On the Effects of Team Size and Communication Load on the

Performance in Exploration Games

Chris Rozemuller

, Mark Neerincx

1,2

and Koen V. Hindriks

Intelligent Systems, Delft University of Technology, Mekelweg 4, Delft, The Netherlands

TNO, Postbus 23, 3769ZG Soesterberg, The Netherlands

Keywords:

Performance, Exploration Game, Communication, Team Size, Topology, Resource Redundancy, Task Size.

Abstract:

Exploration games are games where agents (or robots) need to search resources and retrieve these resources.

In principle, performance in such games can be improved either by adding more agents or by exchanging

more messages. However, both measures are not free of cost and it is important to be able to assess the

trade-off between these costs and the potential performance gain. The focus of this paper is on improving our

understanding of the performance gain that can be achieved either by adding more agents or by increasing

the communication load. Performance gain moreover is studied by taking several other important factors

into account such as environment topology and size, resource-redundancy, and task size. Our results suggest

that there does not exist a decision function that dominates all other decision functions, i.e. is optimal for

all conditions. Instead we ﬁnd that (i) for different team sizes and communication strategies different agent

decision functions perform optimal, and that (ii) optimality of decision functions also depends on environment

and task parameters. We also ﬁnd that it pays off to optimize for environment topologies.

1 INTRODUCTION

Exploration games are games where agents (or ro-

bots) need to search for resources and retrieve these

resources (Hindriks and Dix, 2014). Many real-life

applications are instances of such games including,

for example, package delivery problems (which so-

metimes only require minimal search) to search and

rescue missions (where search typically takes most of

the time). A task in an exploration game is deﬁned

by a speciﬁc ﬁnite (sub)set of all available resources

that need to be located and retrieved in a particular

order (a task is deﬁned as a sequence of resource ty-

pes). The order imposed on the items to be retrieved

is a key difference with typical foraging tasks. We as-

sume that the map (i.e., topology of the environment)

that needs to be explored is ﬁnite and known but that

the initial distribution of resources is unknown. In this

paper, performance in exploration games is measured

by the time to complete a given task.

Task performance in exploration games can be im-

proved by adding more agents because, in principle,

they can perform tasks in paralelle. This is true even if

agents do not communicate with each other. If resour-

ces are sufﬁciently available and agents act rationally,

it is possible to solve an exploration game without any

communication. The “only” condition that agents that

do not communicate need to satisfy is that they do

not waste resources (they need to ensure that resource

consumption is necessary to complete the task). The

performance gain of adding one more agent, however,

decreases relative to the number of agents that are al-

ready deployed. Even worse, if physical size of robots

and the space they occupy is also taken into account,

there typically is a point where adding more robots

will decrease performance again as robots become ob-

stacles blocking each other’s movement (Rosenfeld

et al., 2006). But even if we abstract from such ‘na-

vigational issues’, as we will do in this paper, and we

can safely assume that adding more agents will not

decrease performance, we cannot assume that adding

more agents to the mix will increase performance. Fi-

nite tasks that can be completed can only require at

most a ﬁnite amount of effort, which means that there

must be a point at which adding another agent will not

yield any performance gain any more.

Besides by adding more agents, performance can

usually also be improved by adding communication

between agents. Communication, for example, can

be used to avoid duplication of effort. If agents in-

form each other about the locations they have visi-

ted, for example, agents can avoid exploring that lo-

Rozemuller, C., Neerincx, M. and Hindriks, K.

On the Effects of Team Size and Communication Load on the Performance in Exploration Games.

DOI: 10.5220/0006661002210230

In Proceedings of the 10th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2018) - Volume 2, pages 221-230

ISBN: 978-989-758-275-2

221

cation twice. Similarly, by communicating about the

targets agents set themselves (their goals) agents can

avoid retrieving the same type of resource twice. It

is known from the literature that even a limited ex-

change of messages can already have a huge impact

on performance, see e.g., (Farinelli et al., 2004). Gi-

ven that exploration games are ﬁnite, it also is clear

that there is some point at which more communica-

tion does not lead to any performance gains any more.

