=Paper= {{Paper |id=None |storemode=property |title=Questions of Trust |pdfUrl=https://ceur-ws.org/Vol-954/paper13.pdf |volume=Vol-954 }} ==Questions of Trust== https://ceur-ws.org/Vol-954/paper13.pdf

Questions of Trust

Jason Quinley1 and Christopher Ahern2
1
University of Tübingen
jason.quinley@student.uni-tuebingen.de
2
University of Pennsylvania
cahern@ling.upenn.edu

Abstract. We consider the application of Game Theory in the model-
ing of different strategies of politeness. In particular, we examine how
differences in the linguistic form of requests and proposals map onto
the structure of the game being played by interlocutors. We show how
considerations of social wants [1, 2] and coordination and cooperation
motivate these differences. First, we adapt the notion of other-regarding
preferences [3, 4] to show how linguistic systems with the ability to en-
code politeness strategies allow for requests and cooperation between a
wider range of individuals. Finally, we connect the distinction between
requests and proposals to the notion of a self-enforcing equilibrium [5].

1 Introduction
Questions in their many forms are central to social interaction. Asking someone for
a dollar, or if they would like to see a movie, are commonplace yet revelatory. The
indicate how we use language not only to convey information, but also to negotiate
relationships. A clear case of these distinctions can be had in the use of the modals
will and would in the following requests:

(1) Will/Would you lend me a dollar?
(2) Will/Would you open the door?
(3) Will/Would you turn that music down?
(4) Will/Would you marry me?

Consider asking these questions of a stranger. It would be impolite to omit the
modal. Moreover, between the two modals we also sense a difference in effect. In the
first two cases would is the more polite form of request. In the third either is acceptable,
modulo the degree to which the music affects the speaker. In the last, will seems the
more appropriate form. Moreover, would allows for comedic response: I would if you
were rich/handsome/x!
Why are such questions necessary? One reason is that scarcity and ambiguity drive
interaction. We have neither unlimited resources nor unlimited information with which
to achieve our ends. This leads to the need for cooperation, and with it, strategies to
address its fragility. As humans have access to language, they are availed of multiple
avenues of cooperation. Studying these allows for a fruitful combination of theories of
language and rational interaction.

R.K. Rendsvig and S. Katrenko (Eds.): ESSLLI 2012 Student Session Proceedings, CEUR Work-
shop Proceedings vol.: see http://ceur-ws.org/, 2012, pp. 121–132.
122 Jason Quinley and Christopher Ahern

In what follows, we examine the use of modals in requests and proposals. We
show how modals, and other politeness strategies, when thought of in terms of other-
regarding preferences, allow for expanded interaction between individuals. We also
show how and why the use of the modal will in requests is binding, whereas would is
not necessarily so. We begin by presenting the relevant notions from politeness- and
game theory, then turn to our analysis of requests in these terms and suggest future
directions.

2 Politeness Theory and Speech Acts
Beginning from Goffman’s [1] notion of face, Brown and Levinson [2] articulated an
ur-theory of politeness, which has prompted much subsequent theoretical and empirical
work. Face is the term given to an individual’s basic needs, characterized broadly as
the need for autonomy (negative face) and acceptance (positive face). Broadly, positive
face can be thought of as the wants of the individual, including the desire that those
wants be desirable to or approved of by others. Negative face includes both the freedom
of action and the freedom from imposition.
Preferences of one agent may conflict with those of others, incentivizing them to
make requests, issue threats, or offer proposals. In cases where a request must be made,
speakers must commit a face-threatening act (FTA). In order to mitigate the weight of
a FTA, speakers may use several strategies, as laid out in Figure 1.

Fig. 1. Brown and Levinson’s Politeness Strategies: As we move upwards on the
graph, the potential for a face-threatening act (FTA) increases.

At the two extremes, a speaker might avoid making the FTA altogether, or state
it in a direct manner. In between there are various degrees of deference to the hearer’s
face wants: indirect speech that is “off the record” and addressing the hearer’s positive
or negative face. As a concrete example, consider the situation of having left one’s
wallet at the office while going out to lunch with a group. Here the relevant FTA might
Questions of Trust 123

be taken as requesting some money from a friend. The various strategies of doing so
could be implemented as:

(1) Don’t do FTA: Don’t ask for money.
(2) Off Record:3 “Oh no! I forgot my wallet in my office!”
(3) Negative Politeness:“You don’t have to, but would you mind lending me a bit
of money?”
(4) Positive Politeness:“Congratulations on the raise! Want to lend me some money.”

