First Steps

Goal

In this tutorial, we will build a simple market model with multiple buyers and sellers. Each buyer has a fixed budget and preferences for two goods, x and y. Sellers offer these goods, and buyers purchase from a randomly selected subset of sellers at each time step.

The model illustrates several core concepts in Vahana, including:

1. Defining agent and edge types as structs
2. Initializing a simulation with agents and edges
3. Implementing transition functions to update agent states
4. Tracking simulation results

This simple model serves as an introduction to Vahana's capabilities for agent-based modeling. While relatively basic, it demonstrates how to represent a multi-agent system with different types of agents, connections between agents, and state transitions driven by agent interactions.

Model Overview

Our model simulates a dynamic market with $n$ buyers and $m$ sellers, trading two types of goods: $x$ and $y$. We use good $x$ as the numeraire, fixing its price at 1, while the price of good $y$, denoted as $p$, is variable and adjusted by sellers over time. Each buyer in our market has a unique preference and a constant budget $B$ for purchasing both commodities. These preference is represented by an individual parameter α, which determines the buyer's relative desire for good $x$ versus good $y$. Buyers make their purchasing decisions based on a Cobb-Douglas utility function:

\[\max_{x,y} u(x, y) = x^\alpha \cdot y^{1 - \alpha}\]

subject to their budget constraint: $x + y · p ≤ B$. This utility maximization leads to an optimal demand for each good:

\[\begin{aligned} x &= B \cdot \alpha \\ y &= \frac{B \cdot (1 - \alpha)}{p} \end{aligned}\]

On the supply side, sellers offer both goods $x$ and $y$, which we assume to be joint products. Their primary goal is to balance the production and sales of these two goods. To achieve this, sellers adjust their prices based on the aggregate demand from their customers. The price adjustment mechanism is given by:

\[\begin{aligned} p_t &= \frac{d_y}{d_x} \cdot p_{t-1} \\ \textrm{where } d_x &= \sum_{b \in \textrm{buyers}}x_b ,\quad d_y = \sum_{b \in \textrm{buyers}} y_b \end{aligned}\]

Agent and Edge Types

Now that we understand our market model, let's implement it using Vahana. We'll start by defining our agent types and edge types, then create and initialize our simulation.

First, we need to import the necessary modules:

using Vahana
import Random: rand
import DataFrames

In Vahana, agents and the edges between them are represented by Julia structs. However, these structs must meet specific requirements:

1. They must be immutable.
2. They must be "bitstypes".

A bitstype in Julia is a type that is composed entirely of primitive types (like Int, Float64, Bool) or other bitstypes, and has a known, fixed size in memory. This also implies that the type of a struct variables must be declared.

This restrictions allows Vahana to efficiently manage and distribute agents across processes in parallel simulations.

Let's define our agent types with these requirements in mind:

struct Buyer
    α::Float64  # Preference parameter
    B::Float64  # Budget
end

struct Seller
    p::Float64   # Current price of good y
    d_y::Float64 # Total demand for good y (used for price adjustment)
end

To facilitate agent creation with some randomization, we'll define custom constructors:

Buyer() = Buyer(rand(), rand((1:100)))

Seller() = Seller(rand() + 0.5, 0);

These constructors create:

• Buyers with random $\alpha$ (between 0 and 1) and $B$ (between 1 and 100)
• Sellers with a random initial price $p$ (between 0.5 and 1.5) and zero initial demand.

Now, let's look at our edge types in more detail:

This KnownSeller network is fixed and describes the sellers known to each buyer. In Vahana, the direction of an edge determines the flow of information. Since buyers need price information from sellers to calculate their demand, we define this as an edge from sellers to buyers. We call this network KnownSeller.

