A COMPARISON OF DIPLOMACY GAMEBOARD GRAPH SEARCH

ALGORITHMS

Daniel P. Stormont and Vicki H. Allan

Department of Computer Science, Utah State University, Logan, Utah, U.S.A.

Keywords:

Agent, Diplomacy, Search.

Abstract:

The boardgame Diplomacy has been used as a testbed for multiagent systems almost since the time of its

introduction in 1959. The reason is that the game presents a number of interesting challenges to artiﬁcial intel-

ligence researchers: a state space that is too large to be tackled by brute force searches, imperfect information

due to simultaneous movement, no random elements, and non-binding negotiations between the seven players.

This paper looks at just one aspect of creating an agent for playing Diplomacy – ﬁnding the fewest number of

moves to achieve a victory in the game, if the player was unopposed. This planning function forms the basis

for a more sophisticated move planner that also takes into account the game state and the other players. Three

search algorithms are compared to determine which is the most effective (in terms of the number of map nodes

expanded during the search).

1 INTRODUCTION

Researchers in multiagent systems seek environments

that provide difﬁcult algorithmic challenges and re-

alistic situations in order to advance the state of the

art. The boardgame Diplomacy is just such an en-

vironment. It provides challenges in many areas of

active research for agents: planning, cooperation, ne-

gotiation, trust, and coalition formation, just to name

a few. It is for this reason that there are a number

of testbeds for multiagent systems based on Diplo-

macy, including the Diplomacy Artiﬁcial Intelligence

Development Environment (DAIDE) (DAIDE, 2011)

and DipGame (Fabregues and Sierra, 2009).

This paper addresses one element of creating a

planner for a Diplomacy agent: an efﬁcient search al-

gorithm for determining the shortest path to achieving

victory in the game. For the purposes of this paper,

the search is run from the starting positions for each

of the seven players and the optimal path to victory

is determined without taking into account the posi-

tion of any opposing players or other elements that

need to be considered for an optimal planner; such as

negotiated agreements between players, the relative

strengths of the players, and the need for cooperation

between agents or units of a single agent in order to

achieve the goals. Thus, the planner described here is

just the basis of a more sophisticated planning agent

and the search described in this paper would need to

be rerun or updated as the game state changes during

play.

After a brief introduction to the game Diplomacy

with an emphasis on the gameboard and its represen-

tation, the paper will describe the three search algo-

rithms selected for comparison, describe the design of

the software developed for the comparison, detail the

setup of the experiment, provide expected and actual

results from the comparison, and provide conclusions

and plans for future work on a Diplomacy agent based

on this work.

2 THE GAME OF DIPLOMACY

The game of Diplomacy was created by Allan B. Cal-

hamer in 1959, based on the work of one of his col-

lege professors, Sidney B. Fay (Calhamer, 2000) (Fay,

1934). The game attempts to recreate the political

situation in Europe prior to the First World War and

the system of secret alliances that initially maintained

the peace in Europe, but would eventually lead to the

greatest conﬂict in history up to that time. To do this,

the game incorporates a number of elements into the

game play. There is a deﬁned negotiation period be-

fore every movement phase during a turn of the game.

There are no rules for how these negotiations occur:

they can be secret or public, at the gameboard or in

371

P. Stormont D. and H. Allan V..

A COMPARISON OF DIPLOMACY GAMEBOARD GRAPH SEARCH ALGORITHMS.

DOI: 10.5220/0003753103710374

In Proceedings of the 4th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2012), pages 371-374

ISBN: 978-989-8425-96-6

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

another room, and any agreements reached are non-

binding. The only restriction is that the negotiation

period is typically time limited. After negotiations, all

players submit their planned moves in writing (or via

a computer) and the moves are adjudicated simultane-

ously. There are no elements of chance in the move-

ments (no dice rolling or card drawing) and the initial

strengths of the players will dictate cooperation be-

tween players, at least initially, as no player is strong

enough to win the game without assistance.

2.1 Representation of the Gameboard

Figure 1 shows the standard Diplomacy gameboard.

There are 75 provinces on the board (81 if coastal

areas are taken into account), which are connected

along their borders, complicating the connections be-

tween them. There are also three different types of

provinces: coast, land, and sea. Land areas can only

be occupied by armies, sea areas can only be occupied

by ﬂeets, and coastal areas can be occupied by either.

The small circles on the map are supply centers. The

objective of the game (and the goal of the search al-

gorithms described in this paper) is for one player to

control 16 supply centers by either having been the

last player to pass through that province (it is actu-

ally a little more complex in the game since control

of supply centers is determined on every other turn -

that has been ignored for the purposes of this study)

or to have a unit in the province.

Figure 1: The Diplomacy gameboard.

