Fixed Pattern Deviation Hypothesis of Intention Attribution
Kazunori Terada1 , Seiji Yamada2 , and Akira Ito1

Abstract— A large variety of behavioral cues which invoke
intention attribution to inanimate entities are reported. Although agents, including software agents and physical robots,
have already possessed these features, many people still can
not feel mind to them. We hypothesize that the inability of
attributing intention toward agents is caused by interpreting
agent’s behavior as fixed pattern. In other words, a human
attributes intention to an entity when it deviates fixed pattern of
behavior in an efficient way (fixed pattern deviation hypothesis).
In the present study we theoretically derived the fixed patterndeviation hypothesis and tested the hypothesis with humanparticipants. We prepared an on-line experimental system inwhich a participant and an agent play a repeated pennymatching game with a bonus round. We then conducted
experiments in which different opponent agents (human or
robot) change their strategy during the game. The experimental
results indicated that, as expected, adaptation is faster whena human is competing with robot than with another human.
This implies that a human expect intentional deviation of fixedpattern of behavior against an human and expect deterministic
and algorithmic behavior against robot.

I. INTRODUCTION
A large variety of behavioral cues which invoke intention
attribution to inanimate entities are reported, including rationality [1], [2], [3], goal or goal-directedness [4], [5], selfpropelled motion [6], [7], [8], [9], [10], equifinality [1][11],spatial contingencies [12], violation of Newton’s laws [13],[14], situatedness [14], [15] and motion interruption [16].
Although agents, including software agents and physicalrobots, have already possessed these features, many people
still can not feel mind to them. We hypothesize that theinability of attributing intention toward agents is caused byinterpreting agent’s behavior as fixed pattern. In other words,
a human attributes intention to an entity when it deviates
fixed pattern of behavior in an efficient way (fixed patterndeviation hypothesis). Although contingent behavior, forexample, may cause intention attribution toward an agent in
the beginning of interaction, it will extinct when the behavior
assumed to be generated by computer program. In the present
study we investigated the fixed pattern deviation hypothesis
with a repeated penny-matching game with a bonus round.
The fixed pattern deviation hypothesis is theoreticallyderived from rationality principle [1], [3]. Dennett [17] andGergely et al. [1],[18],[19] suggest that rationality of anaction plays a key roll in inferring goals of an agent. An
agent initiates action on the basis of desire derived frominborn instincts (self-preservation and reproduction), and
1 K. Terada and A. Ito are with the Faculties of Engineering, Dept. ofInformation Science, Gifu University, 1-1 Yanagido, Gifu, 501-1193, Japan.
Terada: terada@gifu-u.ac.jp, Ito: ai@gifu-u.ac.jp
2 S. Yamada is with the National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda, Tokyo, Japan 101-8430

then makes plans according to beliefs about the situation. The
agent will choose to perform particular instrumental action
which will lead to its goal in the most rational manner, suchas one that requires least effort or takes shortest path. The
observer should also consider the rationality of the behaviorof the agent in order to predict its future behavior, because
the observer can only perceive surface behavior of the agent,and perceived behavior per se never indicate what action will
be performed in the next moment.
Gergely et al. hypothesized the goal inference process ofan infant as follows [1]: the infant start to monitor the agent’s
action, and discover an equifinal outcome. The observed
equifinal outcome could provide then the specific content
of the intention to be attributed to the agent. He suggestthat although equifinality [11] contribute to identifying andattributing a goal to an agent, it will not allow the infant toanticipate the agent’s specific future action in a new situation.
This is because knowing the agent’s goal will provide no
information as to which of the multiple possible means
actions that could lead to the goal the agent will choose
to perform.
The rationality (efficiency) principle implies behavior variability principle [18]. Most efficient behavior is not mostefficient in a different situation. As a result, an agent keeps
to find another behavior suitable for the given situation.
This process includes change in behavior. An rational agent
must always evaluate the efficiency of the behavior. Then theagent must change its behavior when the situation changed
and the current behavior is no longer most efficient in thechanged situation. The change in behavior is observed byanother agent before the behavior completed. Threfore theobserved change in behavior of the target agent might trigger
observer’s rational inference.
The behavior variability principle is implicitly consideredin the past researches. In the studies by Luo and Baillargeon[7] and Shimizu and Johnson [20], infants attributed a goal toan agent when it choose its action freely. The most effective
cue for goal-directedness in Biro and Leslie’s [21] study was
also the variability of the goal approach. According to Csibra
et. al [18] “Evidence for ‘freedom’ and for the capability ofchanging the course of action (i.e., what Premack & Premack[22] called ‘motorcompetence’) seems to be sufficient for
infants to identify an object as an agent and to treat it as
worthy of goal attribution”.
Goal-directedness of behavior implies that a variety of
behavior will lead to the same single outcome. Not only intentional agent but also physical phenomenon and machines
have the behavioral variety. Trajectories of a falling rock,for example, differs depending on the situation. Routes of a

