vegan Society, n.d.).

Leitzmann (2014) writes: “The future of vegetarian nutrition is promising because sustainable nutrition is crucial for the well-being of humankind. An increasing number of people do not want animals to suffer nor do they want climate change; they want to avoid preventable diseases and to secure a livable future for generations to come” (see Leitzmann, 2014).

Readings About Sustainability

In this chapter we used several additional by bibliography and sitography about sustainable food succeed: Gourmandelle (2015), Vegan Outreach (2014), MacMillan (n.d.), Universo Vegano (n.d.), Turnbull (2015), One Green Planet (n.d.), Knutson (n.d.), Gavin (2014), Vegan Starter Kit (n.d.), Messina (2010), Vegans of Color (2009), Staying Vegan (2010), Pimentel, D. and Pimentel, M. (2003), Wheeler (2015), Boston University (n.d.), Thomas (n.d.), Wick (2011), National Sustainable Sales (n.d.), AMP (n.d), Albanesi (2013), Lugano (2012), AdnKronos (2015), Oscar Green (2015), Veganblog (2015), Dutto (2015), Sclaunich (2015), Sacchi Hunter (n.d.), Etica Vegana (2016), Zanni (2013), Animalvibe (2015), Fiala (2008), Four Seasons Natura e Cultura (n.d.), Worldwatch Institute (2004), Whole Foods market (n.d.), Petroff (2015), Giambarrresi (2013), Leitzmann (2003), The Vegetarian Resource Group (n.d.), Shanker (2015), Mingolia (2015), Lusk and Bailey Norwood (2007), Mission 2015 (n.d.), Four Seasons Natura e Cultura (n.d.), Saint Louis (2015), Kjaernes, 2010.

Food Sustainability

Food sustainability implies several aspects, already considered widely in literature, for example (see Figure 4):

• Impact of production and distribution on the environment in terms of the use of land and resources, pollution and emissions, genetic diversity.
• Consequences on the external environment in health hazards and in the satisfaction of basic needs.

Figure 4. Sustainable development - Source: Drolc (2013)

Why Go Vegan?

In this section we shall consider some common motivations to go vegan.

• For Your Health: Increased energy, younger looking skin due to diets rich in protein, iron, calcium and other essential vitamins and minerals, high in fiber and packed with antioxidants, helping mitigate some of the modern world's biggest health issues like obesity, heart disease, diabetes and cancer.
• For the Animals: Because no animal is killed, abused and exploited for the preparation of a vegan meal (it does not include any animal products, even eggs, dairy products, milk, cheese, honey).
• For the Environment: Because eating vegan means less impact on the resources of our planet, less energy consumption, less water consumption, less pesticides adoption, less pollutants dispersion, less need for land and therefore less deforestation. Moreover a plant-based diet requires only one third of the land needed to support a meat and dairy diet.
• For Those Who Are Dying of Hunger: Because if we ate vegan food there would be more than enough for everyone (the land used to feed one person who eats meat would be enough to feed well 20 vegans)

(see The Vegan Society, n.d.).

Vegan Diet and Impact on the Territory

The vegan diet is clearly different than in vegetarian and omnivorous because it does not provide any form of intensive animal husbandry, truly responsible for the large consumption of resources caused by the major diets common in the West. Those practicing vegan chooses to minimize the burden on the company due to the chain of transformation of raw materials into food on our tables.

The calculation of the natural resource consumption for meat production is expressed taking into account the energy required for the collection of raw materials, the environmental costs of transportation of animals, the washing of animals, the animal feed and environmental costs also due to distribution. In assessing the impact of different diets on the environment, it does not come into play only quantitative assessments:

• Opting for vegan will also limit the impact in terms of greenhouse food production;
• It is in fact demonstrated how animal breeding on a large scale, especially if aimed at the production of beef, dries up the soil and promotes the destruction of wetlands as forests to pasture land;
• Feeding vegan, on the contrary, easier uses raw materials at 0 km;
• Vegan recipes use organic ingredients, which do not require for their production the adoption of chemicals or genetically modified organisms;
• Even vegetarian feeding, contemplates egg consumption, which poses sustainability problems in establishments where poultry is exploited industrially.

