October 02, 2022

The perspective of game theory:Envy and competition exacerbate social divisions

It is generally believed that birth and education caused the differences between social classes. However, it is still unclear when and under what circumstances the individual’s psychological power will cause the originally homogeneous social group to split and eventually divide. In June 2020, Claudius Gros, professor of theoretical physics at Goethe University, explored this problem in a mathematically precise manner based on game theory.

In this research, the acting individuals (agents) are simulated based on game theory, which means that everyone can optimize their own success according to predetermined rules. The question researchers want to understand is whether social differences will arise on their own if no one has the advantage in the first place, that is, when all participants have the same skills and opportunities, will there still be a crowd grade.

The research is based on the assumption that every society has coveted but limited resources, such as jobs, social interactions, and positions of power. If the highest position is already occupied, then inequality is created, so someone must accept the second best job. With the help of mathematical calculations, Gros was able to prove that jealousy arises from the need for self-comparison with others, and it changes individual behaviors and strategies.

As a result of this changed behavior, two strictly separated social classes have emerged. Like Gros’s research, game theory provides the mathematical algorithms necessary to model decision situations with multiple participants. In general, it is particularly obvious that the decision-making strategies of various participants influence each other. An individual’s success depends not only on his or her own behavior, but also on the behavior of others, which is typical in economic and social environments. Therefore, game theory is firmly rooted in the economy.

The stability condition of game theory, namely “Nash equilibrium”, is a concept put forward by John Forbes Nash in his 1950 paper taking poker players as an example.

It points out that in an equilibrium state, if other participants have not changed their strategies, no participant can gain any benefits by changing their strategies. Only when there are potential benefits, individuals will try new behaviors. Since this causal chain also applies to evolutionary processes, evolution and behavioral sciences often rely on game theory models, such as when studying the migration routes of birds or competing for nesting sites.

forced cooperation: The agent may agree to choose different options in the cooperative game, for example to optimize the overall welfare.

envy: In the context of this research, jealousy is defined in terms of the reward function. For this reason, when a certain option is selected, the income obtained by a particular agent α clearly depends on the income of other agents. Envy will add a non-monetary contribution to the player’s reward. If the player’s overall reward is greater/lower than the rewards of others, it is positive/negative.

evolutionary game: The evolutionary game is not only played once, but over and over again. After each round, the agent needs to update his strategy according to the income obtained when the selection probability is pα(qi).

pure/mixedstrategies: In simple games, such as Hawk and Dove competitions, there is usually no distinction between options and strategies. Choosing an option (to fight or not to fight) is equivalent to the strategy. In general, strategy defines how and when players choose possible options. When the agent is always in the same option, the strategy is pure, otherwise mixed use

Gros believes that even in a class society caused by jealousy, individuals have no incentive to change their strategies. Therefore, it is Nash stable. In a divided jealous society, there is a clear income difference between the upper class and the lower class, and all members of each social class are the same. Gros believes that for members of the lower classes, the typical approach is to spend their time on a series of different activities, which is what game theory calls “mixed strategies.” However, members of the upper class focused on only one task, which is the pursuit of “pure strategy.” It is also surprising that the upper class can choose between various options, while the lower class can only use a mixed strategy. Gros concluded: “The upper class is therefore individualistic, while the lower class agents are lost in the crowd.” One possible explanation is that the common mixed strategy used by the lower classes is an atypical group trait , They do not have the characteristics of adaptive strategies claimed by Darwin.

In Gros’s model, whether an agent falls into the upper class or the lower class is ultimately just a coincidence. It is determined by the dynamics of competition, not by a person’s origin. In his research, Gros also developed a new game theory model, the shopping trouble model, and proposed a precise analysis solution. And from it, it can be concluded that an enviable social class has characteristics that are considered universal in the theory of complex systems. An interesting inference is that it does not matter which strategy the upper class chooses, because their rewards and monetary income will not be affected. One can call this freedom a luxury choice to get rich. As can be seen from the figure below, the strategies of the upper class tend to cluster around the maximum value of the basic utility function, which is purely dynamic. Strategies that favor high quality increase the growth rate while accelerating stability.

When the personal reward is greater than the overall average, jealousy has a self-reinforcing effect.

This argument explains why agents with medium/high pay would adopt a mixed/pure strategy. Evolutionary stable strategies can have different rewards only when the support is different. As the degree of forced collaboration and jealousy increases, the number of mixed strategies continues to increase, which becomes more and more difficult. The support for unique hybrid strategies is exhausted, leaving only the hybrid low-level strategies. From this perspective, class stratification corresponds to the transition of strategic mergers, resulting in atypical group-level characteristics.

In short, this study finds that social stratification is the result of the self-organization process, and the result is that it has general properties that can only be indirectly controlled by external influences. When the social class divides, policy makers lose some tools. In this sense, class stratification is essentially resistant to external influences. And envy tends to consolidate class differences rather than soften them. People at the bottom may want to compare their assets with those at the top, which is tempting, but it actually backfires.

Inspiration from this research

All born equal, the gap is reflected in the choice of competitive strategy;

Before jealousy makes you explode, let it ignite your fighting spirit as much as possible;

Origin and education may not be the most important, but they will affect a person’s strategy and persistence in participating in social competition;

Envy is a gift voluntarily offered to the strong;

Instead of jealous of the excellence of others, it is better to optimize your own strategy.