Public Goods

A public good is anything that is non-excludable and non-rivalous. Best examples of public goods include lighthouses and OTT media services (Netflix, etc). Just because one ship is utilizing a light house does not mean another ship cannot use it, neither does it 'exhaust' the lighthouse. Yet, public goods still require support for establishment and maintenance. For this purpose, governments collect taxes/tolls, and OTT media houses collect monthly subscriptions. However, what happens when system cannot track down the users of the public good? Entities will no longer contribute to the public good and it may collapse. This is known as the free-rider problem (among many other terms). This simulation showcases one way to tackle this problem.



Description

In the above simulation, there are three strategies: loner (green), cooperator (blue) and defector (red). The loner has a constant payoff of \(\sigma\). They neither use nor contribute to the public good because they have their own thing going on. Cooperators and defectors 'participate' in the game. Suppose there are \(S\) participators and \(n_c\) cooperators, then the contribution of these cooperators is multiplied by a factor \(r\) and then distributed amongst all \(S\) participants. Additionally, each cooperator pays a cost of 1 towards the public goods. Hence, the payoff of each strategy are as follows:

\[ P_l = \sigma \] \[ P_c = \frac{r n_c}{S} - 1 \] \[ P_d = \frac{r n_c}{S} \]

In this simulation, every cell plays the public goods game with its 8 neighbors, and thereafter adopts the strategy of its most successful neighbor. The updates are synchronous. The tunable parameters are \(r\) and \(\sigma\). Some straightforward observations are:

  1. If you want loners to even have a chance of existence, then we require \(\sigma > 0\)
  2. In order to make total cooperation better than total defection, we need \(r > 1\)

The dynamics is not only dependent on the above parameters, but also on previous state of the system, and non-extinction of strategies. With \(r = 2.2\) and \(\sigma = 1\), we observe oscillations. This is because it is better to be a defector in a population of cooperators, a loner in a population of defectors, and a cooperator in a population of loners. This rock-paper-scissor interaction makes sure that cooperators always exist, and the public good is always maintained. This kind of continuous evolution, which is required for the system to undergo (even though it comes back to the same state as before), in order to continue 'existing', is called the Red Queen Mechanism.

The system may reach a steady state, oscillate, or showcase short-term oscillations with a period as short as 2. One of the strategies may go exist, in which case it will never come back. The pre-existing spatial structures also have an effect on the evolution of the system, especially when the parameters are changed. Basically, hysteresis plays a prominent role.


Note:
  1. This model was described this Hauert. et al, Science (2002)
  2. This simulation is computationally complex and may lag on lower-end devices

Developed by ChanRT | Fork me at GitHub