Figure 2 shows the graph generated from the map

in ﬁgure 1. In this graph, the provinces are shown as

different colored nodes. Coast provinces are tan, land

provinces are green, and sea provinces are blue. A

unit can traverse any of the edges connecting nodes,

as allowed by the unit type. For example, an army

can not follow an edge from a coast region to a sea

region since only ﬂeets can occupy a sea region. This

unit type-based limitation on movement is the reason

for the three provinces with dashed lines (Bulgaria,

Spain, and Saint Petersburg). These provinces have

more than one coast region, which limits the possible

traversals by a ﬂeet from those provinces to a neigh-

boring province. Provinces with supply centers are

indicated by bold text in the graph.

Figure 2: A graph showing the connections between

provinces on the Diplomacy gameboard.

2.2 Starting Positions

Figure 3 shows the starting positions and unit types

for each of the seven players in Diplomacy: Austria,

England, France, Germany, Italy, Russia, and Turkey.

Each of the players starts with three units, except for

Russia, which starts with four. These starting posi-

tions and unit types are critical to this comparison of

search algorithms as they comprise the ﬁrst ply of the

search tree for each of the players.

Figure 3: A Diplomacy gameboard showing the starting lo-

cations and unit types for each player.

3 SEARCH ALGORITHMS

SELECTED

Three common graph search algorithms were selected

for comparison in ﬁnding the shortest number of

moves for each player to reach the goal state of hav-

ing passed through or occupying 16 supply centers

on the Diplomacy map graph shown in ﬁgure 2. For

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372

each player, the nodes occupied in the starting posi-

tion are selected as the ﬁrst ply of the graph search, as

shown in ﬁgure 4. These starting positions also satisfy

the goal condition for occupying three supply centers

(four for Russia), meaning the algorithms have to ﬁnd

the shortest path(s) through the graph, starting with

the ﬁrst ply of the search in the player’s home na-

tion to pass through or occupy an additional 13 supply

centers (12 for Russia).

Figure 4: An example of the ﬁrst ply of the Diplomacy

gameboard search for the German player.

In ﬁgure 4, the root of the search tree is the na-

tion for that player (Germany in the example). The

ﬁrst level of the search tree are the nodes correspond-

ing to the starting positions for that player. (In the

case of Germany, there are armies in Berlin and Mu-

nich and a ﬂeet in Kiel.) Note that the nodes for

the starting positions are colored green. That is be-

cause these nodes are supply centers that are occu-

pied by the player at the beginning of the game. The

next layer shows the expansion of the graph nodes

for provinces connected to the starting provinces in

the Diplomacy graph. Red nodes are provinces that

can’t be occupied by that type of unit. For exam-

ple, the unit in Berlin can not enter the Baltic Sea

node because it is an army and only ﬂeets can oc-

cupy sea provinces. Gray nodes are nodes that are

in the visited list because they have already been tra-

versed. (The gray nodes in the ﬁgure correspond to

the starting nodes.) Finally, nodes with bold text are

supply centers (goal states). The criteria for selecting

the search algorithms were that the search algorithm

be usable on a highly connected graph, like the Diplo-

macy map graph, and that they use varying degrees of

heuristics. One search was selected that doesn’t uti-

lize heuristic values at all (breadth ﬁrst search), one

was selected that only utilizes heuristic values (greedy

best ﬁrst search), and one was selected that utilizes

both heuristic values and the actual cost of the path

found so far (A* search). The details of these algo-

rithms can be found in (Russell and Norvig, 2003).

Brief descriptions of the algorithms and the heuristics

applied are provided in the sections that follow.

3.1 Breadth First Search

Breadth ﬁrst search was chosen as the non-heuristic

search algorithm. In the example shown in ﬁgure 4,

the algorithm will start by inserting the three start-

ing provinces (Berlin, Kiel, and Munich) into a ﬁrst-

in/ﬁrst-out (FIFO) queue. The goal count is also set

to three, since the three starting positions are sup-

ply centers (goal nodes). Since they are goal nodes,

when they are added to the queue, these provinces are

added to the visited list to prevent cycles. Then, the

provinces will be extracted from the queue in alpha-

betical order (since that is the order they were inserted

in) and the provinces connected to them that are legal

moves for the type of unit occupying the province and

are not already in the visited list will be added to end

of the queue. To take the province of Berlin as an ex-

ample, the Baltic Sea will not be added to the queue

because it would not be a legal move for the army in

Berlin and Kiel and Munich will not be added to the

queue because they are already in the visited list. This

means Prussia and Silesia will be added to the queue

and then Kiel will be removed from the queue for ex-

pansion. This continues until the supply center count

reaches 16, at which time the search is terminated.

3.2 Greedy Best First Search

Greedy best ﬁrst search was selected as an exam-

ple of a heuristic-only search algorithm. Greedy best

ﬁrst search proceeds as described in the breadth ﬁrst

search, except that each node has an associated f-

value where f (x) = h(x). The heuristic value (h(x))

is set to ﬁve initially, for all players except Russia.