A team of agents will only be able to perform better

if they can further improve the coordination of their

actions by communicating more. We aim to increase

our understanding of how much communication can

contribute to the performance of an agent team in ex-

ploration games.

Like foraging games, optimal solutions are

unknown for exploration games in general and the-

refore agent-based simulation approaches are used to

empirically establish the performance of a coordina-

tion strategy (Zedadra et al., 2017). The results from

this empirical research can then be used to design bet-

ter and more efﬁcient coordination strategies for dif-

ferent types of exploration games. Our work is moti-

vated by this and aims to provide guidelines that can

inform this design. As a designer, it is particularly

useful to understand how much performance can be

improved by either adding another agent to the mix

or by increasing the communication load for a given

number of agents. The number of agents (robots) and

number of messages exchanged between agents on

average can be viewed as a budget that is available

to a designer. It is useful for a designer to better un-

derstand the return on investment of adding another

agent or increased the communication load.

In general, from a design perspective, it is sim-

pler to add another agent to a system than to incre-

ase the messages that agents exchange. Exchanging

more messages typically requires a more complicated

coordination strategy to be effective and thus compli-

cates system design because interdependencies bet-

ween agents are increased. A more complicated coor-

dination strategy, moreover, comes at the cost of hig-

her processing power, additional requirements on har-

dware, and higher risks of failure. Additional design

complexity, however, may be justiﬁed when commu-

nication can yield dramatic performance gains. This

is sometimes the case, as we noted above, but to un-

derstand when requires an insight into when such per-

formance gains are to be expected. Providing this

kind of insight is one of the aims of this paper.

The main contributions of our paper are (i) that we

provide convincing evidence that there is not a single

coordination strategy that is optimal for all cases and

(ii) show which type of coordination strategies are

best suited for optimizing performance for speciﬁc

map topologies of an exploration game. We also show

how the performance of different strategies depends

on team size and communication load, and how per-

formance is inﬂuenced by additional factors such as

map and task size, and resource redundancy.

The remainder of the paper is organised as fol-

lows. Section 2 discusses related work. In Section

3 we introduce our approach and discuss the agent

decision functions used in our simulations. Section

4 presents the experimental set-up we have used to

study performance gains. In Section 5 we discuss our

results. Section 6 concludes the paper.

2 RELATED WORK

The effects of coordination and communication on

performance have extensively been studied empiri-

cally for real robot systems; (Farinelli et al., 2004)

provides a good survey. This survey presents a de-

tailed overview of coordination mechanisms that have

been proposed and concludes that to obtain reasona-

ble performance in most cases little communication is

required. However, none of the reported studies pro-

vides a detailed study of the trade-off between com-

munication, team-size, and performance.

(Pitonakova et al., 2016) demonstrates the value

of coordination by showing that both social and non-

social coordination mechanisms, i.e. with and wit-

hout communication, can improve a robot team’s efﬁ-

ciency. (Pini et al., 2013) studies coordination mecha-

nisms in relation to how tasks are partitioned. They

conclude that communication is beneﬁcial to avoid

duplication of effort, but has the drawback of biasing

the exploration, even slowing it down in some cases as

a result. These works focus on issues such as avoiding

collisions and path ﬁnding, whereas our focus is more

on task related coordination issues, such as avoiding

duplication of effort and efﬁcient destination alloca-

tion. Our results, moreover, go beyond these studies

by providing a more detailed overview of which per-

formance gains can be achieved by means of incre-

asing communication and team-size, while taking the

inﬂuence of various environment factors into account.

(Liemhetcharat et al., 2015) uses a set-up similar

to ours, but studies heterogeneous teams instead of

homogeneous teams as we do, and a setting where re-

sources are replenished instead of consumed as is the

case in our work. Our focus, moreover, is on commu-

nication load and we take more environmental factors

into account.

