Cooperation and Contribution on a framework of Public Goods

Cooperation and Contribution on a framework of Public Goods Game (PGG)

Introduction

Essentially, the typical public goods game (PGG) consists in a model of public spending for a community (e.g. roads, pools, bridges), where players could invest their money in the good and the profit would be the surplus redistributed equally for all individuals (Silva, 2007). Many public goods games have been used to investigate features like bargaining, cooperation, competition, altruism, fairness and selfishness, for example (Szabo and Fath, 2007).

The evolutionary game theory has become a reliable approach to study the development of cooperation in many social dilemma situations (Novak, 2006; Szabo and Fath, 2007). The classical paradigms include the prisoners’ dilemma game and the snowdrift game. In the PGG framework, for example, it is proposed a multi-person prisoners’ dilemma game managed by group of interactions (Binmore, 1994). The public goods game and other evolutionary game models has been applied for all types of structure population like lattices, small-world network, scale-free networks, dynamic networks and interdependent networks (Yang and Rong, 2015).

Objective

In public goods games, individual’s motivation may promote pro-social behavior (Silva, 2007), social influences promote cooperative behavior (Wu et. al., 2014), selfishness promotes noncooperation resulting in the “tragedy of the commons” (Song et.al., 2011), punishment can increase cooperation when players may coincide their strategy with the others (Asch, 1952) and endowments may be affected by a scenario of inequality. All these factors are going to be discussed in this synthesis. The study presents a model of analysis for each one described in different sections, showing the main results regarding the effects on cooperation and contribution and under which circumstances they hold.

Section I – Can the Pro-Social Behavior Persist?

The pro-social behavior is a behavior that intends to benefit others in the society, altruistic actions that favors a good distribution of the benefits among groups. The general situation is a condition where there is a profit obtained by the players’ contribution (optional) and each player is unaware of the other players’ contribution. In order to encourage the donations, the amount will be more than the necessary for the public good and at the end it will be redistributed among the players (independently on the given contribution) (Silva, 2007).

This study proposes a new approach to investigate pro-social behavior in an artificial society of players through public good game using Monte Carlo simulation. The author’s model is a return function where pro-social is described as a binary variable for motivation, which drives the players to invest in the public goods by updating the benefits achieved by each player. The analysis also includes noise effects on the density of motivation and consider the motivation chosen according to the return of the neighbors (Silva, 2007).

First step was a comparison analysis testing different scenarios setting different initial values of density of motivation and different values of deterministic returns. After that, a new return function (measuring the average motivation of the neighborhood) was proposed and compared with another one proposed by the same author in a previews paper (Silva, 2007).

Some of the outputs of the model are graphs describing all possible behaviors of the motivation’s density as a function of time. The model also test the outcomes under interaction between the players, with time evolving in a small world network. This approach shows that noise effects really impact the density along the time which requires more repetitions (Silva, 2007).

By interpreting the model’ results, one can conclude there is a high dependence of the density of motivation. The mainly result shows that there is 60% chance of survival probability of the pro-social behavior in a small world network. When added the interaction, the motivation variable changes and the result variable shows that there is a high probability of the player copies the motivation of its neighbor with higher payoff (Silva, 2007).

The next section investigates the context of public good games on a social approach of the cooperation, but the author this time adding an influence-based variable to the model and checking how it is going to affect the cooperation behavior.

Section II – Social Influence Promotes Cooperation?

It is investigated a common analysis approach in other articles concluding that using random selection pattern does not capture all real world circumstances by assuming all players have the same influential level and take all high-payoff players unvaryingly have high influence. Considering that in many groups there is asymmetric and heterogeneous influential effect, how influence-based selection patterns enhance cooperation? Based on the frequency of being imitated, it was estimated an individual’s influence. In order to accomplish a more realistic scenario, it was applied a spatial model, on a context of public good games, to investigate the effects of influence-based reference selection on the enhance of collective cooperation (Wu et. al., 2014).

The main assumption for this model is that all players choose its neighbors as a reference with the probability proportional to this neighbor’s influence. The individual’s influence changes. Every time this individual is imitated its influential level increases (Wu et. al., 2014).

Essentially, the game consists in each player being randomly assigned as cooperator or defector with the same probability. Every player is in 5 groups centered on its nearest neighbors and himself. In all groups the cooperators contribute to the public good and the defectors don not. The public good as shared among the all the group members equally. At the beginning, each player has the same influence factor and at the each of each round each individual choose a neighbor as a reference to learn. So, the probability of being chose is measured and the system enters the strategy updating phase. An individual’s influence increases when someone else adopts her/his strategy. Based on this, a α variable express the influence factor. If α = 0, the model will describe a traditional random reference selection pattern, if α > 0, the neighbor influence increases when the player is imitated, and the higher influential the neighbors become the higher is the probability of being selected as a reference (Wu et. al., 2014).

The cooperation effect is robust against the interactions’ variation, so the model is efficient in exploring the real social behavior. The results show that integrating the influence-based reference selection pattern into the model enhance the level of collective cooperation (α improves cooperation). It was also proved that the more imitated an individual is, the more she/he tends to be imitated in a future, so the frequency of being imitated supports their influence in a large magnitude. Another conclusion also shows how high influential cooperators have a great advantage over high influential factors (Wu et. al., 2014).

The next section presents a different perspective about the cooperation system. It introduces an investigation adding a punishment approach. In this new scenario, there is possible symmetry, where the players can mutually punish each other.

