# IEEE Technology and Society Magazine - Summer 2013 - 37

A's payoff = f(sA)
B's payoff = f(sB)

Do not
Trust

A: Trustor

A's payoff = f(dA)
B's payoff = f(dB)

Defect

B: Trustee

Trust

A's payoff = f(rA)
B's payoff = f(rB)

Cooperate

Fig. 3. Decision to trust or cooperate and its payoff.

f (s A) \$ f (rA) - f (d A)), A will not
initiate the relationship with B and
its payoff remains as f(sA). However,
when A predicts its payoff as more
beneficial by trusting than not trusting (i.e., f ^s Ah 1 f (rA) - f (d A)), A
chooses to trust B. Then, A's payoff
depends on the action of B. If B is
willing to cooperate with A based on
its predicted payoff as greater benefit by being cooperative than not
cooperative (i.e., f (d B) 1 f (rB)), A
will obtain the payoff, f (rA). However, if B refuses to cooperate with
A based on its predicted payoff as
greater benefit by not being cooperative than being cooperative (i.e.,
f (d B) \$ f (rB)), A's payoff remains
as f(dA). In [10], [13], the payoff from
each decision is explained based on
f ^d Ah = 0 1 f ^s Ah = f ^s Bh 1 f ^rAh =
f ^rBh 1 1 = f (d B). The simple net
gain computations to make a decision on whether to trust or cooperate
by a trustor and a trustee are summarized in Table I.
However, in practice, this payoff relationship may not hold due to
dynamics or conditions of networks
(e.g., durability of relationships,
chances of interactions, resource
constraints), complex trust relationships among entities (e.g., propensity
or disposition of entities, reciprocation, altruism), or environmental
or situational conditions (e.g., pressure from control mechanisms or
authority to manipulate reward and
penalty).
In addition, there exists uncertainty derived from incomplete,
incorrect, or a lack of information. Therefore, an entity's payoff
prediction and decision based on
its local information (e.g., greedy

view) may not guarantee the estimated future payoff due to the
uncertainty and dynamics. Jøsang
[11] defines an opinion (or trust)
as a subjective probability based
on belief, disbelief, or/and uncertainty. Similarly, we also design
the payoff based on known payoff
of not trusting (f(sA)), uncertainty
(f(uA)), known payoff of trusting
(f(rA)), and known payoff of being
betrayed (f(dA)) in terms of trustor
A's perspective. Similarly, as trustee
B's perspective, the payoff can consist of known payoff of not being
trusted (f(sB)), uncertainty (f(uB)),
known payoff of being cooperative
(f(r B)), and known payoff of not
being cooperative (f(dB)). These
relations are summarized as:
f (s A) + f (u A) + f (rA) + f (d A) = 1
f (s B) + f (u B) + f (rB) + f (d B) = 1
(1)
Depending on the degree of uncertainty (f(uA) or f(uB)) and any inherent errors introduced by payoff
evaluation processes (e.g., perceived
payoff may not be the same as actual
payoff), risk of the entity's decision
is determined. Eq. (2) computes an
entity's payoff based on the importance of a game where the entity
participates in a repeated game.

IEEE TECHNOLOGY AND SOCIETY MAGAZINE

/ I A (n) Ppayoff ^A, nh
Ppayoff (B) = / I B (n) Ppayoff (B, n)

Ppayoff (A) =

n!S
n!S

(2)

where

/ I A (n) = 1

and

n!S

/ I B (n) = 1

n!S

S is the set of game sessions that
entities A and B participate and n
is a game session number. Importance of a game session to an individual entity, I A (n) or I B (n), can be
measured based on the impact of
the outcome on the entity's current
and future goals or welfare. High
importance under high uncertainty
tends to generate high risk. While
an entity tries to maximize its own
payoff, the system concerns also
its own welfare, the overall system
payoff (i.e., goals), described by:
Ppayoff ^A, Bh
= / I A, B (n) Ppayoff ^A, B, nh (3)
n!S

where

/ I A,B (n) = 1

n!S

I A,B (n) is a weight for the importance of a game session to the
system based on the relationship

Table I
Net Gain Estimation for a Decision on Whether to Trust or Cooperate
Decision
maker

Condition

Decision

Payoff

Trustor A

f (s A) \$ f (rA) - f (d A))

Do not trust

f (s A)

f (s A) 1 f (rA) - f (d A))

Trust

Defect by B: f (d A)
Cooperate by B: f (rA)

f (d B) \$ f (rB))
f (d B) 1 f (rB)

Defect

f (d B)

Cooperate

f (rB)

Trustee B

|

SuMMEr 2013

|

37

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