README for SimBuilder sample simulations.
SimBuilder is distributed with seven sample simulations. Five of these are taken from Skyrms and Pemantle, "A Dynamic Model of Social Network Formation." Proceedings of the National Academy of Sciences, August 1, 2000, vol. 97, no. 16., pp. 9340 - 9346. The remaining two are implementations of two common models.
- uniform_reinforcement_past.sbp
This is a model of Skyrms and Pemantles' Friends I, Friends II and Discounting the Past simulations.
The basic idea here is that every iteration of the simulation each agent chooses another agent at random to form a link with. The choice of whom to form a link with is determined by a vector of weights each agent has assigned to all the other agents. Each element of the vector corresponds the weight of another agent. The probabilty that agent i will form a link with j is the current weight of j divided by the sum of the entire vector of weights. When a link is formed that agent gets a reinforcement of 1, that is, a value of one is added to the current weight of that agent.
So, each iteration for each agent the current probabilities are calculated from the current weights as described above. On the basis of these probabilities each agent i forms a link with some other agent j. Then the weight of agent j in agent i's vector of weights is increased by one.
The simulation can also be run with symmetrical reinforcement. In this case, when agent i forms a link with some other agent j. Then in addition to the weight of agent j in agent i's vector of weights being increased by one, the weight of agent i in agent j's vector of weights is also increased by one. To turn on symmetrical reinforcement, check the symmetrical box once you've compiled and run the simulation.
The simulation can also be run with past weights discounted by a user specified value. In this case, the weights from the previous iteration are multiplied by some discounting factor before adding the current undiscounted payoffs. To turn this feature on, enter a value between 0 and 1 in the pastDiscount box once you've compiled and run the simulation.
In addition, the simulation will dump a matrix containing all the agents weight vectors to the console whenever the simulation is paused. To turn this off uncheck the dump box, once you've compiled and run the simulation.
2. uniform_reinforcement_past_linker.sbp
This is the same as above, but demonstrates how to write the same simulation using the NodeLinker component.
This does not contain the dump or symmetrical features, although they could easily be added.
3. uniform_reinforcement_past_noise_linker.sbp
This is the same model as 2 above, but adds noise to the probability rule. The probability of i linking with j is now some fixed positive number e / (n - 1), plus (1 - e) times what it was in sample 1 and 2, where n is the number of agents.
This simulation also uses the NodeLinker component, and is a good example of the use of it.
4. stag_hunt.sbp
Stag hunt indexes the reinforcement to the following payoff matix:
| Hunt Stag | Hunt Rabbit
------------+-----------+-------------
Hunt Stag | (1, 1) | (0, .75)
------------+-----------+-------------
Hunt Rabbit | (.75, 0) | (.75, .75)
------------+-----------+-------------
Half the agents begin as stag hunters and half as rabbit hunters. If a stag hunter i forms a link with a stag hunter j then each is updated in the other's weight vector by 1. If rabbit hunter forms a link with a stag hunter then the stag hunter's weight in the rabbit hunter's vector is increased by .75 and the rabbit hunter's weight in the stag hunter's vector is increased by 0. And so on for the other cells in the payoff matrix.
You can also discount the past in this simulation.
5. stag_hunt_with_switch.sbp
This is identical to stag hunt, but after all the agent's have played the game and formed new links. Each agent is given the opportunity to switch to the strategy that yielded the best payoff. An agent will switch according to a user specified probability.
This also implements discounting the past.
Note that this is probably not be how Skyrms and Pemantle implemented switching.
6. schelling.sbp.
This is an implementation of Schelling's segregation Model as described in Models of Segregation (in Strategic Theory and Its Applications). Thomas C. Schelling. The American Economic Review, Vol. 59, No. 2, Papers and Proceedings of the Eighty-first Annual Meeting of the American Economic Association. (May, 1969), pp. 488-493. The basic idea here is that there are types of agents and each agent has a tolerance level that determines the percentage of its neighbors that can be of the other type before the agent moves to a new more tolerable location.
7. prisonners_dilemma.sbp
This is a basic implementation of Iterated Prisoner's dilemma. The implementation is based on Cohen, Michael D., Riolo, Rick L. and Axelrod, Robert. "The Emergence of Social Organization in the Prisoner's Dilemma: How ContextPreservation and other Factors Promote Cooperation." Note that this SimBuilder implementation does not completely implement the various models described in the paper. Rather the SimBuilder implementation works as follow:
A run begins by creating the agents and assigning them a strategy to play. The four strategies are always cooperate, always defect, tit-for-tat, and anti-tit-for-tat. The percentage of agents playing each property is determined by model parameters. The agents are then distributed randomly across a grid. Each iteration of the simulation, all the agents are initialized, setting their payoff and number times played fields to 0, and setting their current strategy to the new strategy chosen in the adapt action mentioned below. Then each agent will play each of its Von Neumann neighbors 4 times. After all the agents have played each agent is give a chance to adapt its strategy by polling its neighbors to see which strategy resulted in the best payoff. The agent then adopts that strategy to play in the next round.