NetLogo User Community Models

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## WHAT IS IT?

This model studies social influence in randomly formed networks for two classes of games. Games with strategic complements where agents want to coordinate in the same action, and games with strategic substitutes, where agents want to anti-coordinate.

Agents in the model can be of two types: bips and bops. Bips are agents that prefer action 1 and are represented as triangles. Bops prefer action 0 and are represented as circles. Independently of the type, if an agent chooses action 1 her color will be cyan, and if 0 her color will be pink.

The first choice made is randomly assigned to players. From there, in every period of time, an agent myopically best responds to the choices made by her neighbors in the previous period. When an agent has no incentives to change her choice, she is in the nash set and will display the number 1, otherwise she displays 0. If all agents reach nash the simulation stops, if not, it will continue until the maximum number of iterations is reached.

Agents that choose the action they prefer are said to be happy. This is used to characterize the final outcome (most likely in equilibrium) as satisfactory if all agents are happy, and frustrated if at least one is not. Also as specialize if all agents choose the same action, or hybrid if both actions coexist.

## HOW TO USE IT

There are 6 parameters you can decide on before initializing the model. (1) The COMPLEMENTS? switch that sets games as strategic complements if ON and sets games as strategic substitutes if OFF. (2) The NUMER_NODES slider controls the size of the network. (3) The NUMBER_BIPS slider controls how many of the total agents are bips. Note that if the number of bips you choose is greater than the total number of agents, by default all agents will be bops.(4) The PROPORTION_OF_LINKS slider controls the level of connectivity in the network. You cannot decide the exact number of links you want, but the percentage of the total possible links [(n*(n-1))/2]. (5) The I_LIKE_FIRST_CHOICE slider controls the probability that all agents first choice is their preferred action. If 100% all agents will choose with probability 1 the action they like: bips choose 1 and bops choose 0. (6) The MAX_ITERATIONS monitor controls the number of iterations the model will run in case it has not reached equilibrium. Choose the values for the five controllers and then press SETUP.

Pressing the GO ONCE button sets the revision of the first initial choice. To repeatedly make agents revise their choices, press GO.

The FORMED_LINKS monitors shows the exact number of connections formed by the proportion of links you determined. This is a fixed value along the run of the model. A1 and A0 monitors show how many agents choose action 1 or 0 repectively, in each round. Monitors HAPPY and NASH, show how many agents choose the action they like and how many agents are in the nash set and don't want to change their choice in the next round, respectively.

The ACTION and EQUILIBRIUM plots illustrate the entire path of choices 1 and 0 and of happy and nash agents along the run of the model.

## THINGS TO TRY

Let the model run until the end. Does it always stop before the maximum iterations? Does it always reach an equilibrium where all agents are in the nash set?

Run the model again, this time slowly, a step at a time. Watch how agents change their choices. What is happening when the network is highly connected? What is happening when there are no links in the network?

Run it with a small proportion of bips (or bops). What happens when all agents are identical? What happens when there is a large majority of one type and few agents of the other type? What happens when both types of agents are close to 50%?

## EXTENDING THE MODEL

Right now the probability of any two nodes getting connected to each other is the same. Can you think of ways to making any two nodes more attractive to be connected to each other? Perhaps (1) that the more connected an agent is the more likely to create a new link, or (2) the more likely two nodes to be connected if their types is the same, or (3) or the more likely to nodes to be connected if their type is the opposite, or (4) even that all agents will necessarily have the same number of connections. How would that impact the likelihood of reaching equilibrium? How would that impact the class of equilibria reached?

## RELATED MODELS

See other models in the Networks section of the Models Library.

## CREDITS AND REFERENCES

This model is adapted from:
Hernandez, Penalope, Munoz-Herrera, Manuel, Sanchez, Angel, 2013. Heterogeneous Network Games: Conflicting Preferences. Games and Economic Behavior. Forthcoming.