(see Non solo Vegan, 2014).

Case Study: The “Muscle of Wheat”

We will analyze the case of the “Muscle of wheat”, a food created by the Italian-Calabrese Enzo Marascio, from high quality agricultural product of his land.

It is a real evolution in the food industry, because it shows a nutrient value similar to that of meat, while it results totally vegetable. Wheat and pulses reveal the basic ingredients and make the muscle of wheat more complete than seitan, soy and tofu. It represents a good substitute for those who decide to limit or abolish the own consumption of meat and fish, by following a diet free of dangerous animal fat and cholesterol.

Thanks to a special processing and fermentation, a mixture of wheat flour and pulses it assumes a consistency surprisingly similar to that of meat. Marascio is able to reproduce, with this new raw material - from himself named “Muscle of wheat”, given his impressive consistency - many traditional plates of meat, such as dried beef, some salami, roast beef, etc (see Figure 5, Figure 6, Figure 7).

There seems to exist a big difference between the invention of Marascio and substitutes meat more known and consumed by vegans, like seitan, tempeh, soy steaks. While the latter are derived from a de-structuring of the raw material used, Muscle of wheat develops exclusively on the basis of a dough, without the intervention of artificial modifications of the basic molecules. Moreover, this new product gains a specificity from legumes and cereals put together, not from a major modification of a single raw material: for this reason, the nutrient profile of the muscle of wheat is better.

Muscle wheat has undergone numerous surveys: in particular, in 1992 was analyzed by Prof. Fernando Tateo of the University of Milan and, surprisingly, turned out to be a food very particular: it contains, in fact, 20 amino acids, including the essential 7 amino-acids from 8, is composed of a type of protein which is not found either in the derivative of soy or in food of animal origins. It contains no fat, nor cholesterol - if we except the good cholesterol of extra virgin olive oil - or carbohydrates, resulting therefore be an ideal food for diabetic and celiac people, despite coming from grain.

According to many tasters, the taste of Muscle of Wheat is strikingly similar to that of meat.

Marascio found, proportionally, a greater interest from people out of the universe of vegetarians and vegans, because very often these individuals react with surprise, admitting the goodness of food consisting exclusively on vegetable.

The invention of Marascio is truly innovative, the traditional dishes may be reformulated without significant changes, as it is not the case with traditional seitan, tempeh, soy nuggets, tofu, that frequently require an additional food that gives them flavor. In addition, this food is not derived from soy beans, whose massive use, especially by some vegans, is currently the subject of frequent discussions, but from veggie products traditionally adopted in Italy - in particular, the grain used to produce “Muscle of Wheat” belongs to the “cultivar Senatore Cappelli”, renowned for its nutritional qualities (see Seclì, 2007).

Figure 5. Image of Muscle of Wheat dish: “arrosto con verdure”

Source: Muscolo di Grano (n.d.)

Figure 6. Image of Muscle of Wheat dish: “Muscolo di Grano alla Pizzaiola”

Source: Muscolo di Grano (n.d.)

Figure 7. Image of Muscle of Wheat dish: roast beef

Source: Muscolo di Grano (n.d.)

Muscle of Wheat Wins the Oscar Green Prize at Expo Milan 2015

Muscle of Wheat wins the first prize in the category WeGreen in the occasion of the national competition Oscar Green at Expo Milan, in Italy, as the best and original truly innovative food (see Figure 8, Figure 9). The victory of Muscle of Wheat represents an historical steps towards the production of eco-sustainable food, because it stimulates world's attention upon a product that will solve many problems, both ethical and healthy, for generations to come. The population is increasing exponentially and consequently, to meet the protein need, we see an unsustainable adoption of intensive farming, at the expense, of course, of the quality and ethical issues. Intensive farming goes against nature, by modifying the natural cycles of growth of animals, all with the addition of hormones that, as a result, we assimilate by feeding. Muscle of wheat, contains all the necessary proteins, right calories, zero carbohydrates and zero saturated fat, does not intend to eliminate meat, but stands as an alternative food, at least in the days that you want to save a bit your body, and especially our liver (see Napolitano, 2015).

