=Paper=
{{Paper
|id=Vol-1829/iStar17_paper_17
|storemode=property
|title=Towards Reasoning About Strategic Moves and Reciprocity With i* and Game Trees
|pdfUrl=https://ceur-ws.org/Vol-1829/iStar17_paper_17.pdf
|volume=Vol-1829
|authors=Vik Pant,Eric Yu
|dblpUrl=https://dblp.org/rec/conf/istar/PantY17
}}
==Towards Reasoning About Strategic Moves and Reciprocity With i* and Game Trees==
https://ceur-ws.org/Vol-1829/iStar17_paper_17.pdf
Towards Reasoning About Strategic Moves and
Reciprocity With i* and Game Trees
Vik Pant1, and Eric Yu1, 2
1Faculty of Information, University of Toronto, Toronto, Canada
2Department of Computer Science, University of Toronto, Toronto, Canada
vik.pant@mail.utoronto.ca
eric.yu@utoronto.ca
Abstract. Reciprocity is an important motivator of human judgement and is
frequently used to justify decisions. It is a common feature of social relation-
ships wherein beneficial conduct is encouraged through rewards while deleteri-
ous behaviors are discouraged via punishment. However, despite its ubiquity
and pervasiveness in intra- and inter-organizational relationships, there are cir-
cumstances when reciprocation can yield mutually injurious outcomes for im-
pacted actors. Game theorists have proposed game trees for analyzing strategic
decisions such as those pertaining to reciprocation. However, game trees are
lacking in certain respects and only codify limited aspects of a focal decision as
well as its problem and solution spaces. This paper discusses exploratory re-
search into the modeling of strategic moves and reciprocity using i* and game
trees. It discusses the main ideas that are relevant for developing a framework
for analyzing strategic moves and reciprocity in a systematic and structured
manner via a combination of these modeling techniques. Such a framework can
help organizational decision-makers to exhaustively contemplate decisions con-
cerning reciprocation by accommodating their predispositions and prerogatives.
Keywords: Coopetition. Reciprocity. Design. Modeling. Review.
1 Introduction
Reciprocity is an important consideration in many intra- and inter-organizational relationships
[1][2]. It serves as a guideline for action whereby one actor is assured that its benefi-
cial/deleterious actions towards other actors will be met by an equivalent response from those
other actors. Reciprocity also impacts trust between actors because it incorporates mutuality
into a relationship such that good behavior by an actor is rewarded with an increase in trust
while bad behavior is punished with a decrease in trust [3]. Reciprocity is simple to justify in
any relationship because it signifies the universal qualities of balance (symmetry) and fairness
(equality). In this paper, we share our vision for a framework that supports the analysis of stra-
tegic moves and reciprocity in a systematic and structured manner using i* and game trees.
Analysis of reciprocity is an important aspect of strategic dependency (SD) analysis because
the balance of dependencies going in the two directions between two actors, sometimes mediat-
ed via other actors, can determine the viability of the relationships between those two actors.
However, in current i*, the model is static (i.e., there is no provision for action over time),
which makes it difficult to represent the notion of strategic moves and reciprocality in i*.
2 Strategic Moves and Reciprocity in Social Relationships
Reciprocity refers to "rewarding kindness with kindness and punishing unkindness with un-
kindness" [4]. It facilitates cooperative relationships among actors by serving as a guarantor of
favorable treatment and a protector against injurious treatment. It "is a rather stable behavioral
response by a nonnegligible fraction of the people" [5] and thus each social actor should "ex-
pect this behavior from others" [6]. Strategic reciprocity has been observed in many industrial
settings [7]. However, despite its ubiquity and enduring nature as an influencer of social behav-
ior, there are circumstances in which reciprocity can yield counter-productive decisions that
lead to detrimental courses of action. Therefore, decision-makers within organizations can
benefit by analyzing reciprocity using a systematic and structured approach.