The edges of the KnownSeller network don't carry additional information, so we define them as an empty struct. We'll use this as a kind of tag later to select only the edges of this type.

struct KnownSeller end

The Bought network represents actual transactions between buyers and sellers. This network is dynamic, with edges created during the simulation runtime. Each edge in the Bought network carries information about the quantities of goods purchased in a transaction. Specifically:

struct Bought
    x::Float64  # Quantity of good x bought
    y::Float64  # Quantity of good y bought
end

To make working with Bought edges easier, we'll define an addition operation:

import Base.+
+(a::Bought, b::Bought) = Bought(a.x + b.x, a.y + b.y);

This allows us to easily sum up multiple Bought edges, which will be useful when sellers calculate total demand.

Defining the Model Structure

In Vahana, the ModelTypes constructor is the starting point for defining the structure of your agent-based model. To populate this instance, we use the register_agenttype! and register_edgetype! functions. These functions tell Vahana about the types of agents and edges in your model, allowing it to set up the necessary internal data structures and optimizations. The |> operator can be used for function chaining, providing a concise way to register multiple types.

const modeltypes = ModelTypes() |>
    register_agenttype!(Buyer) |>
    register_agenttype!(Seller) |>
    register_edgetype!(KnownSeller) |>
    register_edgetype!(Bought);

Defining Model Parameters and Globals

Vahana offers two ways to define parameters for your model: using register_param! or creating a custom parameter struct. The register_param! function allows you to register individual parameters with your model. For example, you might use:

modeltypes |>
    register_param!(:numBuyer, 50) |>
    register_param!(:numSeller, 5) |>
    register_param!(:knownSellers, 2);

With this approach, the parameters can then be set to values other than the default value via set_param! calls until the simulation is initialized with finish_init!.

Alternatively you can define a custom parameter struct and then pass an instance of this struct to create_simulation.

In addition to parameters, Vahana allows you to manage global state variables that can change during the simulation. This is particularly useful for tracking aggregate statistics or maintaining shared information across all agents. Similar to parameters, you can register individual global variables:

modeltypes |>
    register_global!(:x_minus_y, Vector{Float64}()) |>
    register_global!(:p, Vector{Float64}());

Again, you could alternatively, you can define a custom struct for globals and pass an instance of this struct to create_simulation as shown in the other tutorials.

Please note that Vahana's global state is distinct from the functionality of the global keyword in Julia programming language. The two concepts are unrelated and should not be conflated.

Create the Model and Simulation

In Vahana, the term "model" is used in a somewhat unconventional way compared to other agent-based modeling frameworks. In Vahana, a model created via create_model does not contain any rules about how the state of a simulation changes over time. Instead, a Vahana model is more akin to a specification of the possible state space - it defines the set of all possible graphs that can be created with the specified agent and edge types.

Think of a Vahana model as a blueprint or a schema. It outlines the structure of your simulation - what types of agents can exist, what types of relationships (edges) can exist between them, and what global parameters and variables are available. However, it doesn't dictate how these elements interact or evolve over time.

A simulation, on the other hand, is a concrete realization within this state space. It's an actual graph with specific agents and edges, representing the current state of your simulated world at a given point in time.

Transition functions, which we'll define later, are the mechanisms that actually change the state of the simulation over time. These functions operate on the current state of the simulation (the current graph of agents and edges) and produce a new state by modifying agent attributes, creating or removing agents and edges, and updating global variables.

To create a model in Vahana, we use the create_model function. This function takes the ModelTypes object we've been building through our type registrations and parameter/globals definitions, and the name of the model:

const model = create_model(modeltypes, "Excess Demand")

Model Name: Excess Demand
Agent(s):
	 Type Buyer
	 Type Seller
Edge(s):
	 Type KnownSeller with Hint(s): Stateless
	 Type Bought
Parameter(s) with default values:
	numBuyer: 50
	numSeller: 5
	knownSellers: 2
Global(s) with init values:
	x_minus_y: Float64[]
	p: Float64[]

Once we have a model, we can create a simulation based on that model using the create_simulation function:

const sim = create_simulation(model)

Model Name: Excess Demand
Simulation Name: Excess Demand
Agent(s):
	 Type Buyer with 0 agent(s)
	 Type Seller with 0 agent(s)
Edge(s):
	 Type KnownSeller with 0 edge(s) for 0 agent(s)
	 Type Bought with 0 edge(s) for 0 agent(s)
Parameter(s):
	 :numBuyer : 50
	 :numSeller : 5
	 :knownSellers : 2
Global(s):
	 :x_minus_y (empty) 
	 :p (empty) 
Still in initialization process!.