The goal of the speaker is to craft the appropriate message to convey the intent
and the weight of the FTA. The greater an imposition a FTA carries, the more care
needs to be taken. However, too much politeness is inappropriate given certain FTAs.
It would seem odd to be asked, rather circuitously, “Excuse me Sir/Ma’am, but I was
hoping that it might be possible if it’s not too much trouble that you would be able to
tell me the time.” Similarly, when expediency is called for, “Please, if you could, move
out of the way of that speeding car,” would be inappropriate. Thus we might think
of different forms of politeness as strategic responses to situations where face may be
threatened. Again, the goal of the speaker is to select the appropriate form for the FTA
in question; neither too much nor too little deference can be paid. With this notion
of strategy in mind we turn to the game-theoretic framework that will figure in our
analysis.

3 Basic Game Theory
Game theory gives a mathematical model of strategic interaction between agents. We
begin by presenting canonical examples from the field. Crucially, we focus on the differ-
ence between cooperation and coordination in sequential play. Sequential play allows
for an optimal outcome under rational behavior in cases of coordination, but not for
cooperation.
Formally, a sequential game is a tuple hN, O, Aj , Ui i. N is the set of players in
the game. O is a sequence over N that determines the order of play; for j ∈ O, Aj
is the set of actions available to the jth player in the order of play. Finally, Ui is a
preference for player i over the set of possible paths of play. The payoffs are represented
as numeric values, where higher values are taken to be more preferred outcomes. The
Prisoner’s Dilemma (PD) offers the canonical example of choosing between coopera-
tion and defection. The game reflects a scenario wherein two prisoners must choose
between cooperatively staying silent (C), telling the police nothing about their crime,
or defecting on each other (D) and confessing the details to the police. Jointly, both
prisoners do better if they remain silent, but individually, they do better by ratting out
their accomplice. We represent the structure of the Prisoner’s Dilemma in extensive
form in Figure 2. Each node in the game is labeled with the letter of the player whose
turn it is to take an action, O = hX, Y i. The payoffs, as determined by the utility
functions, are listed as (UX , UY ) at the bottom of the tree.
We use the notion of a rollback equilibrium to examine expected behavior in the
game. The reasoning proceeds as follows. We begin by considering the lowest nodes
in the game and putting in bold the best action available. For any node where Y can
make a choice, she should choose D as it is always the better option. Knowing that
3
See Pinker et al. [6] as well as Mialon [7] for game-theoretic treatments of indirect
speech.
124 Jason Quinley and Christopher Ahern

Fig. 2. A Sequential PD Fig. 3. A Sequential PCG

this is the case, X should always choose D, as it always the best option based on what
Y will do. That is, cooperation will only ever be met with defection, so it should never
be explored. We will refer to those instances where players have diverging interests
but come together to yield the optimal outcome for all as instances of cooperation. In
instances of cooperation, as in the PD, reaching the best outcome for the players as a
group requires some sacrifice in terms of individual payoff. That is, each player must
forgo the temptation payoff of defecting in order to maintain cooperation.
In contrast, in cases of coordination, players’ incentives do not conflict. Consider
the case of a Pure Coordination Game (PCG) in Figure 3. Here players are ambivalent
between the actions they take, they only prefer to take the same action. An example
might be a scenario where two friends want to meet up for lunch at noon. If one player
suggests a restaurant, then the other should indeed go to that restaurant. If X plays
A (B), then Y should play A (B). Sequential games allow for the optimal outcome for
both players in pure coordination games.
These game structures allow us to distinguish between the notions of cooperation
and coordination. We might think of the first as exemplified in the Prisoner’s Dilemma,
and the latter in the case of Pure Coordination Games. With this background in place,
we now turn to the analysis of modals in requests and examine the different rationales
for polite behavior.