Figure 8. Muscle of Wheat wins Oscar Green 2015

Source: Oscar Green (2015)

Figure 9. Muscle of Wheat wins Oscar Green 2015

Source: Napolitano, U. (2015)

MAIN FOCUS OF THE CHAPTER

In this chapter the authors propose the possible agreement among a large globalized food producer and Muscle of Wheat. We think that Muscle of Wheat cannot enter a global market without the help of a large food producer already in the market, for example like McDonald's or other globalized food chains. At this aim, we propose a game theory model based on a coopetitive reasoning, representing a possible asymmetric R&D alliance between two subjects: McDonald's and Muscle of Wheat. This asymmetric alliance will benefit different players in the game, Muscle of Wheat will enter a globalized market and export its production worldwide, McDonald's will gain another part of the global food market and society will gain from health improvement.

The Economic Model

Assumption 1: The authors assume that, to achieve its goals, McDonald’s, our 1^st player, is forming horizontal alliances (that is food-food alliances), instead of producing new innovative food, with the small (but research-oriented and highly efficient) Muscle of wheat firm, our 2^nd player.
Assumption 2: The Muscle of wheat firm (2^nd player) is engaged in the discovery eco-sustainable development, creation of new food produced entirely from eco-sustainable sources.
Assumption 3: To cope with global competitive pressures, McDonald’s is allying in triad with another mid-size or small-size food firm (our Muscle of wheat) and with a venture capitalist (let us call VC or Cap), our 4^th player (which we won’t consider one of our principal players, because of its elementary actions and simple payoffs) in order to spin out a new food development program into a new renewable joint venture firm (the authors call RJV, research joint venture), our 3^rdplayer.

Semi-Quantitative Description of the Payoffs

At the end of this R&D alliance, the benefits for the three partners can be summarized as follows:

• McDonald’s buys a certain amount x of food from RJV and gains from the selling of the product x on the Market;
• Muscle of wheat firm produces a bi-quantity z = (z₁, z₂) of a new 100% safe and eco-sustainable food; MW gains by selling a quantity z₁ to RJV and a quantity z₂ on the Market;
• RJV gains by selling x of the Muscle of wheat production to McDonald’s and z₁ - x of the food on the Market;
• Cap receives from McDonald’s (at time 2) the capitalization k' of its initial investment k (money given to McDonald’s at time 1);
• Market/Italy gains from the sunk costs k of RJV, from the research-costs y of Muscle of wheat and it gains a value b(z₁+z₂) by improving food production and health.

The Formal Construction of the Game Model

Axiom 0: We consider a five-player game.

The players are:

1. McDonald’s (or LF, large firm);
2. Muscle of Wheat (or SF, small firm);
3. the 3^rd player is the RJV (Research Joint Venture) constituted by McDonald’s and MW;
4. VC (venture capitalist);
5. Market.

The authors distinguish between principal players and side players: principal players are LF and SF, side players are RJV, VC and the Market (civil society).

Strategies

Axiom 1 (strategies of the 1^st player): Any real number x represents the production that McDonald’s decides to buy (x in E, compact interval of the positive real semi-line) from the Research Joint Venture founded by McDonald’s and MW.
Axiom 2 (strategies of the 2^nd player): Any real number y represents investments for research and food production (y in F, compact interval of the real line, with first end-point greater or equal to 1) employed by MW, we assume that an investment in research of at least 1 is needed for creating the 100% eco-sustainable food.
Axiom 3 (strategies of the 3^rd player - coopetitive strategies of the first two players): Any vector z = (z₁, z₂), with z in C= C₁×C₂, where C₁ and C₂ are compact intervals of the real line, such that the first end-point of C₁ results greater or equal to the maximum of E, represents the bi-production of MW.

We assume that:

• The vector z is decided together by McDonald’s and MW;
• The RJV buys only the z₁ component of z;
• By convention, the strategy of the third player;
• The vector z represents, equivalently, the coopetitive strategy of the first two players.

In other terms, we shall use the strategy z of the 3^rdplayer as a cooperative strategy of the couple (LF, SF) in a coopetitive game.

Axiom 4 (strategies of the 4^th player): The number k represents the loan that VC decides to offer to the McDonald’s (the strategy set of VC is reduced to the singleton {k}).
Axiom 5 (strategies of the 5^th player): Any couple z represents the coopetitive production branded by RJV that the Market decides to buy: we assume, by classic microeconomic assumption, that this z coincides with the bi-production branded by RJV, decided together by McDonald’s and MW.

