How Can You Apply Game Theory in Politics, Ecology and Sociology?

Game theory is the study of mathematical models of conflict and cooperation between decision-makers. It can apply practically to any situation where people get together and are involved in each other's business. The theory is applicable in different fields, like business, psychology, economics, political science, evolutionary biology, sociology, computer science, etc.

It provides insight into peculiar behavioral interactions and is an umbrella term for the science of logical decision-making in humans, animals, and computers. Mathematician John Nash pioneered game theory in the 1950s. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. This theory can be best explained by the classic example of a prisoner's dilemma.

Game Theory in International Politics

Game theory is a good tool for analyzing the problem of strategy. If properly used, it is likely to increase the success rate of the strategy. In some ways, it provides real solutions to real problems, and real problems are exceptionally difficult to handle within the game matrix. There are three major principles from the model of game theory to apply to empirical or historical data: size, strategy, and disequilibrium.

The size principle suggests that attempts to form a coalition are not aimed at merely enlarging themselves. The size of the coalition is kept as large as the decision-makers believe will ensure winning. This also depends on the information available regarding the various principles of the coalition.

According to the strategic principle, the players keep changing their strategy for the purpose of having the best possible payoff.

The disequilibrium principle suggests that politics is always unstable. In every coalition, there is always an element of instability and disequilibrium.

Each country pursues its own national interests to the greatest extent possible. The key to managing relations with other countries is to be able to tolerate each other. Countries that treat others harshly and refuse to accommodate occasional harm, like the United States, tend to make too many enemies, and eventually suffer serious harm.

The various nation-states in the international system interact in thought-out and strategic ways. Game theory, a discipline that uses strategic frameworks to investigate various conflict scenarios, can be used to evaluate these ways of interacting. Even though game theory analysis scenarios operate in highly idealized and organized environments, they can still provide insight into the strategies used by nation-states to accomplish certain objectives.

In all game theory models, analysts make these assumptions that the players are rational and self-interested, and each actor works to maximize payoff and maintain security. Every state in the international system work hard to maintain their safety, which causes a positive feedback loop. As one state increases its security through defense expenditure or other means, other states feel threatened. This prompts them to strengthen their security and defense posture, and so on.

These assumptions are useful in predicting the future actions of states and are applicable to real-world conflicts. In actual circumstances, nation-states frequently interact with one another over a longer and more recurrent period of time. States are self-interested actors, therefore there is a larger tendency for mutually beneficial interaction, creating a foundation for cooperation.

Through game theory modelling, each state relationship can be broken down into two common games: Bully and Leader.  China and Taiwan and also China and United States are engaged in the adversarial game of Bullying. United States and Taiwan are engaged in the cooperative game of Leader.

In each game theory model, actors play with the intention of utilizing their dominant strategy regardless of what the other does, because it provides a larger payoff. All games have certain payoff structures and give the player two options: cooperate (DC) or defect (DD).

For example, in the Prisoner’s Dilemma, both players have the same payoff structure where they prefer to defect (DC), then mutually cooperate (CC), then mutually defect (DD), leaving the worst outcome to be cooperating while the other defect (CD).

This payoff structure is arranged as DC>CC>DD>CD, and then further simplified where DC is equal to 4, as being the highest payoff, then CC as 3, DD as 2, and CD as 1, since it is the worst option.

In this case, the dominant strategy is to defect, but if both players use that method, then they will get their second-lowest payoff (DD). This could encourage a chance for mutual cooperation (CC) since it has a higher payoff, but it comes at the risk of cooperating while the other defects, consequently leading to the lowest payoff of CD.

There are a variety of games that indicate different situations in international relations. Some are symmetric, meaning players have the same payoff structure as in the Prisoner’s Dilemma, and others are asymmetric, where players have different payoff structures.

Bullying can be used as a prism through which to view the relationship between China and Taiwan. China keeps on undermining political, economic, and military stability in an effort to "bring Taiwan to heel" and this worries Taiwan's foreign minister. Taiwan is worried about possible cyberattacks and Chinese influence with oil. China is playing a game of deadlock because it has no interest in working with Taiwan and is preparing to annex Taiwan. Taiwan, on the other hand, is playing chicken, with mutual defection being the worst possible outcome.

The United States and China -The game is generally repeated, and extensive cooperation on various international issues has been conducted after mutual exchange. Their trust in each other will increase to varying degrees because they repeat the game. There are countless opportunities to beat other at their own game.