4 Trust and Modals
In this section we show how face-addressing forms allow for requests between a wider
range of individuals. This serves as a broad motivation for using such forms with
strangers. We then turn to a distinction between requests in general and marriage
proposals in particular, where we argue for a distinction between the different sorts of
speech acts involved as they relate to the notion of self-enforcing equilibria.

4.1 Requests as Extended Trust Games
Quinley [8] adapts Trust Games [9] as a model of requests. We borrow techniques
and insights from this approach and introduce Extended Trust Games to capture the
sequential dynamics of requests. We note the effects of repetition, reputation, and
observation on polite forms in requests, but suggest that they are not sufficient to fully
explain the use of politeness strategies. Instead, we propose other-regarding preferences
Questions of Trust 125

as a means to explain the use of modals and other forms of linguistic politeness in a
variety of situations.
Trust games are an appropriate model for requests due to several factors. First,
individuals are rarely if ever entirely self-sufficient. Moreover, agents possess different
aptitudes and abilities, and this asymmetry prompts requests. Requests entail a loss of
face on the part of the requester; so to speak, the requester makes a face “payment” to
the requestee. Finally, the requestee is not obligated to grant the request, presenting
the agent in need with the risk of both a loss of face and having their request denied.
Trust games depict a scenario where Player X has an initial option to defer to Player
Y for a potentially larger payoff for both. We extend this notion further, incorporating
a third step in the order of play. Here the play of the game is shown in extensive form in
Figure 4 and consists of the first player asking or not asking for some favor, the second
player granting or not granting the request, and the requester thanking or not thanking
the requestee. We considered a more detailed motivation of the utility structure below.
If X does not ask (¬A), then the status quo remains and X is left to her own
devices. Let cx be the cost to X to achieve the desired outcome. Let cy be the cost
to Y to achieve the same outcome. As noted before, assume an asymmetry in ability
or disposition such that cy < cx ; Y is in a better position than X to bring about X’s
desired state of affairs. If X does ask (A) for help, using a polite request, Y should
experience some boost in self-esteem based on the attention received. That is, by acting
in accordance with Y ’s face wants, X increases Y ’s face. Let the amount of face paid
by X to Y in the request be fr . Let mr be a multiplicative factor that acts upon fr to
determine the payoff to Y . If talk is cheap, then flattery is certainly sweet; a little bit
of face goes a long way, so we assume that mr > 1. Even if Y chooses not to grant the
request, Y still comes away with some benefit based on the face paid by X, mr fr . If Y
denies the request (¬G), X has incurred the face cost of asking without receiving any
benefits, and must also bear the cost of performing the action, cx . If Y chooses to grant
the request (G), then Y incurs some cost of the action, but still receives the benefit
of face from X. Let the benefit to X of Y granting the request be bx . In general, we
assume that bx < cx . If the request is granted, then X has an opportunity to express
to Y some sort of thanks (T ) or not (¬T ). This expression of thanks, again, comes at
some cost ft , and, again, carries with it some face benefit to Y as determined by a
factor mt > 1.
We are faced with the same problem as the prisoner’s dilemma; requests are FTAs
that require cooperation. X prefers ¬T to T , Y prefers ¬G to ¬T , and X prefers
¬A to ¬G. Thus, if we are only maximizing individual utility, it never makes sense
in a one-shot scenario to ask, grant, or thank, even though both players might prefer
the interaction under certain assumptions. We thus consider the effect of repetition,
reputation, and observation on the outcome.

4.2 Repetition and Reputation
Under various conditions, repetition engenders cooperation [10]. More specifically, with
a given probability of another round of play, group welfare becomes individual welfare;
i.e. a PD becomes a Stag Hunt [11]. In a Stag Hunt, players’ interest are highly aligned,
and the only pitfall is the possibility of mis-coordination. Importantly, in a Stag Hunt
players wish to coordinate, but may not necessarily know how when playing simul-
taneously. In Figure 5, the Stag Hunt structure assumes that players have aligned
preferences, and shared preferences over outcomes.
126 Jason Quinley and Christopher Ahern

Fig. 4. Request Trust Game: Player X can choose to Ask (A) something from
Player Y , who can then choose to Grant (G) the favor. Player X can choose to Thank
(T ) or not Thank (¬T ) player Y .