This function creates a new simulation instance based on our model. At this point, the simulation is empty - it doesn't contain any agents or edges yet. It's essentially a blank canvas ready for us to populate with agents and edges according to our model's specifications.

Populating the Simulation

After creating our simulation, the next step is to populate it with agents and edges. Vahana provides add_agent!, add_agents!, add_edge!, and add_edges! functions for this purpose.

The add_agent! function returns an AgentID, while add_agents! returns a vector of AgentIDs. These identifiers are unique to each agent at the current state of the simulation.

In parallel simulations, the AgentID incorporates information about the process number to which the agent is assigned. Consequently, the ID may be modified if an agent is reassigned to a different process. In the current implementation of Vahana, agents only change processes during the finish_init! function. However, this design allows for potential future implementation of dynamic load balancing.

It is also possible that the same AgentID is utilized multiple times for distinct agents. Consequently, an AgentID returned by a Vahana function call or passed as an argument to a callback function (refer to the Transition functions section below for more details) is only valid within a specific scope. This scope is limited to either the period before the finish_init! function is invoked or until the callback/transition function has completed its execution. After these points, the ID should not be considered reliable for further use or reference.

If your model requires persistent identification of agents, you should implement this yourself by adding an ID field to your agent struct. For example:

struct BuyerWithID
    id::UUID  # created via the UUIDs standard library
    α::Float64
    B::Float64
end

You would then manage these IDs yourself, ensuring they remain constant throughout the simulation.

In our case, we use the IDs returned by add_agents! to iterate over all buyer IDs, randomly select numSellers seller IDs for each buyer ID, and then create edges between them in the KnownSeller network.

We can see in the following code snippet also how parameters of the Simulation can be accessed via the param function.

buyerids = add_agents!(sim, [ Buyer() for _ in 1:param(sim, :numBuyer)])

sellerids = add_agents!(sim, [ Seller() for _ in 1:param(sim, :numSeller)])

for b in buyerids
    for s in rand(sellerids, param(sim, :knownSellers))
        add_edge!(sim, s, b, KnownSeller())
    end
end

sim

Model Name: Excess Demand
Simulation Name: Excess Demand
Agent(s):
	 Type Buyer with 50 agent(s)
	 Type Seller with 5 agent(s)
Edge(s):
	 Type KnownSeller with 100 edge(s) for 50 agent(s)
	 Type Bought with 0 edge(s) for 0 agent(s)
Parameter(s):
	 :numBuyer : 50
	 :numSeller : 5
	 :knownSellers : 2
Global(s):
	 :x_minus_y (empty) 
	 :p (empty) 
Still in initialization process!.

As you can see from the result of the code block above, Vahana has "pretty print" functions for some of its data structures.

Finally, we call finish_init!. This crucial step completes the initialization process, setting up data structures and, in parallel simulations, distributing agents across processes.

finish_init!(sim)

Defining Transition Functions

In Vahana, transition functions define how your simulation evolves from one state to the next. They encapsulate the rules and behaviors of your agents, determining how agents interact, make decisions, and change their states. The transition function is called for each agent separately.

A typical transition function in Vahana has the following signature:

function transition_function(state, id, sim)
    # Function body
    return new_agent_state
end

A transition function must have three parameters. The first represents the current state of the agent, allowing it to make decisions based on its own attributes and conditions. The second parameter is the temporary ID of the agent. This ID can be used within the transition function to access other elements of the graph that are visible to the agent via functions like edges or neighborstates. It's important to note that this ID should not be stored, as it may change between time steps. Finally, there's sim, which is the simulation object. This provides access to the global state and parameters of the simulation. These three parameters together give the agent all the context it needs to determine its next state.

The first transition function we are implementing calculates the demand for the goods $x$ and $y$.