Several simulation-based studies that also investi-

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

222

gate the relation between team-size, communication,

and performance have used the Blocks World for Te-

ams (BW4T) simulation environment. BW4T is a tes-

tbed for exploration games (Johnson et al., 2009) with

blocks of different colors as resources and has been

speciﬁcally designed for analysing and evaluating the

ability to cooperate in multi-agent teams. Both (Har-

bers et al., 2012) and (Wei et al., 2014) use BW4T to

investigate the impact of different types of communi-

cation on team performance. These works examined

agents that use four different communication proto-

cols: (i) agents that do not communicate, (ii) agents

that only exchange information about the knowledge

they have about the environment, i.e. the location of

resources, (iii) agents that only communicate their in-

tentions, i.e. what they plan to do, and (iv) agents

that both communicate about their knowledge and in-

tentions. (Harbers et al., 2012) concludes that it is

more effective to communicate about intentions than

about knowledge. (Wei et al., 2014) shows, moreover,

that interference between robots can diminish the po-

sitive effects of communication. Running simulations

using BW4T takes time, however, which has limited

the size of the experiments that could be run to less

than 10 agents and small environments. In contrast,

we vary the size and topologies of environments in

our experiments, systematically explore the impact of

various other environment parameters, and vary team

sizes from 1 to a 100 agents.

3 SIMULATION APPROACH

We use a discrete simulation model to empirically

investigate performance of various agent decision

functions for exploration games. In our approach we

systematically vary parameters that deﬁne exploration

games, including map topology and size, distribution

of different types of resources, task size, and num-

ber of agents (team size) deployed for completing the

task. We also systematically vary basic tactics that

agents use for exploration and coordination.

3.1 Simulator

We use a very fast multi-agent system simulator

for exploration games developed in MATLAB cal-

led MEG (short for Matlab Exploration Game). The

map topology of an exploration game is modelled by

a (symmetric) distance matrix that consists of distan-

ces between each pair of locations on the map. We

assume that a unique location is singled out on the

map as the target location where resources need to be

delivered called the drop zone. Even though a single

drop zone somewhat simpliﬁes the task, we believe

this constraint is reasonable for the purposes of this

paper and also limits the number of topologies that

we need to simulate to a feasible number. The simu-

lator keeps track of which resources are being retrie-

ved and moved to other locations. Each time an ex-

ploration game is loaded and initialized the simulator

randomly distributes a pre-deﬁned amount of resour-

ces on locations on the map. The initialization of the

task sequence is based on the redundancy of resources

and on task length parameters. All agents initially are

located in the drop zone.

MEG is a discrete event simulator where all agents

perform actions simultaneously at a discrete point in

time T and the effects of these actions on the envi-

ronment are computed at the end of each time step.

After each step the global clock T is increased to

T + 1. Agents maintain a model of the environment

(their beliefs) and set targets (goals to go somewhere

or retrieve a known resource). The simulator auto-

matically updates the beliefs of agents based on the

resources perceived at the location an agent is at and

the messages received from other agents at the end of

each time step. The performance of the simulator thus

effectively only depends on the time needed to com-

pute a decision on which action to perform next for

each agent and to compute the effects of performing

these actions simultaneously on the environment. Our

simulator is fast enough to run millions of simulations

in a reasonable time (compared with, for example, a

real-time simulator such as the BW4T we gain a speed

increase of roughly a factor 25, 000).