Stag Rabbit
Stag 4,4 0,1
Rabbit 1,0 1,1

Fig. 5. Stag Hunt (SH):
in strategic form

Fig. 6. Stag Hunt (SH):
in extensive form

Here, as in the case of coordination games, sequential play allows the players to
achieve the optimal outcome. That is, if the first player plays Stag, then the second
player should as well. Repetition transforms a Prisoner’s Dilemma to a Stag Hunt.
However, repetition cannot be all there is to the outcome of the interactions we consider
here. People are polite to strangers they will never see again.

The effects of reputation and observation on different strategies in trust games
are explored in Quinley [8]. Namely, asking requests of other agents is rational when
there is a sufficient likelihood that the request will be granted based on the requestee’s
reputation. Or, in the case here, granting requests is rational when there is sufficient
likelihood that X will play T . If Y has sufficient experience or knowledge about the
behavior of X with regards to P r(T ), then this suffices to render granting the request
rational strategy or not. The novel contribution of Quinley is the inclusion of face effects
due to third-party observation. In line with experimental results [12], such observation,
framed as a loss (gain) in face for Y when denying (granting) a request, is shown to
ensure that requests are asked and granted by and large. This can be extended similarly
to X’s actions when choosing to thank Y or not.
Questions of Trust 127

4.3 Other-Regarding: Reciprocity Without Repetition
While reputation and observation offer rationales for asking and granting requests, they
are unlikely to explain all of the behavior we observe. Modals are used to make requests
in one-shot interactions where nothing is known about the other individual and there
are no third-party observers. In fact, the polite use of modals is even more expected in
these sorts of situations. This suggests that reputation and observation are not alone
in explaining the behavior observed in requests A rationale for politeness strategies in
such situations can be found when we consider other-regarding preferences.
There exists a wealth of theoretical work on [13–15], and behavioral [16, 17] and
neurobiological evidence [18] of other-regarding preferences. Here we adapt the notion
of sympathy as advanced by Sally [3, 4] to explain the observed behavior. The central
notion is that of a sympathy distribution over the payoffs of all the agents P involved in
the game. For each agent, there is a distribution, δi ∈ ∆(U ), such that j δi (Uj ) = 1,
which determines how much that agent cares about her own payoffs and those of others.
For example, the perfectly self-interested agent of classical Economic theory is such that
δi (Uj ) = 0 for all j 6= i. A selfless agent would be such that δi (Ui ) = 0.
Here we consider the limiting case of a single interlocutor. Based on the sympathy
distribution and the utility function U of the original game, we define a new utility
function V .

Vi = δi (Ui ) · Ui + (1 − δi (Ui )) · Uj (1)
The impact of other-regarding preferences can be seen in the following. Consider
what values would suffice to make thanking rational for X in the Extended Trust Game
of Figure 4. Namely, we wish to determine the condition under which the sympathy
distribution of X renders thanking (T ) preferable to not thanking (¬T ). This holds
just when:

Vx (¬T ) < Vx (T )
1 (2)
< δx (Uy )
1 + mt

Given that mt > 1, the highest threshold will be bounded from above by 12 . As mt
increases, the threshold approaches 0. The greater the benefit to Y for thanking, the
less X has to care about Y ’s payoff to do so. This undoes some of the unraveling effect
of divergent preferences. We move on to determine the conditions on Y ’s preferences
that suffice to allow for cooperation. That is, we wish to determine when Y prefers T
to ¬G.

Vy (¬G) < Vy (T )
(cy − mt ft ) (3)
< δy (Ux )
(cy − mt ft ) + bx + cx − ft

There several important points to consider. First, the thresholds we have outlined
here are the conditions under which the underlying game of cooperation is transformed
into one of coordination. That is, if these thresholds are surpassed, then the game is
one of coordination rather than cooperation, and we should expect requests to be
made, granted, and thanks expressed. If X’s condition on thanking is not met, then
the request should be granted if Y prefers ¬T to ¬G, which is true just when:
128 Jason Quinley and Christopher Ahern