This transition function is called for all Buyers. First, the neighborids function is used to get a vector that contains the (temporary) IDs all the sellers known by the actual buyer.

One of the IDs of the sellers is selected using the rand function. For this seller, the state is accessed via the agentstate function. In cases where the type of the agent whose state we want to access is unknown, it's possible to use agentstate_flexible instead.

Then the agent calculates it's demand for the goods $x$ and $y$, and adds an edge with the information about the demand to the Bought network, which is then used in the next transition function by the sellers to sum up the demand and calculate the new price.

function calc_demand(b::Buyer, id, sim)
    seller = rand(neighborids(sim, id, KnownSeller))
    s = agentstate(sim, seller, Seller)
    x = b.B * b.α
    y = b.B * (1 - b.α) / s.p
    add_edge!(sim, id, seller, Bought(x, y))
end;

In the calc_price transition function, sellers summarize all the goods $x$ and $y$ they sold. They do this by summing the state of all incoming Bought edges.

If a seller hasn't made any sales (i.e., no incoming Bought edges exist), edgestates returns nothing, and the seller's state remains unchanged. Otherwise, edgestates returns a Vector containing the states of all relevant edges. We aggregate this vector using the reduce function, leveraging the previously defined + operator for Bought.

Finally, we construct a new seller state. The new price is calculated as q.y / q.x * s.p.

function calc_price(s::Seller, id, sim)
    sold = edgestates(sim, id, Bought)
    if isnothing(sold)
        return s
    end
    q = reduce(+, sold)
    Seller(q.y / q.x * s.p, q.y)
end;

Applying Transition Functions

To apply these transition functions to the current state of a simulation, Vahana provides the apply! method. This method is the key mechanism for evolving the simulation state over time, executing our defined transition functions across the population of agents. Let's examine its signature and behavior in more detail:

apply!(sim, func, call, read, write; add_existing = [], with_edge = nothing)

sim is the simulation instance and func is the transition function to be applied to the simulation state.

The call argument in apply! specifies which agent types the transition function should be applied to. This can be either a single agent type or a collection of agent types. In most cases, as in our market model, call will contain only a single type. For example, when we apply calc_demand, we only want to call it for Buyer agents. However, Vahana allows for more complex scenarios where a single transition function can be applied to multiple agent types. This flexibility allows for more complex agent interactions and behaviors within a single transition function, which can be particularly useful in models where different types of agents share similar behaviors or decision-making processes.

The read argument must include all agent and edge state types that are accessed in the transition function. This is particularly important in parallel simulations, as it ensures that all necessary data is transmitted to the processes that need to access it. When Vahana's assertion system is active, it checks that only these specified types are accessed. However, if assertions are disabled via enable_asserts, forgetting to include a type in read can lead to incorrect results without raising an error. It's worth noting that while including unnecessary types in read doesn't cause errors, it can negatively impact performance.

A noteworthy scenario occurs when the call type is excluded from the read set. In these instances, the transition function's first argument is altered. Rather than representing the agent state, it becomes a Value Type corresponding to the 'call' type. Consequently, the state of the agent for which the transition function is invoked becomes inaccessible within the function itself.

The write collection must contain all agent and edge state types that are modified in the transition function. Conceptually, one might think of the resulting graph after a transition as the union of all agents and edges returned by individual transition function calls. However, this approach would be inefficient, requiring the reconstruction of even stable parts of the graph. Instead, Vahana optimizes this process by removing only the parts of the graph specified in the write collection. This means you can only change the state of agents or edges of a type if you're also re-adding the state of constant elements of that type.

But in cases where you want to add new elements (like additional edges) without modifying existing ones, you can use the optional add_existing keyword. This keyword takes a single or a collection of agent or edge state types. For all types in this collection, existing agents or edges will be preserved, even if the type is also in the write collection. This provides a flexible way to extend the graph without completely rebuilding it. But there is the restriction that agent types in add_existing can not be also in call.