Figure 1 shows the control ﬂow that is executed by

the simulator. Choices are in blue, actions are in gray,

and for each time step T the green block repeats the

same cycle again by executing all agents for as long

as the task set has not been completed yet. For each

agent a, the simulator keeps track of two important

parameters: the target location R(a) and N(a) the time

that agent a is estimated to arrive at and occupy that

location. As long as N(a) > T , at a time step an agent

performs one step towards its target location lowering

the distance that still needs to be travelled. Once an

agent reaches its target location, i.e. N(a) = T , it gets

access to this location if it is not occupied by another

agent. If the agent gets access, it occupies the location

and the boolean mapping occupied is updated to mo-

del this fact. We note that agent movement is not ob-

structed by locations that are already occupied but can

move freely past such locations. An agent that occu-

pies a target location either drops a resource that it

retrieved previously, retrieves a resource that is avail-

able at the location if it believes that resource still

On the Effects of Team Size and Communication Load on the Performance in Exploration Games

223

Figure 1: Control Flow of MEG Simulator.

needs to be delivered at the drop zone, or otherwise

selects a (different) target location. Selection of a tar-

get location depends on the agent’s exploration stra-

tegy. If the agent cannot access the location yet, the

estimated time of arrival N(a) is increased with one

and at the next time step it is checked again whether

the agent can access the location.

At a target location agents can observe which re-

sources are available at that location. At the beginning

of each turn agents are updated on task progress, i.e.

on the resource types that still need to be delivered.

The simulator also allows agents to communicate up-

dates on perceived resources (belief updates) as well

as changes to the targets that they set for themsel-

ves (their goals) to all other agents. That is, agents

can broadcast their belief updates and goals. Whether

agents do so depends on the decision function they

use. Messages sent to an agent are available to that

agent at the beginning of the next turn.

The output of a simulation run consists of the

number of turns, i.e. T , that were needed to retrieve

and deliver all resources required to complete the task

and the average number of messages each agent sent.

3.2 Environment and Task Parameters

The simulation model allows for varying a number of

parameters, including the following:

• Size of the map, i.e. the number of locations;

• Map topology, or structure of the map, i.e. whet-

her locations are connected and, if so, what the

distance between these locations is;

• Task size, or the length of the task sequence, i.e.

the number and order of the resource types that

need to be located and retrieved;

• Resource redundancy, i.e. a multiplier r that

ensures that a the number of items of a particu-

lar resource type available on the map is r times

the number that is actually needed to complete the

task; r = 1 means that the resources available ex-

actly match what is needed.

The map size and topology parameters determine

the cost of travelling to a location. By varying the

distances between locations we aim to establish when

a random exploration tactic will perform better than

a greedy tactic. If, for example, the distance bet-

ween any two locations is the same, then randomly

selecting a room cannot result in increasing the tra-

velling costs. If, on the other hand, some locations

are much more distant than other locations, then at

some point it may become more efﬁcient to apply a

greedy tactic and select the closest location to avoid

having to travel long distances.

By increasing the task size, we aim to establish

which tactics will increase the efﬁciency of larger te-

ams more because they facilitate multiple agents to

perform more subtasks effectively in parallel. Finally,

we aim to verify whether a higher resource redun-

dancy factor r will favour greedy and communication

tactics because resources can be assumed to be avai-

lable closer to an agent’s current location.

3.3 Agent Decision Functions

In order to complete a task, agents need to explore and

coordinate their efforts to locate and retrieve resour-

ces. We therefore specify basic tactics for exploration

and coordination which can be combined to obtain

different types of agent decision functions. In this

work we assume agent teams are homogeneous, i.e.

all agents use the same strategy, and do not consider

heterogeneous teams.

Exploration Tactics The basic tactics that we con-

sider for exploration are a greedy and a random tactic.

We assume that agents are always greedy, i.e. select

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

224

the closest location, if they know a location where a

resource can be found that is needed next. (Recall

that we assume the map is known.) If an agent uses

the greedy exploration tactic it will also select the clo-

sest location that has not yet been visited. By default,

we assume that an agent is a greedy explorer. The

random tactic instead selects a random location from

those that have not been visited yet. We further diffe-

rentiate by considering when the random exploration

tactic is applied: at the beginning of a game (random

start tactic) and thereafter during the rest of the game

(random exploration tactic). Of course, an agent may

both select a target location randomly at the start as

well as during the game, thus effectively applying the

combination of both tactics. Furthermore, we assume

that our agents are persistent: They will keep trying to

get access to a location until it becomes available and

will not select a new target location before they have

gained access to their current target location. We thus

have two tactics that an agent can use instead of the

default greedy exploration tactic:

• Random Start Tactic. At T = 0, agents randomly

select a location that has not yet been visited to go

to instead of going to the closest location ﬁrst.