Vy (¬G) < Vy (¬T )
cy (4)
< δy (Ux )
c y + bx + c x

Otherwise, we should expect requests not to be made.
Second, we find that if mt ft > cy , then the request should be granted for anyone,
regardless of the sympathy distribution. We might be tempted to think of T in terms
of expressing a future commitment to cooperation. While T has this flavor, it does not
have this force; thanks, like talk, are cheap. For the expression of thanks to outweigh
the cost, cy , would require either something particularly important to Y , or some strong
guarantee on the part of X. Again, future guarantees are not available in the case of
single interactions with strangers.
Third, note that cx − ft > cy − mt ft given that cx > cy and m > 1. Moreover, note
that bx > cx , and thus bx > cy − mt ft . As such, as we collapse the non-fixed values
towards zero, we see that 13 serves as an upper bound on the threshold. The use of a
face addressing form, such as the polite use of modals, allows for a lower threshold of
other-regarding preferences for requestees compared to requesters. This makes intuitive
sense as requesters are more inherently self-interested.
Finally, the use of politeness strategies that address face allow for a lower threshold
than a system without such forms. Consider a faceless Trust Game, where ft = fr = 0
for the payoffs in Figure 4. We can think of this as a system where no transfers of face
are possible. The structure of the game reduces to a choice on the part of Y between
granting or not granting the request. The corresponding threshold of other-regarding
preference can be given as follows:

Vy′ (¬G) < Vy′ (G)
cy (5)
< δy′ (Ux′ )
c y + bx + c x

From Eq. (3) and (5) we know that a system with face requires a lower sympathy
threshold than one without face just when:

δy (Ux ) < δy′ (Ux′ )
cy (6)
< mt
bx + c x
c
Given cy < cx , we know that bx +cy
x
< 1. Since, mt > 1, it is always the case that
a system with face requires a lower threshold than a system without, thus allowing for
requests between a wider range of individuals. In this sense, when considered in the
context of other-regarding preferences, face allows for cooperation by smoothing out
the payoffs of the interlocutors. By “investing” in each other’s face, we can guarantee
cooperation more easily, even with people we do not know.

4.4 Proposals and Credible Signaling
In contrast with requests, proposals encode an interaction potentially to the benefit
of both participants. Returning to marriage, we noted the use of modals in certain
contexts differs. For purposes of both humor and invoking the undercurrent of common
Questions of Trust 129

knowledge, we observed that would allows for a certain amount of disavowal whereas
will does not. For example, the following dialogues can be completed for comedic effect:

Xavier: Would you marry me?
Yvonne: I would...if you were rich.
Xavier:*Sigh*
(or)
Yvonne: Yes!!!
Xavier:Woah, I was just asking hypothetically!

Xavier: Would you like to see a movie?
Yvonne: Yeah, there are a few I’d like to see.
Xavier: Great! When can I pick you up?
Yvonne: Oh! I didn’t realize you meant with you.
(or)
Yvonne:Yeah! When do you want to go?
Xavier:Oh! I didn’t mean with me, just in general.

We argue that will and would, for the most part, have the same illocutionary force.
However, they differ in that would allows for disavowal. To tease out how they do differ,
we consider the notion of self-enforcing equilibria.
Aumann considers the game in Figure 7 with pre-play communication. The game
has two Nash Equilibria: combinations of actions from which neither player can prof-
itably deviate from unilaterally. The equilibria are (C, C) and (D, D). It would seem
that both players should settle on playing C, since it is the payoff dominant equilib-
rium. However, this outcome is not guaranteed, even with communication. Suppose
both players agree to play C. Suppose X pauses to think about Y . If Y does not trust
him, then Y will play D despite the agreement to play C. Y would still want X to
play C regardless of what Y does. So, just because both players have agreed to play
C, it does not mean that they will; the agreement and the associated equilibrium are
not self-enforcing.