Payoffs

Axiom 6: The payoff function of McDonald’s is defined by
f₁(x, y, z) = (p - p')x - k' - ay,

where:

1. px is the profit from selling x at price p in the Market;
2. p'x is the cost to buy x from RJV at price p';
3. k' are the sunk costs faced by McDonald’s itself;
4. ay is the extra-payment to MW for research and development y (a > 1).
- Axiom 7: The payoff function of MW is defined by
  f₂(x,y,z) = p''z₁ + ay - y - F + p''' z₂,

where:

1. p''z₁ is the payment received from RJV selling the product z₁;
2. ay is extra-payment for research y, (with a >1), received from McDonald’s; y is the investment in research;
3. F is the fixed cost to produce energy, this cost is not afforded by RJV, which pay only the variable cost;
4. p'''z₂ is the revenue obtained by selling z₂ in the Market of price p''', with p''<p'''<p.
- Axiom 8: The payoff function of the RJV is defined by
  f₃(x,y,z) = p'x + p(z₁ - x) - cz₁ - p''z₁ -cz₂;

where:

1. p'x is the profit from selling x at price p' to McDonald’s;
2. p(z₁ - x) is the profit from selling z₁ - x at price p > p' on the Market;
3. (z₁+z₂) is the variable cost for the production of (z₁+z₂), faced by MW and paid by RJV;
4. p''z₁ is the payment paid to MW to buy the product z₁, with p > c + p''.
- Axiom 9: The payoff function of VC is defined by
  f₄(x,y,z) = k' - k

where:

1. k' represents the money which 1^st player has to give back to VC;
2. k is the number that represents the loan that VC decides to offer to the McDonald’s.
- Axiom 10: The payoff function of the Market is defined by
  f₅(x,y,z) = - p(z₁ - x) + cz₁ + k - px +y + bz₁+ cz₂ -p'''z₂ + bz₂

where:

1. px is the cost from buying x at price p from LF;
2. p(z₁ - x) is the cost from buying (z₁ - x) at price p from RJV;
3. c(z₁+z₂) is the indirect gain from the production of z, faced by MW and paid by RJV;
4. y is the indirect gain coming from the research activity of MW;
5. k is the indirect gain coming from the foundation of RJV;
6. b(z₁ + z₂) is the social indirect gain (beneficial effects) coming from the use of the quantity z₁ + z₂ of the new sustainable food.

The following Figure 10 shows the formal situation.

Figure 10. Formal representation of the game

Economic Interpretation

Axiom 11: In this model we have three formal players interacting together and one player, the venture capitalist VC, acting only at the beginning of the interaction (time 1) and at its end (time 2).
Axiom 12: We assume that:
- • Our 1^st player is a Large Firm (LF) (in our study case, it is the McDonald’s) that, in order to develop new totally eco-sustainable, decides to form an horizontal alliance with a Small Firm (SF) (in our case, it is the MW), our 2^nd player, operating in the same sector (food production).
- • 1^st and 2^nd player, in order to cooperate, constitute a Research Joint Venture (RJV), our 3^rd player. The RJV is financially supported by the VC, our 4^th player, at the level of initial costs, and it supports SF, at the level of variable costs.
Axiom 13: The 2^nd player produces a quantity z (decided together by 1^st and 2^nd player) of new vegan food and sells a quantity z₁ to the RJV, at price p'' (fixed by contract).

When the research of the RJV of the good (in our case the food) has already begun, then the production of sustainable food is conducted by 2^nd player and the Large Firm decides the amount x of production to buy from the RJV.

Axiom 14: The revenue of LF is given by the difference between the sale price p'x and the purchase price px, of the quantity x of production bought by the RJV at price p'.

To begin the RJV research, the VC offers a financial support k to RJV, to cover the initial sunk costs.

After the cooperative production of 2^nd player is started, the 1^st player pays the capitalized sunk costs k'>k to the RJV, in order to compensate the VC and to conclude the participation of the VC in the game.