Because Russia starts with four units instead of three,

the initial heuristic value is set to four. These heuris-

tic values reﬂect a theoretical minimum value for the

distance to the number of nodes that unit needs to con-

tribute to the overall goal of 16 supply centers. When

a goal node is entered into the queue, the heuristic

value for it is decremented by one, so in the case of

Germany as illustrated in ﬁgure 4, the initial heuris-

tic will be h(x) = 5. When Berlin, Kiel, and Munich

are added to the queue, the heuristic value associated

with each of these provinces will be decremented to

h(x) = 4. The queue is a priority queue, so lower f-

values will be extracted from the queue ﬁrst in FIFO

order. In this case, there will be no difference in

the extraction order from the queue; however, when

Denmark and Holland are added to the queue, their

heuristic values will be h(x) = 3 because they are goal

nodes, so they will be extracted from the queue before

the remaining provinces on the same level of the tree

– and their children will also have h(x) = 3, unless the

child is also a supply center, in which case it will have

a value of h(x) = 2. The search essentially becomes a

depth ﬁrst search on these nodes at this point.

A COMPARISON OF DIPLOMACY GAMEBOARD GRAPH SEARCH ALGORITHMS

373

3.3 A* Search

A* search was selected as an example of a search that

uses both heuristic and actual cost values. The f-value

for A* search is f (x) = h(x) + g(x), where the h(x)

is the same as described in the previous section on

greedy best ﬁrst search, but g(x) is a cost function

that is incremented by one for every level of expan-

sion of the search tree. Using the example of ﬁgure 4,

the initial f-value is f (x) = h(x) + g(x) = 5 + 0 = 5.

After the ﬁrst three nodes are inserted into the prior-

ity queue (the same as for greedy best ﬁrst search),

the f-values are f (x) = 4 + 1 = 5 so they will still be

extracted in FIFO order. When Denmark and Hol-

land are inserted into the queue, their f-values will

be f (x) = 3 + 2 = 5, but the f-values of the other

provinces that are not supply centers (for example,

Helgoland Bight) will be f (x) = 4 + 2 = 6, so these

two provinces will be extracted from the queue ﬁrst

for expansion.

4 EXPERIMENTAL SETUP

To test the search algorithms, the three algorithms are

used to search the graph of starting positions for each

of the seven players in Diplomacy. The number of

nodes expanded during the search for each of the na-

tions and the total nodes expanded are used as the ba-

sis of comparison for the three algorithms. Because

the starting positions never change, there is no reason

to run the tests more than once for each algorithm.

5 RESULTS

The following sections summarize the results of the

search algorithm tests for each of the three search

algorithms. The theoretical results are a hand-

calculated value of expanding the search tree for the

German player, as was illustrated for the ﬁrst two lev-

els in ﬁgure 4. The actual results are the results of

executing the code for each of the three search algo-

rithms for all seven players.

5.1 Theoretical Results

Table 1 shows the result of manually exercising

the three search algorithms on the starting positions

shown in ﬁgure 4. It is somewhat surprising that, at

least for the starting position of Germany, breadth ﬁrst

search expands fewer nodes in the search tree than ei-

ther greedy best ﬁrst search or A* search. This may

be an aberration due to the unique starting position of

Table 1: Nodes Expanded by Search Algorithms for Start-

ing Position of Germany.

BFS Greedy BFS A* Search

33 41 36

Germany in what is essentially the center of the map,

so other starting positions also need to be evaluated.

5.2 Actual Results

Implementation and testing of the search algorithms

described here continues in simple agents that play a

“no-press” (no negotiations) game of Diplomacy.

6 CONCLUSIONS AND FUTURE

WORK

The search described in this study is just a preliminary

planning step for a practical planning agent for play-

ing the game of Diplomacy. A planning agent would

also need to take into account the locations of other

units on the gameboard (both hostile and friendly), the

relative strengths of the other players, any negotiated

agreements with other players, the need to protect ter-

ritory already captured, the need to provide support

to other units in order to capture territory, changes in

the numbers of units on the board, retreats, and the

changing state of the gameboard each turn.

REFERENCES

Calhamer, A. B. (2000). Calhamer on Diplomacy: The

Boardgame “Diplomacy” and Diplomatic History.

1stBooksLibrary, Bloomington, Indiana.

DAIDE (2011). Reading.

Fabregues, A. and Sierra, C. (2009). A testbed for mul-

tiagent systems. Technical Report IIIA-TR-2009-09,

Autonomous University of Barcelona.

Fay, S. B. (1934). The Origins of the World War. The

Macmillan Company, New York.

Russell, S. and Norvig, P. (2003). Artiﬁcial Intelligence: A

Modern Approach. Pearson Education, Upper Saddle

River, New Jersey.

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