C D
Mr Mi
C 3,3 0,2
Ar v − fn , v + fn −fn − fp ,fn
D 2,0 1,1
Ai 0,−fp 0,0

Fig. 8. Adjusted Aumann’s Game
Fig. 7. Aumann’s Game

In light of the dialogues above, we might think of the strategies available to X(avier)as
either asking for information (Ai ) or asking as a request (Ar ). Similarly, think of the
strategies available to Y (vonne) as interpreting the question as asking for information
(Mi ) or as a request (Mr ). We motivate the utility structure as follows. Suppose that
(Ai , Mi ) results in some baseline payoff where both players receive 0. Now, suppose that
X intends the question as a request, Ar , but Y takes it as a request for information,
Mi . X has made some effort to address Y ’s negative face, and thus is out some effort,
fn , which is transferred to Y . Moreover, X is embarrassed by the miscommunication
and loses some amount of positive face because Y does not have the same wants as
130 Jason Quinley and Christopher Ahern

him. Similarly, if Y assumes a request, but X does not, then Y loses some amount of
positive face. Finally, when X intends a request and Y interprets it as such, then both
achieve some payoff, v, modulo a transfer of negative face. These payoffs are given in
Figure 8.
On the reasonable assumption that v > fn , there are two pure Nash equilibria:
(Ai , Mi ), (Ar , Mr ). The payoff dominant equilibrium, (Ar , Mr ), is not self-enforcing.
X prefers for Y to play Mr regardless of what X intends to do; Y prefers for X to play
Ar regardless of what Y intends to do. Thus, we can predict the disavowals that occur.
However, by and large, we do commit ourselves to making requests, Ar , with would
and this is because other-regarding preferences transform the payoff structure. The
use of would is self-enforcing just in case 0 < δx (Uy ) and 2fnfn+fp < δy (Ux ). There are
two things to note. First, the comedy of the dialogues above stems from the mismatch
between a generally expected amount of sympathy and that displayed. Second, the
disavowal on the part of the speaker seems far crueler than what could be an honest
mistake on the part of the hearer, as predicted by the fact that δx (Uy ) < δy (Ux ).
The crucial distinction between would and will, and why will is the appropriate
choice for a marriage proposal is evidenced by the effect of not paying negative face
to the hearer, as in Figure 10. That is, in a marriage proposal, (Ar , Mr ) is a self-
enforcing equilibrium much like the classical Stag Hunt, where both players benefit by
coordinating on the payoff-dominant choice.

Stag Rabbit
Mr Mi
Stag 4,4 0,1
Ar v, v −fp ,0
Rabbit 1,0 1,1
Ai 0,−fp 0,0
Fig. 9. Stag Hunt (SH): in strategic Fig. 10. Marriage Game
form

Thus, using the modal will ignores the listener’s negative face, but renders the
request self-enforcing. This aligns perfectly with our intuition that one cannot back
out after asking “Will you marry me?”. Moreover, this reasoning about face and other-
regarding preferences provides a rationale for why commissive speech acts are possible,
and the form they take.

4.5 Summary
We have shown that the transfer of face via politeness strategies with other-regarding
preferences allows requests and trust between a wider range of individuals. Specifically,
we have shown the necessary amount of sympathy between two individuals that suffices
to transform a game of cooperation into one of coordination, and that face lowers this
threshold. In addition, we have shown that would and will differ fundamentally in
terms of illocutionary force, and the underlying structure of the interaction. would
allows for disavowal and is not necessarily self-enforcing, whereas will as a commissive
speech act commits the speaker to a course of action. In parallel to results from dynamic
epistemic logic [19], saying will creates common knowledge between the participants
of the hearer’s commitment to future action, and thus it is only rational in the case
that both participants have a benefit towards taking that action and that the action
cannot be repeated.
Questions of Trust 131

5 Conclusion
This work follows in the vein of approaches to pragmatics and politeness from a strate-
gic viewpoint. It defines the conditions under which politeness strategies are rational
in those situations where repetition, reputation, and observation do not hold. A central
result is that a system with face allows for a greater level of trust between agents with
other-regarding preferences. Also, it outlines how the modals will and would map onto
fundamentally different game structures and predicts both the humorous possibilities
of denial and the real power of socially-binding statements. Future directions include
extending the current analysis to threats such as Will you cut that music out! and
requests for information Will you be here later?, and providing a broader theoretical
framework for the description of speech acts. The results presented here demonstrate
the growing ability of game-theoretic methods to model pragmatic phenomena, includ-
ing politeness. Moreover, though reciprocity and coordination existed outside of and
prior to language, language nonetheless serves as an efficient tool for managing them
in relationships.

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