• Random Exploration Tactic. At T > 0, agents

randomly choose a target location that has not

been visited to explore next.

The effect of randomly selecting an (initial) tar-

get location is that agents will more evenly distribute

over the map. This usually will reduce duplication of

effort as fewer agents will try to visit the same room.

The downside of an agent that applies a random tactic

is that on average it will increase the distance travel-

led compared to an agent that uses a greedy tactic.

The random start tactic will only initially give rise

to a more even distribution on the map whereas the

random exploration tactic will ensure exploration of

all parts of the map more evenly later on in the game.

Coordination Tactics. Agents that are careful not

to waste resources do not need communication to

complete a task in an exploration game. By default,

we therefore assume that agents do not communicate.

Agents, however, can coordinate their efforts better

when they exchange information. We consider two

communication tactics. First, agents that use the up-

dates communication tactic exchange updates on the

locations that they visit: They inform other agents

about which locations they have visited and share the

information about resources found at those locations

with other agents. Other agents use this information

to not (re)visit a location already visited by another

agent and to (greedily) select locations where resour-

ces needed can be retrieved by using the information

about resources they thus obtain. In contract with ex-

ploration tactics, which only affect the agent’s own

behaviour, it is important to realize that communica-

tion tactics have an effect on the behaviour of other

agents. Second, agents that use the target communi-

cation tactic share with other agents which resource

they are delivering when they retrieve that resource

at a location. Other agents use this information to not

also then target the delivery of that same resource type

but instead will focus on delivering the resource nee-

ded next.

• Updates Communication Tactic. Agents com-

municate about which locations they have visited,

and about which resources are (no longer) availa-

ble at a location. Other agents will not consider

exploring locations that have been explored alre-

ady and will retrieve resources based on informa-

tion received from other agents.

• Target Communication Tactic. Agents commu-

nicate about which resource they are delivering

when they retrieve a resource at a location that is

required next to complete the task sequence. Ot-

her agents will anticipate and not deliver the same

resource.

The cost of communication is based on the total

count of all messages that are sent from one agent

to another agent. That is, all individual messages

are counted instead of counting the single broadcast

action that sends a message to all other agents as a sin-

gle message. We do so because each individual mes-

sage demands resources and requires establishing the

reliability of the transmission of a message from one

agent to another agent. Generally speaking, the target

communication tactic results in fewer messages being

sent than the updates communication tactic. The for-

mer tactic only requires one message to be sent for

each resource needed to complete the task whereas

for implementing the latter tactic a message needs to

be sent for every resource discovered and each room

that is visited for the ﬁrst time.

Admittedly, our tactics are quite basic and can be

reﬁned to obtain more sophisticated variants of these

tactics. We believe, however, that for our purposes

these tactics are useful as they provide for basic but

fundamentally different strategies to complete tasks

Since communication is only available at the beginning

of the next turn this introduces a new issue: Multiple agents

can decide to deliver the same resource. Therefore, at the

drop zone, agents also check if their resource is still required

eventually. If not, they will abandon it and continue with the

remainder of the task.

On the Effects of Team Size and Communication Load on the Performance in Exploration Games

225

in an exploration game. They allow us to establish

the effects of almost completely opposite tactics, i.e.

those of greedy versus random exploration tactics and

of no communication versus the communication of

updates and chosen target locations. For exploration,

for example, we thus can establish whether focus (on

nearby locations) versus spread (aiming for visiting

as many different locations as possible) improves per-

formance in an exploration game. This allows us to

investigate the efﬁciency of tactics that are generally

applicable to robots that are tasked with exploration

rather than to focus on details of very speciﬁc instan-

ces of exploration games.