Strategic relationships are characterized by long-term associations and diversified interactions
between two or more actors. These are distinct from transactional contacts between two or
more actors where the extent of the dealing is limited to a single exchange or deal. In transac-
tional contacts, reciprocity may offer a useful guide for action because the short-term and non-
recurring nature of such engagements may necessitate the threat of retaliation as a safeguard
against exploitation and abuse. For example, in a spot (i.e. one-shot) transaction, an actor may
cheat a cheater out of a desire for fairness and equity as well as to teach that cheater a lesson.
By contrast, in strategic relationships, it may be necessary for an actor to eschew reciprocity if
it is expected to further exacerbate and deteriorate that relationship. This might be unavoidable
for sustaining the relationship and ameliorating it over time. Such countervailing longer-term
considerations may compel a decision-maker to override the desire for short-term reciprocation.
The organizational scenario of knowledge expropriation within inter-partner learning arrange-
ments offers an illustration of reciprocity in action within the industry. Knowledge sharing is
identified as an important reason for the formation of business partnerships [8]. However, in
such arrangements, it is possible for one or more actors to siphon off knowledge from their
partners while hiding their knowledge from those partners [9]. If the opportunism of a cheater is
detected by the actor that is cheated then that cheated actor might choose to retaliate immedi-
ately against the cheater. It might attempt to do so by cheating the cheater in return or shut it
out of the learning alliance. This can lead to a series of reprisals that destabilize and undermine
the relationship to the detriment of all affected actors. Conversely, the actor that is cheated may
decide to forego the impulse for short-term reciprocation by comprehensively evaluating the
long-term implications of tit-for-tat behaviors.
This means that a reflexively reciprocal reaction can be possibly short-sighted in that it entails
one actor retaliating to the most recent move by an opponent by taking the most self-interested
immediate action, thus potentially foregoing longer-term strategic interests. The universality
and timelessness of reciprocity, as a motivator of actions/reactions in strategic relationships,
necessitate a framework for analyzing it in a detailed and deliberate manner. Such a framework
can enable a decision-maker to take history into account and make tradeoffs between long and
short-term interests. Without such a framework decision-makers are likely to follow their gut
instincts, that are potent in all humans, of reciprocating under all circumstances. This may
expose those actors to errors and mistakes due to omissions and confusions.
3 Towards Modeling Strategic Moves and Reciprocity Using i*
and Game Trees
Reciprocity has been studied extensively by researchers of economics, sociology, and psychol-
ogy to explain moves and countermoves of actors in many types of social relationships. In
game theory, it is a basic assumption in many sequential move games, such as gift-exchange
game and ultimatum game [10]. A game tree offers an approach for decision analysis when the
decisions of one actor impact the decisions of other actors and vice versa. It is relevant for
modeling reciprocity because such decisions can trigger tit-for-tat moves/countermoves among
actors. Game trees are variations of decision trees in that, while decision trees depict the deci-
sions of a single focal actor, game trees portray the decisions of multiple actors [11].
Zigler [12] notes that "a game tree is a graphical representation of the players' possible choices
(also called their action sets) at each point in time, the sequence in which these choices are
made, and the payoffs resulting from any combination of choices." It supports the depiction of
decisions, their sequence in terms of precedence and subsequence, as well as the payoffs asso-
ciated with each decision path from root to leaf nodes. Borovska and Lazarova [13] point out
that game trees can be used to “find the optimal strategy as a sequence of best possible moves
of a given player taking into account possible moves of the other player up to a given depth.”
Since the decisions, their sequence, and payoffs are included in game trees they can be used to
solve optimization problems by searching the space of alternatives and outcomes.
Figure 1 presents a simple game tree with two actors and one decision for each actor. Let us
assume that two rival firms, namely A and B, form a strategic alliance to achieve a shared ob-
jective. This is a common feature of coopetitive relationships whereby two or more firms coop-
erate and compete simultaneously. This game tree shows a dichotomous choice that is faced in
multifaceted relationships where the actors share a partially convergent and partially divergent
interest structure. The decision-makers in these firms are aware that they are in a partnership
with their adversary and so the possibility for opportunism exists more so than in a relationship
with a benefactor (e.g., a subsidiary or a parent firm).