Moreover, at the beginning of the RJV, 1^st player funds directly the researches of the small firm SF, by a sum ay, for any investment y in research of the 2^nd player, with a > 1.

Axiom 15: When, cooperatively, 1^st player and 2ⁿ^d has decided the pair z that the 2^nd player has to produce and sell.

Revenues for the 2^nd player are equal to

p''z₁ + p'''z₂,

where:

1. p'' is the unit price at which 2^nd player sells to RJV;
2. z₁ is the quantity of production sold to RJV;
3. p''' is the unit price at which 2^nd player sells to Market;
4. z₂ is the quantity of production sold to the Market.

The cost is represented by the investment for research and is equal to y.

Axiom 16: For the Research Joint Venture revenues are calculated as
p'x + p(z₁ - x) + k

where:

1. p'x is the profit from selling x at price p' to LF;
2. p (z₁ - x) represents the profit from selling (z₁ - x) at price p > p' on the Market;
3. k is a positive constant for the RJV because the sunk costs are paid by the 1^st player.
- Axiom 17: Lastly, the authors assume that the cost cz for the production of z (by the second player) is paid by the RJV and so the costs for the RJV are equal to:
  cz₁+ cz₂ + p''z₁ + k,

where:

1. c(z₁+ z₂) is the cost of z₁+ z₂ (paid by RJV to 2^nd player);
2. p''z₁ is the payment given to the small firm for the product z₁;
3. k is a sunk cost payed by RJV to the Market.

SOLUTIONS AND RECOMMENDATIONS

Once defined numerically the Payoff functions and strategies of the players, we can develop and analyze completely the numerical game and find classic and less classic solutions of the game: from a competitive, cooperative and coopetitive perspectives. As usual, such solutions show specific economic meanings.

Specifically, we suggest to analyze the game following the general lines proposed by David Carfì in his complete analysis of a differentiable game.

Complete analysis of differentiable game consists in the following points of exam:

0a: Classify the game (linear, semi-linear, symmetric, invertible, symmetric in the strategies, ...);
0b: Find the critical zone of the game and its image by f;
0c: Determine the bi-gain space im(f) (image of the function f);
0d: Determine inf and sup of the game and see if they are shadow optima;
0e: Determine the Pareto boundaries of the bi-strategy space and their images by f;
1a: Specify the control of each player upon the boundaries;
1b: Specify the non-cooperative reachability and controllability of the Pareto boundaries;
1c: Find the possible Pareto solutions and crosses;
1d: Find devotion correspondences and devotion equilibria;
1e: Specify the efficiency and non-cooperative reachability of devotion equilibria;
2a: Find best reply correspondences and Nash equilibria;
2b: Study the existence of Nash equilibria (Brouwer and Kakutany);
2c: Evaluate Nash equilibria: non-cooperative reachability, position with respect to and, efficiency, devotion;
2d: Find, if there are, dominant strategies;
2e: Find strict and dominant equilibria, reduce the game by elimination of dominated strategies;
3a: Find conservative values and worst gain functions of the players;
3b: Find conservative strategies and crosses;
3c: Find all the conservative parts of the game (in the bi-strategy and bi-gain spaces);
3d: Find core of the game and conservative knots;
3e: Evaluate Nash equilibria by the core and the conservative bi-value;
4a: Find the worst offensive correspondences and the offensive equilibria;
4b: Specify non-cooperative reachability of the offensive equilibria and their efficiency;
4c: Find the worst offensive strategies of each player and the corresponding gain of the other;
4d: Find the possible dominant offensive strategies;
4e: Confront the possible non-cooperative solutions;
5a: Find the elementary best compromises (Kalai-Smorodinsky solutions) and corresponding bi-gain;
5b: Find the elementary core best compromise and its corresponding bi-gain;
5c: Find the Nash bargaining solutions and corresponding bi-gains;
5d: Find the solutions with closest bi-gains to the shadow minimum;
5e: Find the maximum collective utility solutions;
5f: Confront the possible cooperative solutions;
6a: Study the transferable utility case.