motor-driven toy car differs depending on the shape of theroad surface and obstacles. However, although the outcomesof the falling rock and the moving toy car differs, only an
intentional agent can pursue the same goal and reach thesame single outcome [11].
A goal-directed rational agent sometimes produces fixedpattern of behavior. Fixed pattern of behavior is usually
evolutionally shaped and produced by a neural network
known as the innate releasing mechanism in response to
an external sensory stimulus. Reinforcement learning agentsalso produce fixed pattern of behavior. Exploiting a reward
in a most efficient way leads an optimal action sequence andthe agent need not change it’s behavior unless the situationis changed.
Design process is creating optimal fixed pattern of object’s
behavior to fulfil one’s desire. Fixed pattern of object’s
behavior is realized by algorithm or mechanism. These
underlying principle guarantees constancy of input-output
relations of behaviors. Although physical phenomenon isgoverned by law such as gravity, physical objects neverproduce fixed pattern of behavior without intentional design
because of chaotic properties.
From the above discussion we can make a clear distinction
between intentional agents and machines in terms of behavior
recognition. The distinction is whether it can deviate fixedpattern of behavior or not. Although both intentional agentsand machines are able to produce fixed pattern of behavior,
only agents are able to violate the fixed pattern. We hypothesize that the core concept of intentionality is the intentional
deviation of fixed pattern of behavior.
II. E XPERIMENTS
In this experiments we tested the fixed pattern deviation
hypothesis which leads to the following hypothesis:
H
A human expect intentional deviation of fixed pattern of behavior against a human and expect deterministic and algorithmic behavior against robot.
The hypothesis was tested through an experiment withhuman participants in a competitive game. In the game,
opponent agents (human or robot) efficiently deviated fixedpattern in a critical situation of the game. The deviation was
designed to be easily recognized as deception if participantsof the game clearly understood the rules of the game. If theobvious deceptive behavior is treated as intentional one, a human expects further change in behavior, therefore, adaptation
to the deviation is slower when a human is competing witha human. If the deceptive behavior is treated as deterministic
and algorithmic one, a human expect pattern fixedness of the
future behavior, therfore, adaptation to the deviation is faster
when a human is competing with a robot.
A. Penny-matching game with bonus roundA repeated penny-matching game with a bonus round wascreated for validating the hypotheses. The penny-matchinggame is a zero-sum game and is played between two players,
players A and B. Each player has a penny and must secretly
turn the penny to heads or tails. The players then reveal their

TABLE IT WO STRATEGIES ( STRAIGHTFORWARD AND DECEPTIVE ) IN
PENNY- MATCHING GAME WITH BONUS ROUND USED IN EXPERIMENT.
B LACK AND WHITE CIRCLES REPRESENT HEADS AND TAILS ,RESPECTIVELY. O NLY DIFFERENCE BETWEEN STRAIGHTFORWARD AND
DECEPTIVE STRATEGY IS CHOICE IN SIXTH ROUND .