(-1, -1)
B
(1, -1)
A (-1, 1)
Legend
A Alternative (A, B)
B
Actor Decision Payoff for A,
(1, 1) Payoff for B
Figure 1. Simple game tree of two actors with one decision each and their resulting payoffs
In this configuration, two options that are available to each firm which are to cheat or not to
cheat. The terms and conditions of the strategic alliance between firms A and B are enshrined
within a partnership contract. However, due to information imperfection/asymmetry during
contract negotiation it can be assumed that the contract is incomplete. Therefore, in spite of the
presence of a formal legal document codifying the rules and regulations of the relationship
between firms A and B there exists the opportunity for each of these actors to cheat the other
actor. The numbers in the parenthesis represent the payoffs to firm A and firm B respectively as
the outcome of each decision path. These numbers are presented purely for comparative pur-
poses and their unit of measure is irrelevant.
In this example, we assume for the purposes of reasoning that an outcome of positive 1 is fa-
vorable to an outcome of negative 1 for each actor. Figure 1 shows that if each firm cheats then
each firm earns a payoff of negative 1. Conversely, if neither firm cheats then both firms earn a
payoff of positive 1. However, if one firm cheats while the other firm does not cheat then the
cheater earns a payoff of positive 1 while the cheated earns a payoff of negative 1.
Intuitively, it may appear that neither firm should cheat as that would lead to each firm earning
a payoff of positive 1. This rationale would be reinforced by examining the decision path where
both firms cheat because in that case each of these firms would earn a payoff of negative 1.
However, this simplistic line of reasoning relies on certain assumptions that may not be realis-
tic. For example, since partners in coopetitive relationships are also rivals, a firm may be
tempted to cheat the other firm in order to harm it regardless of its own payoff. It may also
reason that if its opportunism goes undetected (i.e., by hiding, shielding, masking, or spinning)
then it will benefit while the other firm will be harmed.
Conversely, if its deception is detected then the other firm will retaliate by attempting to cheat
it and in which case both firms will earn a payoff of negative 1. In both cases, the first mover
can guarantee a payoff of negative 1 for the second mover by cheating it. If the possibility of
earning a payoff of negative 1 is an outcome that the first mover is willing to tolerate, while
ensuring that the second mover definitely earns a payoff of negative 1, then the first mover is
better off cheating. Likewise, the second mover may be tempted to retaliate by cheating the first
mover upon the detection of cheating by the first mover. However, the second mover may
forego the urge for reciprocation due to its priorities. For example, the second mover may be
more conscious about its reputation in the industry than the first mover. Thus, it might be will-
ing to overlook cheating by the first mover by deciding not to cheat and maintain its goodwill.
The reasoning presented above highlight different ways of analyzing decision paths and in
doing so points to a key limitation of game trees. Game trees can be used to depict the interre-
lated decisions of different actors, their sequences, and payoffs related to various decision
paths. However, game trees cannot be used to represent the intentions and motivations of the
focal decision-makers. Each decision maker can have unique priorities and preferences. There-
fore, each decision-maker may analyze its space of alternatives (represented as decision paths)
differently with respect to its particular goals, and objectives (represented as payoffs).
Analysts can solve optimization problems using search algorithms on game trees but search
algorithms apply many domain assumptions such as those about the subject and measurement
of optimization (i.e., what must be optimized and what is meant by optimization – e.g., minimi-
zation, maximization, etc.). These assumptions are absent from the game trees and the inability
of representing the assumptions that are critical for solving a particular optimization problem
on a specific game tree means that either assumptions are excluded from the record or they are
denoted as accompanying text. Neither option is optimal as the former implies the preservation
of an incomplete record that is not conducive to auditing while the latter implies the storage of
unstructured and free-form documentation that does not readily allow automated evaluation.