In the present work, we do not analyze completely the game but we propose a complete, general and detailed economic model. For some examples, of similar economic models, completely studied by using the technic of a differentiable game completely analysis, you can find in Baglieri, Carfì and Dagnino (2016a, 2016b, 2012), Carfì and Donato (in press), Carfì and Lanzafame (2013), Carfì and Musolino (2015a, 2015b, 2014a, 2014b, 2013a, 2013b, 2013c, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b), Carfì and Romeo (2015), and Carfì and Schilirò (2014a, 2014b, 2013, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b, 2011c, 2011d).

In particular, we want to emphasize the following solution points:

1. Nash equilibria, those representing the (static non-coopetitive) competitive solution.
2. The purely coopetitive solution: representing the best Nash equilibrium (payoff) of the coopetitive game, or, more correctly, a compromise solution on the Pareto boundary of the coopetitive Nash zone, that is the dynamic trajectory determined by the Nash equilibria during the coopetitive evolution of the game.
3. Super-cooperative solution without the 3^rd player: representing a possible compromise solution determining the maximum collective gain of the first two players without taking into account of the gains of the third player, which (in this case) remain outside the sharing a solution maximizing the collective profit for both players.
4. Super-cooperative solutions with the 3^rd player: representing a possible compromise solution determining the maximum collective gain of the first three players, taking into account of the gains of third player, which (in this case) remain inside the sharing.

Remark

Maximum-collective solutions consists in finding a compromise maximum collective gain solution (if any) and in sharing fairly the corresponding total profit.

The share of collective gains among players can respect the Kalai-Smorodinsky method.

Sharing the maximum collective profit by using a Kalai-Smorodinsky method allows to obtain a win-win solution, in the sense that, our solution will be better than the initial Nash payoff for both players.

FUTURE RESEARCH DIRECTIONS

Future and Emerging Trend

It appears now clear, without any possible doubt, that the world future of feeding goes towards non-meat and non-seafood consumption, essentially because of global environmental issues, linked with a severe climate change and an exponential growing of the current mass extinction. The food production and veggie-products, feasible for that new future feeding scenarios, reveals perfectly matching the Marascio's production of the Muscle of Wheat. Our research and solutions proposal appears perfectly fitting the future scenarios and obliged emerging trends. This consideration provides an insight about the future of the book’s theme from the perspective of the chapter focus.

From an economic point of view, the viability of the proposed paradigm and model is shown by the already employed successful similar R&D alliances in biopharmaceutical industry. The implementation issues of the proposed program might be devised in the difficulties of proposing new feeding habits to an entire society. But, as we explained before, the right way - from an economical, political, health, environmental, ethical and social points of view - appears the road which we traced.

Future Research Opportunities within the Domain of the Topic

Our economic model allows to find easily the optimal transferable utility solutions for the two main participants, when the real data come into the arena. In the future we shall consider numerical models and computer simulations for realistic case, considering also probabilistic scenarios.

As we said above, knowing the data relative to the economic problem, that is:

• Selling prices in the Market,
• Market interest rates,
• Maximum possible quantities of product, which the players can produce and sell,
• The research costs,
• The precise agreements between the two main participants of the game

it becomes possible to analyze and solve the game by calculating all the Carfì's solutions and - among all - those solutions of cooperative nature that give to the main players the optimal solution on a rich Pareto boundary.

We recall two fundamental aspects of our approach:

• First of all, the optimization problem we face is not mono-variate but multivariate, so, in general it does not exist a maximum of the problem but we construct various optimal boundaries, on which we shall find and select special solutions;
• The most convenient of those optimal boundaries could be obtained by a multiple stage cooperation among the main economic players involved in order to adopt a transferable utility approach (examples of such analytical approach could be found in Baglieri, Carfì and Dagnino (2016a, 2016b, 2012), Carfì and Donato (in press), Carfì and Lanzafame (2013), Carfì and Musolino (2015a, 2015b, 2014a, 2014b, 2013a, 2013b, 2013c, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b), Carfì and Romeo (2015), and Carfì and Schilirò (2014a, 2014b, 2013, 2012a, 2012b, 2012c, 2012d, 2012e, 2011a, 2011b, 2011c, 2011d).

Another possible future research consists in the observation that our model allows us to forecast, at the beginning of the game, the future gains in the case of uncertain selling scenarios, that is, we can consider scenarios in which we don't know how much product will be bought by the Market and only a part of the total production is actually sold. We shall introduce parameters indicating what percentages of production is actually sold. Such complete approach could be found in Carfì and Donato (in press).