Section III – Can Mutual Punishment Promotes Cooperation?

This section introduces the impact of punishment in the public process of cooperation. Through the spatial public goods game the new model innovates with mutual punishment in its approach. The mechanism of mutual punishment allows individuals to punish others and being punished in return when different strategies are chosen. No matter if the neighbors are cooperators or defectors, anyone who holds a different strategy can be punished. In this case, the cost of punishment can be absorbed into the punishment fine (Yang and Rong, 2015).

Essentially, the model consists in players on lattice point with four neighbor points. Each individual participates in five PPG groups, which means that each PPG group has a sponsor and its four neighbors. Each player pays a total unit cost shared by all the members of the PPG group equally and defectors don’t contribute. The total cost of each group is calculated by a factor and redistributed to all the members equally. At the beginning, cooperators and defectors are randomly assigned following the same probability 0.5. After that, all players update their strategy at the same time, each one chose a neighbor and uses the same strategy. By forming clusters, cooperators can help each other in order to outweigh the loses against defectors (Yang and Rong, 2015).

The finding is robust with respect to variations in the system’s size and different levels of noise.  As main result, in the spatial public goods game, if the punishment fine increases the cooperation will also increases. The author also find out that when compared to no punishment systems, it is possible to see very large groups of collaborators emerging. Thereby, following the majority is a very important to compose public opinion (Yang and Rong, 2015).

Punishment is a good strategy to stimulate cooperation, in contrast to rewards, it has the ability to stabilize the level of cooperation. Another way to efficiently improve cooperation is through volunteering mechanism, but in contrast to the punishment system, it is able to improve the average payoff of populations.  The next section presents a different investigation regarding the best approach to capture higher contributions. Introducing the volunteer mechanism into the public goods game, the idea is to identify cooperation behavior and the effects on the average payoffs.

Section IV – Optional Contributions Effects for Volunteering Public Goods Games?

This section introduces the volunteering system with optional contributions to the public goods game, investigating how this is going to affect cooperation and average payoffs. According to the initial investigation, optional contribution may encourage players with bonded rationality to contribute. In this system, there are three kinds of players: cooperators, defectors and loners. The cooperators pay a contribution to the public good, defectors exploit the group, and loners play the conservative strategy seeking to obtain constant payoffs. Thus, loners protect cooperators leading the system to a rock-paper-scissors dynamic for replication equations (Song et. al., 2011).

The study proposes a simulation of logit dynamic and compares the results with a spatial VPG games. As assumptions, there are two levels of contribution to be picked, low or high contributions. The low contribution is a inducing mechanism because it may encourage other individual to choose cooperation under bounded rationality. Because of this, logit dynamics pointes to a direct relationship between optional contributions and more individuals to choose cooperation (Song et. al., 2011).

As a conclusion, the logit dynamics simulation demonstrate that optional contributions are able to improve cooperation comparing with the classic scenario with only one kind of cooperators. The simulation with larger number of cooperators in the groups came up with higher average payoff with compared to the scenario with only one cooperator. Another result shows that the cooperators in the classic scenario seem more generous than the cooperators who choose the low level of contribution and more willing to cooperate. It was also proved that there is no effect of the group size on threshold. In this game the players are not completely rational, so the small payments will induce other players to contribute to the public good, what improves the high-level contributions along with low level contributions, the total number of cooperators definitely is larger than in the typic scenario. In addition, willing to capture the best response, it was added a synchronized updating strategy to the optional contributions in special VPG games. Very similar to the results analyzed on the logit dynamic system, this simulation concludes that optional contributions can enhance cooperation and improve the average payoff. Thus, under bounder rationality, adding different levels of contribution can be a very good option in motivating cooperation among players and improve payoffs (Song et. al., 2011).

Section V analyses how endowment inequality impacts the total contributions to a public good. The model used came up with a new idea of how to isolate inequality effects on a context where individuals respond to existence of inequality and their endowment at the same time.

Section V – Endowment Inequality in Public Goods Games

This section proposes an investigation through public good games to capture the effect of inequality on the level of contribution to the public good. To contextualize the scenario, it three main groups are investigated: poor, middle and rich, and we are looking for their behavior as tax payers (Heap, Ramalingam and Stoddard, 2016).

There are evidences showing how inequality leads to lowers contributions, proving that increasing inequality promotes a worse economic performance. The model uses the volunteering contribution to public goods (VCM) approach. People were separated in 3 member groups and analyzed under two different conditions. First condition is equality, when everyone receives the same endowment, and the experiment tests for different varies. The second condition is inequality, where each person receives different endowments (Heap, Ramalingam and Stoddard, 2016).

During the investigation, they found that poor and middle players contribute the same in both scenarios. However, the rich players tend to contribute less in the scenario with inequality. The reduce in the rich’s contribution relative to the poor players is a robust pattern and this difference in behavior leads to a reduce in overall contribution in the second scenario, which mean the game is efficiently isolating inequality and also that it is a very difficult social challenge (Heap, Ramalingam and Stoddard, 2016).

In an inequality context, it is intuitive to attack inequality by increasing taxes for the riches and lowering the taxation for poor. However, in this case where the contribution to the public good is a decision to tax oneself, the results pointed to the circumstance where rich people are less inclined to tax themselves. In order words, when there is more pressure to tax rich people pay more taxes they are less likely to do it (Heap, Ramalingam and Stoddard, 2016).