round
payoffstraightforward
deceptive

1
1

uniform
alternate
uniform
alternate

•
•
•
•

2
1

•
◦
•
◦

3
1

•
•
•
•

4
1

•
◦
•
◦

5
1

•
•
•
•

6
20

•
◦
◦
•

own choices simultaneously. If the pennies match (both heads
or both tails) player A keeps both pennies and gets to keep
player B’s penny (+1 for A, -1 for B). If the pennies do
not match (one heads and one tails), player B keeps bothpennies (-1 for A, +1 for B). While this game has no purestrategy Nash equilibrium, the unique Nash equilibrium of
this game is in mixed strategies: each player chooses heads
or tails with equal probability.
We modified the game rules so that players are able to use
a deceptive strategy. The penny-matching game was played
repeatedly. One game consists of six rounds, and ten games
were played in the experiment. The payoff of the sixth roundin every game is increased twenty times: the bonus round. An
apparent reasonable strategy for this game is to strive to win
the bonus round and abandon the other five rounds becauseof the large payoff gap. A player is able to trap the opponent
by making a series of choices during the normal five rounds
so that the opponent’s prediction of the player’s sixth choice
will be wrong. Note that the unique Nash equilibrium of thepenny-matching game with a bonus round is still a mixed(random) one even though the bonus round is added.
The agents used as opponents in our experiment used only
the two strategies (straightforward and deceptive) listed inTable I. The two strategies are realized with two series of
uniform and alternate choices. Uniform and alternate choicesin the first five rounds were suggestive of the opponent; i.e.,
those exposed to the obvious trapping choices are forced
to anticipate that the opponent’s sixth choice will be either
deceptive (violating regularity) or straightforward (keeping
regularity).
B. Experimental setup and measurement
The game was implemented with JavaScript and HTMLand played in a Web browser (Firefox). Figure 1 shows thegame interface. A Flash video of the opponent (robot orhuman) is displayed at the top of the interface. The bearlike robot moves its head and arms randomly in the video.
The behavior of the human was recorded when he played thegame in advance. The agents’ behaviors, such as choosing aside of the coin, are automatically controlled by JavaScript
program. Participants were told that the opponent is online.
To make the participants believe the game is online, theparticipants’ faces captured using a web camera mounted
on the monitor were displayed at the bottom of the interface.

100
90

Robot condion

Human condion

1st game䐠(Total 5 games)䐥

Wining percentage (%)

80
70
60
50
40
30
20
Opponent’s
Score
1

䐣
䐟

Your
Score
3

Heads

Tails

䐢

Against robot
Against human10䐤Choose a sidefor 5th round.

0

1

Fig. 2.

2

3

4

5
6
Game no.

7

8

9

10

Percentage of participants who won sixth round of ten games.

5 seconds remaining䐡Fig. 1. Interface of on-line experimental system: 1) participant’s face,2) opponent agent’s appearance, 3) remaining time, 4) choice buttons, 5)histories of both players’ choices, 6) scores for both players, and 7) game
number.

Participants were instructed to click the button corresponding
to his/her choice within 10 seconds for every round. Scoresfor both players are shown in the interface. The choicesof both players remain displayed so that the participant
is able to recognize the opponent’s strategy. Before themain experiment, all participants played five games only fortraining.
A single-factor two-level between-subject experimental
design was used. Twenty-eight graduate and undergraduate
students participated in the study. Participants were randomly
assigned to either a robot or human opponent condition andwere seated in front of a desktop computer. Participants were
informed that the point of the experiment was to access theusability of an online game system.
A total of eight series of choices including another four series beginning from tails equivalent to the four series shownin Table I were used. The agents used a straightforward
strategy, one of the four series of straightforward strategy was
randomly selected, in the first three games and a deceptive
one for the rest. This is the change in agent’s behavior
strategy during the game, and observing human adaptation
to it is our aim of the experiment.
The outcomes of the sixth round for all ten games wererecorded because the participants’ expectation of their opponents’ strategies, i.e., which strategy, straightforward or
deceptive, did they expect, was of interest. Winning thesixth round against an agent indicates that the participants
expectation of the agent’s strategy is correct.
III. R ESULTS
The percentages of the participants who won the sixthround for all ten games are shown in Figure 2. Almost