The with_edge keyword restricts the application of the transition function to agents that are targets of a specified edge type. It's equivalent to manually checking for the presence of the edge for each agent before applying the function, but allows Vahana to optimize this operation internally. with_edge should only be used when a small proportion of agents have edges of the specified type. If most agents have this edge type, using with_edge may decrease performance compared to a manual check inside the transition function.

The implementation process, while seemingly complex, is quite straightforward in practice. Begin by crafting your transition function as previously demonstrated. Then, follow these steps:

1. Identify the agent types for which the transition function should be invoked and include these types in the call parameter.
2. Examine the function calls, such as edgestates, to determine which types are utilized. Add these types to the read parameter.
3. If you access the first argument of the transition function (representing the agent's state), include that type in the read parameter as well.
4. Should you intend to return a modified agent state, add that type to the write parameter.
5. If your function includes additional add_edge! or add_agent! calls, incorporate their respective types into the write parameter.
6. Be aware that all existing agents and edges will be removed from the simulation unless their types are also specified in the add_existing parameter.

Following this schema we get for our transition functions

apply!(sim, calc_demand, Buyer, [ Buyer, Seller, KnownSeller ], Bought);

and

apply!(sim, calc_price, Seller, [ Seller, Bought ], Seller);

Working with Globals

To summarize the state of a simulation, Vahana uses the map-reduce combination from functional programming. First, a function is applied to each agent or edge state, and then the result is reduced using a binary function.

E.g. to calculate the excess demand we write

mapreduce(sim, b -> b.x - b.y, +, Bought)

-643.4508421278501

The last argument of Vahana's mapreduce specifies the agent or edge type for which the aggregation should be performed. The anonymous function in the second position describes the assignment for each instance of that type. In this case, the function receives an edge of the 'Bought' type and calculates the additional quantity of good x that was purchased. This value is then summed across all edges of the specified type.

To calculate the average price we define a helper function

function calc_average_price(sim)
    m = mapreduce(sim, s -> s.p * s.d_y, +, Seller)
    q = mapreduce(sim, s -> s.d_y, +, Seller)
    m / q
end

calc_average_price(sim)

1.6138812107905367

And now we have all elements to run the simulation, e.g. for 5 steps:

for _ in 1:5
    apply!(sim, calc_demand, Buyer, [ Buyer, Seller, KnownSeller ], Bought)
    push_global!(sim, :x_minus_y, mapreduce(sim, b -> b.x - b.y, +, Bought))
    apply!(sim, calc_price, Seller, [ Seller, Bought ], Seller)
    push_global!(sim, :p, calc_average_price(sim))
end

To get a resulting timeseries, we use the get_global function:

get_global(sim, :p)

5-element Vector{Float64}:
 1.287669931251145
 1.173269381255291
 1.1540756786786697
 1.3430127391888713
 1.3728599329103153

Investigating the Simulation State

Vahana offers several methods to examine the current state of your simulation. For example, the user-defined show methods for the model and simulation instances, which provide a quick summary of your model/simulation:

model

Model Name: Excess Demand
Agent(s):
	 Type Buyer
	 Type Seller
Edge(s):
	 Type KnownSeller with Hint(s): Stateless
	 Type Bought
Parameter(s) with default values:
	numBuyer: 50
	numSeller: 5
	knownSellers: 2
Global(s) with init values:
	x_minus_y: Float64[]
	p: Float64[]

sim

Model Name: Excess Demand
Simulation Name: Excess Demand
Agent(s):
	 Type Buyer with 50 agent(s)
	 Type Seller with 5 agent(s)
Edge(s):
	 Type KnownSeller with 100 edge(s) for 50 agent(s)
	 Type Bought with 50 edge(s) for 5 agent(s)
Parameter(s):
	 :numBuyer : 50
	 :numSeller : 5
	 :knownSellers : 2
Global(s):
	 :x_minus_y |> last : -43.26708128590373 (length: 5) 
	 :p |> last : 1.3728599329103153 (length: 5) 