Table 1: Labels of agent decision functions.

Random Random Updates Target Optimal

Start Exploration Comm. Comm. (Sometimes)

A Yes

B X Yes

C X No

D X X No

E X Yes

F X X Yes

G X X No

H X X X No

I X Yes

J X X No

K X X Yes

L X X X No

M X X Yes

N X X X Yes

O X X X Yes

P X X X X No

Decision Functions. The four tactics introduced

above can be used to create variations of the default

greedy exploration agent that does not communicate

at all. This gives rise to 16 different agent decision

functions. Table 1 introduces labels (single letters)

used to reference these decision functions in the re-

mainder of the paper. For example, agents that use

decision function G initially choose to visit the loca-

tion closest to it and then randomly visit unexplored

locations until a resource that is needed is located;

upon retrieving a resource they communicate to all

other agents that they will deliver this resource but

do not update other agents about locations visited and

resources discovered. The last column in the table in-

dicates whether a decision function is optimal at least

some of the time, i.e. dominates other decision functi-

ons for a speciﬁc experimental condition. Decision

functions that are never optimal are always outperfor-

med by another decision function.

Table 2: Topologies used in our simulations.

Equidistant Manhattan

Circle Straight line

4 EXPERIMENTAL SETUP

In our simulation experiments we varied the parame-

ters discussed in Section 3.2. For map size, we varied

the number of locations and used 10, 20 and 40 loca-

tions. We deﬁned 4 different topologies illustrated

in Table 2. Edges that connect locations in Table 2

have a distance of one.

In the equidistant topology

the distance to every other location is the same. In the

Manhattan topology all locations are placed on a grid

with the drop zone located in a corner of the grid. In

the circle topology all locations are placed in a circle

around the drop zone. Finally, in the straight line to-

pology all locations are placed on a straight line with

the drop zone located at either end of that line.

We varied task size and used sequences with

length 3, 6 or 12 resources. In our simulations we

used 7 resource types. A task sequence of 7 resources

thus could require agents to retrieve resource items

each of a different type in a particular order. The con-

straint that resources need to be delivered to the drop

zone in a particular order complicates the task if mul-

tiple agents work on it in parallel as coordination may

be required to avoid duplication of effort. Resources

needed are randomly distributed over available locati-

ons with a redundancy factor of 1, 2 or 4. If, for ex-

ample, the task requires 2 resource items of type τ and

the redundancy factor is 4, then 8 resource items of

type τ wil be made available on the map. The choice

of resources that need to be collected to complete a

task and the distribution of resources in the environ-

This may not always result in a feasible geometry in 3d

space using only straight lines; we use these structures to

demonstrate coordination issues related to connectivity and

distance.

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

226

ment, moreover, was randomized for each simulation

run. Finally, we varied team size and performed simu-

lations with 1, 2, 3, 5, 10, 20, 30, 50, and 100 agents

and used all 16 agent decision functions speciﬁed in

Section 3.3.

Combined, these variations of parameters deﬁne

3 ∗ 4 ∗ 3 ∗ 3 ∗ 9 ∗ 16 = 15, 552 conditions. Each type

of simulation condition is repeated a 100 times to

average out variation, thus giving a total of 1, 555, 200

different simulation runs that were performed.

The parameter settings that we have chosen for

our simulations allow us to evaluate the efﬁciency of

a range of coordination strategies and tactics in the

smallest possible environments that are still interes-

ting as well as in very complex environments. We

have also included team sizes that are more than twice

as large as the largest number of locations which ensu-

res we will reach a saturation point in which all locati-

ons will be permanently occupied and adding another

agent can at best only have a marginal effect.

4.1 Performance Normalization

The main performance measure of a simulation run is

the number of time steps T it takes to ﬁnish a task.