The US and Taiwan are engaged in an alliance game of Leader. They prefer to work together rather than with anyone else, in this case China. Given that Leader is symmetrical, both receive the same payoffs (DC>CD>CC>DD).  Bully can also be used to illustrate the interaction with China because the US and Taiwan are allies. The US will retaliate in response to China's threats towards Taiwan. For instance, "the U.S. can also warn Beijing that if Taipei's energy goes out, Shanghai's electricity may also go out.

Game Theory in Evolution and Ecology

Although the natural world is frequently cruel and dog-eat-dog type, many diverse animals do cooperate. Game theory can be used to simulate the cause of this coexistence. For instance, birds known as zigzags consume parasites inside the mouths of crocodiles. Both the crocodiles' oral health and the zigzags' access to a satisfying food are improved as a result. The crocodiles and the zigzags have presumably learned the advantages of collaboration over the eons of evolutionary action, the "equilibrium point."

Game theory is important for all areas of ecology where there is frequency dependence in the reproductive success of phenotypes, so that the best phenotype of an individual depends on the phenotype of others. In addition to sex allocation, other examples from life-history evolution are dispersal morphs and alternative reproductive phenotypes.

Evolutionary stability

How do we expect natural selection to shape behavioral strategies when there is frequency dependence?

In evolutionary game theory, the basic approach is to seek stable endpoints of the evolutionary process rather than following an evolutionary trajectory under detailed assumptions about the underlying genetics. It is easier to characterize stable endpoints at which the population is monomorphic.

Suppose that almost all population members follow the same strategy x. Then we refer to x as the resident strategy. Let x′ be a rare mutant strategy in this population and denote the fitness of this mutant strategy by W(x′, x).

By applying game theory, we can introduce two standard criteria that must both be met for a strategy x* to be considered as a stable endpoint.

1. If the resident population is x* then no single mutant strategy can invade under the action of natural selection.

A necessary condition is that-

W (x′, x∗) ≤ W (x∗ , x∗) for all mutants x′.

This is the Nash equilibrium condition of game theory. In order to deal with mutants that are equally fit as residents, there is a second condition demanding that-

if W(x′,x∗)= W(x∗, x∗) for some x′≠ x∗ then W(x′,x′)< W(x∗, x′).

A Nash equilibrium strategy x* satisfies this second condition.

2. If the resident population is perturbed away from x* then natural selection will lead back to x*.

When the trait x is one-dimensional, this will happen if the selection gradient F(x) near x = x* satisfies

F(x)>0 for x<x∗ and F(x)<0 for x>x∗, where F(x)=∂W∂x′(x,x).

The strategy x* is then said to be convergence stable.

If x* satisfies both criteria above, we can regard x* as a realistic endpoint of the evolutionary process.

The first criterion is a global condition, whereas the second is a local condition.

Game Theory in Sociology

In sociology, game theory can be used to determine the behavioral and communication patterns of people in groups and to enable amazing insights about the different kinds of efforts that human beings make in virtually every field of human activity. Game theory helps in understanding the origin of human behavior and in understanding why people behave in particular ways and how the given behavioral patterns of human societies have changed across different ages.

Let us consider this statement:

"If we were all better people, the world would be a better place".

This statement is applicable to every individual; it may not necessarily be applicable to a group as a whole. Game theory provides a detailed connotation of both sides of a statement, which allows for the refutation of a given statement under particular circumstances. This aspect is best demonstrated through the prisoner’s dilemma, which is a true reflection of game theory.

An illustration of how game theory can be successfully applied below -

The primary goal of a football team competing in the World Cup is to work together to win the match. Each player has a specific job and is accountable for playing a part in reaching the team goal. Due to their exceptional skill and performance, some players will take on the role of lead players. Other players take on supporting ones and the team as a whole may succeed.

The solution to this dilemma also comes from game theory.

 Conclusion

Game theory goes beyond mathematical representations to describe real-world events where decisions made by players affect other players’ interests. Game theory may not be very efficient in the prediction of behavior, though in some unique cases, it might take up that role. The only challenge with game theory lies in the trade-off between realism and solvability in the real world, a problem that the common assumptions of rationality and common knowledge try to smooth out.

Therefore, game theory can be said to be a basis for making rational decisions whereby the given decisions create impacts on the decision-making of other entities in the group while also impacting one’s own decisions at the given time.