More, assuming the existence of probability distributions on the space of possible sold production we can calculate the aleatoric variable representing the uncertain gains in function of the selling parameters.

CONCLUSION

In this chapter, we propose a possible coopetitive agreement among a large globalized food producer/seller and Muscle of Wheat, a small, local but strongly innovative healthy food producer of southern Italy.

We think that the small enterprise Muscle of Wheat cannot enter significantly a global market, without the help of a large and famous food producer, already in the global market: for example, McDonald's or other globalized food chains.

On the other hand, we strongly believe that Muscle of Wheat should enter the globalized market because of the quality of its food innovation, which is capable to address global issues such as climate change and even the current mass extinction, human-determined and linked with the extreme soil exploitation, due to all the necessities induced by the meat industry, for the feeding of animals.

Muscle of wheat represents an extremely good alternative to meat and seafood, with optimal healthy features and a minimal environmental impact.

Moreover, McDonald's might see great motivations to change towards the vegan and vegetarian productions, because the world food politics are changing in those directions.

At this aim, we propose a game theory model based on a coopetitive reasoning, representing a possible asymmetric R&D alliance between two subjects: McDonald's and Muscle of Wheat.

This asymmetric alliance will benefit different players in the game:

• Muscle of Wheat will enter a globalized market and export its production worldwide,
• McDonald's will conquer another part of the global food market,
• Society will gain from health (and ethical) improvement.

In this chapter, specifically, we use D. Carfì’s new coopetitive game definition, which considers both collaboration and competition together and simultaneously. Coopetition may advance the understanding and control of asymmetric R&D alliances, those between small (and/or young) firms and large (e.g. Multinational Enterprises).

The results of the mathematical study has proved that we can find more solutions advantageous both for the firms involved for the

• World environment,
• Human healthy,
• Human population sustainability,
• Climate change.

The mathematical solution we propose are:

• Purely coopetitive solutions;
• Super-cooperative solutions without the 3rd player;
• Super-cooperative solutions with the 3rd player;
• Maximum-collective solutions.

Our contribution is twofold:

• Firstly, we have explained the advantages of a vegan diet for the human health, environmental issues, food sustainability, population sustainability and how global food producers could improve environmental, social and health conditions of world population;
• Secondly, we have shown how game theory normal-form and extensive-form games can be used in coopetition studies
- o To increase health conditions of people,
- o To address climate change,
- o To address hunger in the world,
- o To improve welfare in a particular market.

So, we encourage McDonald’s and other large food companies to look more closely at the model to understand that compete with biological and vegan small producers and innovators is not always the right way to “get rich” and to create wealth.

From an Economic point of view, we are sure that the competition is not the right way to have success.

Food enterprises should decide not to “fight” with other small food companies to grab a good share of the market, but they have to cooperate to reach the maximum collective gain, for them and for the social communities. Indeed, it's important, for a world looking to the future, to study what is the best combination of richness for enterprises and welfare for the community and for our planet.

Our study, as it is presented, is fully applicable. It can be surely implemented by other scholars and entrepreneurs interested in the food area, and/or in living conditions of all humans and/or in sustainable food production.

Surely, the model can be improved by widening the points of view, for example by studying not only a particular global food producer and only one innovators, but taking into account entire firm-clusters, by using other innovative vegan food resources, that - during time - could be discovered.

If we want to live all in good conditions, we'll have to be more smart and more “green” to save our life and our future and so we hope that enterprises should think the same to increase world health conditions and welfare.

Nowadays, we also need that McDonald’s and other food companies should use more sustainable vegan food product, in order to use less primary resources; so we're looking to stimulate more interest on these global issues.

This research was previously published in Sustainable Entrepreneurship and Investments in the Green Economy edited by Andrei Jean Vasile and Domenico Nicolò, pages 100-143, copyright year 2017 by Business Science Reference (an imprint of IGI Global).

ACKNOWLEDGMENT

The authors wish to thank two anonymous referees for their precious and stimulating remarks about the work, which help to improve significantly the subject matter and the form of the present chapter.

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