The value T for a speciﬁc run depends on environ-

ment and task parameters, tactics, and team size and

therefore these values can differ widely for different

simulation runs. To be able to compare the perfor-

mance for different parameter sets we normalize T by

scaling it to a value between 0 and 1. We do so by me-

ans of the theoretically minimal time needed to com-

plete a task T

opt

, i.e. the optimal lower bound to com-

plete the task possible, and use the average time T

single

to complete a task by a single greedy agent as an up-

per bound. It is reasonable to assume that multiple

agents should be able to outperform a single greedy

agent and would need fewer than T

single

steps.

We can compute the lower bound T

opt

analytically

by assuming that the locations of all resources are

known and the agents available perform sub-tasks in

parallel. Of course, without prior knowledge of re-

source locations it is very hard to get close to this

theoretical optimum as it requires each agent to tra-

vel directly to the right locations. We determine the

upper bound T

single

empirically by running simulati-

ons for each set of environment and task parameters

also for a single agent. We use the greedy agent A (see

Table 1) as our results show that it is most efﬁcient if

we use only a single agent to complete a task.

The normalized performance measure T

norm

then

is computed for each team size consisting of a speciﬁc

type of agent as follows:

norm

T − T

opt

Single

− T

Opt

(1)

Note that we must always have T

opt

< T

single

for tasks

of length > 1 as multiple agents can perform subtasks

in parallel. The value T

norm

is independent from en-

vironment and task parameters and therefore provides

an indication of the ability of the agents to coordinate

their efforts.

5 RESULTS AND DISCUSSION

We computed the average performance measure T

norm

and the communication load of agents (i.e., the num-

ber of messages exchanged per agent) for each si-

mulation condition that was run a 100 times. We

thus obtained performance measures for different ty-

pes of budgets (i.e., different investments of number

of agents and communication load). We plotted these

outcomes in a 3D point cloud with coordinates per-

formance, team size, and communication load. For

each conﬁguration of agent type, task size, and en-

vironment type (map size, topology, resource distri-

bution), an optimal performance point can be found

in this cloud for any team size and communication

load coordinate. We averaged the best performance

for each of these coordinates and linearly interpolated

between the data points to obtain the 2D heat map of

Figure 2, assuming that performance never degrades

when more resources are invested. The colours in this

map show the best performance T

norm

that we found

for each type of budget. Blue corresponds with a lo-

wer T

norm

value, i.e. better performance, and red with

a higher T

norm

value. The color of each point in this

map thus indicates the best possible performance for

a given budget of agents and messages.

Figure 2 shows different bands of the same co-

lour, e.g., green for T

norm

= 0.5, where performance

is the same. These iso-performance frontiers or per-

formance levels visualize the trade-off between the in-

vestment of more agents or communication resources

that designers of a multi-robot system can make to

obtain a desired performance. For example, the ﬁgure

shows that a performance of .4 can be achieved with

about 20 agents but also with only 7 agents that com-

municate with each other. Interestingly, all of these

frontiers show a more or less sharp edge around 20

messages per agent. This suggests that agents with on

average that kind of communication load are a good

choice to obtain a desired performance level. The

performance gain of investing more agents that com-

municate less is small and increasing the communica-

tion load would still require almost the same number

of robots to achieve a similar or better performance.

Our results thus suggest that providing agents with ba-

sic communication skills can signiﬁcantly reduce the

On the Effects of Team Size and Communication Load on the Performance in Exploration Games

227

Figure 2: Performance heatmap with optimal agent types.

number of robots that are needed to achieve a speciﬁc

performance level.

5.1 Performance and Tactics

Figure 2 also identiﬁes for a given budget which agent

types (see Table 1) are able to perform best and at

what performance level. It is interesting to observe

that for different budgets different agent types per-

form best. In other words, there is no single agent type

that dominates all others and performs bests for arbi-

trary budgets. For example, for budgets with less than

10 agents, agent types A, B, E, and F perform best

but performance is rather low with a normalized per-

formance T

norm

> .6, whereas for budgets with more

than 10 agents types K, M, N, and O perform nearly-

optimal. For small budgets agent type E, a greedy

agent that communicates about target delivery, seems

a particularly attractive choice. For larger budgets M,

a greedy agent with random start and target commu-

nication tactics, is a particularly attractive choice.