all the participants lost the fourth game because the agentschanged their strategy from straightforward to deceptive.
After the fourth game, the winning percentage with both
opponent agents gradually recovered to the level of the thirdgame. A chi-square test was conducted to investigate whether
the winning percentages of the fourth to tenth games weredifferent from that of third one (see Table II). The results
indicate that at least two games were required to adapt tothe change in strategy of both agents.
The differences between recovery speeds of the winning
percentage between those playing against the robot and thoseagainst the human agent (plotted on the graph in Figure 2)
were statistically confirmed. Table II indicates that those who
played against a human agent required one more game foradapting to their opponent’s change in strategy than those
who played against a robot. This implies that participant’s
adaptation speed against a human is significantly slower thanagainst a robot, confirming hypothesis H.
IV. D ISCUSSION
The participants did not equate the robot to the human interms of adaptation speed against the opponent’s change instrategy. While the strategy equally changed in the fourthgame for both opponents, what caused the inequality inparticipant’s adaptation speed is the difference in the video
the participants watched. Slow adaptation of the participants
who played against the human indicates that they werecautious but not optimistic against the opponent’s strategies
after the strategy change in the fourth game. This is because the human appearance made the participants anticipate
another change in the human opponent’s strategy, and therobot appearance gave the participants the impression that its
strategy was stable. The behavior of the designed artifacts,
including robots and computers, is governed by laws such asmechanical, algorithmic, or structural constraints; therefore,
the input-output relations of the artifacts are stable. This
prototypical concept of artifact’s regulated behavior mightmake the participants expect the simpler and less complicatedstrategy of the robot.

Game no.
Against robot condition
Against human condition

4
24.26, p<.01
14.29, p<.01

5
19.33, p<.01
7.34, p<.01

62.15, n.s.
5.60, p<.05

7
1.04, n.s.
0.85, n.s.

83.36, n.s.
2.80, n.s.

94.67, p<.05
2.80, n.s.

10
6.09, p<.05
0.85, n.s.

TABLE IIC HI -S QUARE VALUES ( DF =1) AND SIGNIFICANCE LEVELS FOR THE WINNING PERCENTAGES OF FOURTH TO TENTH GAMES COMPARED WITH THAT OF
THE THIRD ONE .

There are two causes for the gradual increase in thewinning percentage in the adaptation phase: 1) Each participant changed his/her strategy just once in the adaptation
phase (during games 5 to 7) and the timings of the changes
varied across the participants. 2) Each participant changed
his/her strategy plural times to find the most suitable strategy.
To investigate these causes, we compared the number ofstrategy changes in the adaptation phase in two conditions.
The average number of strategy changes by the participants
was 1.07 under an ”against robot” condition and 1.57 underan ”against human” condition was 1.57, so there was amarginally significant difference (t(26) = 1.919, p = 0.066).
This suggests that strategy changes by the participants were
one-shot deterministic under an ”against robot” condition
bat indecisive and exploratory under an ”against human”
condition.
We consider the drop of winning percentage in the eighth
game could be accounted for by meta-adaptation. Our gamedesign requires at least two levels to be adapted. The first is
adaptation for regularity of the agent’s choice in the first fiverounds. The second is adaptation for strategy change in the
fourth game. The third, which was beyond our expectations,is an adaptation for periodic change in an agent’s strategy.
Participants might think the agent’s strategy changes once
every three games and so expect to change again in theseventh game.
Not only the appearance but also the behavior of the agentsdiffered between the two videos. We did not separate the appearance and motion factors in our experiment. Investigating
which factor contributes to the change in human adaptation
speed to an agent is for future work.
V. CONCLUSION
In the present study we theoretically derived the fixedpattern deviation hypothesis and tested the hypothesis withhuman participants. We conducted a penny-matching gamewith a bonus round in a web browser for investigating how
humans adapt to an opponent agent’s change in strategy. The
experimental results indicated that, as expected, adaptation
is faster when a human is competing with robot than withanother human. This implies that a human expect intentional
deviation of fixed pattern of behavior against an human and
expect deterministic and algorithmic behavior against robot.
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