We posit that i* is fit for the purpose of depicting the decision rationale that is used to solve an
optimization problem on a game tree. i* is well suited for this because it supports the analysis
of tradeoffs between alternatives in terms of quality objectives. i* supports the depiction of
softgoals that can be used to compare and contrast the impact of each alternative. It also sup-
ports the representation of dependencies between actors that serve as sources of opportuni-
ties/vulnerabilities thereby supporting/constraining different courses of action. i* permits allo-
centric analysis through its support for the presentation of multiple viewpoints (e.g., for each
actor). This characteristic of i* is crucial for performing qualitative analysis of goal satisfaction
that reflects the perspective of each decision-maker. Furthermore, typical search algorithms on
game trees assume that the problem space is fully known, and that the solution space is given
and fixed. i* provides representation for exploring and elaborating on the problem understand-
ing as well as the solution space.
Figure 2 presents a simple i* strategic rationale diagram of the goal models of abovementioned
firms A and B. We use alternatives from figure 1 in figure 2 to simplify the correlation between
these diagrams. A more sophisticated i* strategic rationale (SR) diagram would elaborate and
expand these alternatives beyond those that are included in figure 1. This diagram shows that
each actor has a distinct worldview that will impact its perception of the desirability of a partic-
ular course of action (i.e. decision path). Firm B is risk averse, values the goodwill that it en-
joys in the market, and prefers to engage in fair dealings. It does not like to gamble or take bets,
as it relates to its contractual relationships, and thus it avoids cheating its partners. Conversely,
Firm A prefers to take risks, harm its adversaries, and force renegotiations of its agreements to
continually obtain favorable terms and conditions. It is unconcerned with its reputation in the
market and is comfortable with cheating.
B A
Contract be Agreement be
Agreement
signed reached
Invigilate
Do Not [Agreement] Do Not
Cheat Cheat
Cheat Cheat
Goodwill Gamble Contract Harm Rival
Reputation
Monitor
[Contract]
Loss Compel
Fairness Risk Taking
Aversion Revision
Legend
Help Contribution Hurt Contribution Satisficed Denied
Goal Softgoal Task Resource Link Link
Actor
Conflict
Goal Softgoal Task Resource Means-End Decomposition Weakly Weakly
Dependency Link Make Contribution Break Contribution
Actor Actor Boundary Link Link Satisficed Denied
Link Link
Figure 2. Simple i* Strategic Rationale diagram of two actors, their alternatives and goals
4 Conclusion
Section 3 used an example to show that, even though Firm A, the first mover in figure 1, will
cheat Firm B, the second mover, it is preferable for Firm B to eschew its impulse for hasty
retaliation due to its long-range proclivities and propensities. This suggests that there are cir-
cumstances when certain intentions override the urge of an actor to get even with another actor
by reciprocating immediately. Thus, modeling reciprocity necessitates the means of represent-
ing extended temporal sequence of strategic moves, and how the decision by one actor at any
point in time should consider past moves by each actor, and possible future moves. i* can be
used in combination with game trees to expose and highlight such situations to help decision-
makers arrive at defensible decisions about reciprocation.
This example illustrated that two firms in a business partnership can evaluate the same game
tree in completely different ways. The idiosyncratic goals and objectives of each firm, which
are underpinned by their motivations and intentions, determine the attractiveness of each option
for them. Analysis of payoffs in game trees can be supplemented by analysis of softgoals in i*.
Our technique of using i* models and game trees in a complementary manner can help each
decision-maker to evaluate its space of alternatives in line with its particular intentionality.
Gans et al. [14] propose a TCD (Trust–Confidence–Distrust) approach for continuous require-
ments management in inter-organisational networks. Our work is synergistic to this approach
which "combines the structural analysis of strategic dependencies and rationales, with the inter-
action between planning, tracing, and communicative action." [14] Both of these approaches
consider path dependency, history, and strategic dependency between actors during analysis.
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