If we average over environment and task parame-

ters, moreover, we can conclude that 7 of our 16 agent

types are dominated by some other agent type. Gene-

rally speaking, we ﬁnd that an initial random distri-

bution of agents becomes more important when team

size becomes larger and that target communication

makes a larger team more effective. Somewhat remar-

kably the updates communication tactic is only useful

for small budgets; this appears to be the case because

the target communication tactic provides sufﬁcient in-

formation for coordinating larger agent teams. Note,

however, that if we do not average over all parameters

Figure 3: Heatmaps for different topologies.

Figure 4: Heatmaps for environment parameters.

other tactics may become relevant again. For exam-

ple, for speciﬁc topologies such as e.g. the equidistant

topology and for small budgets the random explora-

tion tactic (agent type G, see Figure 3) can outperform

other tactics.

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5.2 Environment Inﬂuence

Figures 3 and 4 show how different environment and

task parameters inﬂuence the performance for diffe-

rent budgets. These ﬁgures show best performance

for speciﬁc values of a parameter while averaging

over all other parameter settings. For example, the

left-upper heatmap in Figure 3 shows the performance

heat map for the equidistant topology.

By comparing heat maps for different redundancy

factors, we can conclude that impact of redundancy

on performance is rather small; there is less need for

communication for higher redundancy factors. The

impact of map size on performance is as one would

expect: larger maps require more agents to achieve

similar performance levels. In contrast, if the task size

is increased, more communication between agents is

needed to achieve similar performance levels.

Finally, we ﬁnd that the type of topology has a rat-

her large effect on the shape of the performance levels

that are visible in the heat maps (see Figure 3). Most

notably, whereas for most parameters the agent types

that perform best match those of Figure 2, this turns

out to be not the case for different topologies. The

heat map for the Manhattan topology matches best

with the heat map of Figure 2 averaging over all pa-

rameters. But for other topologies the heat maps are

quite different. For example, we ﬁnd that on a line and

equidistant topology the target communication tactic

can signiﬁcantly increase efﬁciency (agent I versus M

and K versus O), but the update communication tactic

only yields signiﬁcant performance gains on a Man-

hattan topology. We conclude that it is particularly in-

teresting to ﬁne-tune and optimize an agent decision

function for a speciﬁc topology.

6 CONCLUSIONS

This paper investigates what the best performance is

that can be achieved with a given budget, i.e. an in-

vestment of a speciﬁc number of agents and commu-

nication load per agent. We use a simulation approach

and a discrete event simulator for exploration games

to empirically obtain insights in how performance de-

pends on different tactics used for composing a stra-

tegy for deciding what to do next. Several explora-

tion tactics including greedy and random exploration

tactics and several communication tactics are evalua-

ted. We ﬁnd that there does not exist one dominant

strategy but that for different budgets different sets of

tactics perform best.

Our results can inform designers of multi-agent

systems for exploration game type applications. First,

our results can inform the choice of budget itself and

can be used to make a trade-off between budgets and

performance. Moreover, we found that certain combi-

nations of tactics are outperformed by other strategies

and thus are best avoided. Finally, we have shown

that for different environment and task parameters dif-

ferent strategies perform best. In particular, we found

that ﬁne-tuning of agent coordination strategies is par-

ticularly useful if agents only have to handle a speciﬁc

type of environment topology.

In future work we plan to reﬁne and evaluate the

agent tactics used in this paper and to study particu-

lar mechanisms for optimizing performance in speci-

ﬁc types of environment topologies.

ACKNOWLEDGEMENTS

This work was supported by European Union’s Se-

venth Framework Programme for research, techno-

logical development and demonstration under the

TRADR project No. FP7-ICT-609763.

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