Vahana offers the show_agent function to inspect the state of individual agents. This function displays comprehensive information about a randomly selected agent of the specified type. Additionally, users have the option to specify a particular agent identifier if they wish to examine a specific agent. The show_agent function returns the identifier of the selected agent.

show_agent(sim, Seller, 1)

Id / Local Nr: 0x0200000000000001 / 1
State:
    p=0.9110613021731456
    d_y=366.2879763958845
Edge(s):
    Bought
	from:              edge.state:
	0x0100000000000002 Bought(17.067849697434912, 3.952401487539065)
	0x0100000000000008 Bought(18.568427199691737, 80.1109808515726)
	0x010000000000000a Bought(15.338337003796982, 29.198908723698427)
	0x0100000000000011 Bought(35.654331612710834, 66.51565336432876)
	0x0100000000000014 Bought(54.367406213244216, 19.72405213973325)
	... (5 not shown)

0x0200000000000001

The show_agent function has an optional keyword argument, neighborstate, which enables the user to examine the state of neighboring agents. The neighborstate argument should be a vector of symbols representing the field names that should be displayed.

show_agent(sim, Seller, 1; neighborstate = [ :B ])

Id / Local Nr: 0x0200000000000001 / 1
State:
    p=0.9110613021731456
    d_y=366.2879763958845
Edge(s):
    Bought
	from:              edge.state:
	0x0100000000000002 Bought(17.067849697434912, 3.952401487539065) B=20.0,
	0x0100000000000008 Bought(18.568427199691737, 80.1109808515726) B=78.0,
	0x010000000000000a Bought(15.338337003796982, 29.198908723698427) B=37.0,
	0x0100000000000011 Bought(35.654331612710834, 66.51565336432876) B=85.0,
	0x0100000000000014 Bought(54.367406213244216, 19.72405213973325) B=69.0,
	... (5 not shown)

0x0200000000000001

As mentioned in the Agent and Edge Types section, all agent and edge types in Vahana must be of type bitstype. This has the usefull side effect that the state of the agents and edges can be nicely converted into a DataFrame.

It is important to note that the DataFrame in a parallel simulation contains only the agents or edges of the process in which the function is called, and not those of the complete simulation. If the latter is required, all_agents or all_edges can be used.

first(DataFrame(sim, Bought; types = true), 10)

To get the DataFrame for the Globals, we call the GlobalsDataFrame function for our sim. Be aware, that only global variable that are vectors are added to the DataFrame.

GlobalsDataFrame(sim)

Finish the Simulation

Vahana employs an internal C library for memory allocation during simulations. Upon completing a simulation, it is necessary to invoke the finish_simulation function to properly deallocate the memory resources utilized. This function returns the global variables associated with the concluded simulation.

finish_simulation!(sim)

Vahana.var"Globals_Excess Demand"([-92.84518265560759, -173.41767821162122, -60.5229521761736, -20.17287682197647, -43.26708128590373], [1.287669931251145, 1.173269381255291, 1.1540756786786697, 1.3430127391888713, 1.3728599329103153])

Understanding Vahana's Edge Structure

When we define edge types like KnownSeller or Bought, you might notice that these structs don't contain any information about the source or target agents of the edge. This is by design in Vahana, which uses a specific internal structure to represent edges efficiently.

Internally, Vahana declares a parametric type for edges:

struct Edge{T}
    from::AgentID
    state::T
end

In this structure, T is the type of our edge (like KnownSeller or Bought), and from is the ID of the agent at the source of the edge. You might wonder why there's no to field for the target agent. The reason lies in how Vahana stores these edges.

Vahana uses container structures (like dictionaries) to store edges. The exact type of container depends on certain optimization hints (see Edge Hints for more details), but a typical structure might look like this:

Dict{AgentID, Vector{Edge{T}}}

This design means that the target agent's ID is implicitly stored as the dictionary key. Adding it to the Edge struct would be redundant and would unnecessarily consume memory and CPU cycles. As a user of Vahana, you don't need to interact with this internal structure directly, but understanding it can help you design more efficient models and better understand how Vahana works under the hood.

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