International Journal of Business and Management Technology in Society 2025, 3.
, 28-37 International Journal of Business and Management Technology in Society Available at https://journal.
id/index.
php/ijbmts/ Cooperative Game Theory: Examining Promise.
Trust and Contract Interplay Lazuardi Al-Muzaki Department of Business Management.
Institut Teknologi Sepuluh Nopember Article History Received : 2025-08-05 Revised : 2026-01-09 Accepted : 2026-01-09 Published : 2026-01-13 Keywords:
Cooperative Game Theory.
Moral Hazard.
Trust and Reputation.
Incomplete Contracts Corresponding author:
lazuardialmuzaki@its.
Paper type:
Research Paper Cite this article:
Al-Muzaki.
Cooperative Game Theory: Examining Promise.
Trust and Contract Interplay.
International Journal of Business and Management Technology in Society.
, 28-37.
Abstract Purpose Ae This study aims to examine the interplay between promise, trust, and contract in cooperative game theory under conditions of moral hazard and information asymmetry.
It seeks to identify how intrinsic promise-keeping behavior influences agent decisions, utility distribution, and social surplus maximization, with application to publicAeprivate contracting contexts.
Methodology Ae Building on ChenAos .
framework, the study develops a cooperative game model applied to a case study of a local governmentAecontractor bridge project governed by an incomplete contract.
The model stresses a critical value parameter .
representing the contractorAos intrinsic utility from keeping a A numerical simulation is conducted using hypothetical parameters to evaluate how varying ycu impacts contractor behavior .
onest vs.
, parties utility, and social surplus.
Findings Ae The simulation identifies a behavioral tipping point at ycu = 6000, below which opportunistic behavior dominates, reducing social surplus and government utility.
When ycu meets or exceeds this threshold, honest behavior becomes utilitymaximizing for the contractor, significantly improving outcomes for both parties.
Originality Ae The studyAos novelty lies in simulating the behavioral threshold of the trust parameter .
within a cooperative game model, quantifying its impact on agent behavior and social surplus under incomplete contracts.
Practical implications Ae The findings suggest that intrinsic trust mechanisms, such as long-term partnerships, reputation systems, and community accountability, can serve as cost-effective substitutes or complements to formal enforcement in incomplete Introduction The concept of Moral Hazard has been extensively studied in game theory.
It is a situation where one party is encouraged to take risks, knowing that another party will bear the consequences of those risks.
A classic example of this is the relationship between insurers and the insured.
The insurer bears the financial risk if the insured party suffers a loss, but the insured party may be less worried about taking more risks because they are not bearing the full cost of the loss.
ISSN 3025-4256
Copyright @2025 Authors.
This is an open-access article distributed under the terms of the Creative Commons Attribution License .
ttp://creativecommons.
org/licences/by-sa/4.
Cooperative Game TheoryA In the business context, moral hazard can manifest in relationships between buyers and sellers, or service providers and clients.
The seller or service provider may have an incentive to provide lower quality goods or services, knowing that the buyer or client is not fully informed or cannot easily assess the quality being delivered.
Reputation and trust then play an important role in mitigating moral hazard.
Reputation can serve as a signal of quality and can help buyers and clients assess the trustworthiness of the seller or service provider.
Trust, on the other hand, can serve as a foundation for building longterm relationships between parties.
This is where the concept of promise, a non-binding commitment, and contract, a binding agreement with enforceable terms, enters the theoretical scene.
Contracts aim to align incentives and reduce moral hazard through formal obligations.
Yet, some contracts are not complete.
many real-world transactions, not all contingencies can be foreseen or fully specified.
Hence, the interplay of promise, trust, and contract forms a rich and nuanced framework for understanding cooperation and value creation under conditions of uncertainty and asymmetry.
This study aims to extend the idea of reputation and trust in understanding the behaviour of two parties in market transactions bound to shape outcomes under conditions of moral hazard and information asymmetry.
Building on foundational work such as Chen .
, we explore theoretical models, practical applications, and emerging trends, including the role of technology in enhancing verifiability and trust.
Additionally, we integrate a case study of a local governmentAecontractor relationship in infrastructure development to illustrate how these concepts operate in practice and influence social surplus.
Literature Review Game theory offers a structured framework for analyzing interactions between players or The offered framework can be distinguished into two broad categories: non-cooperative and cooperative games.
Non-cooperative games are executed on the premise that agents would make decisions independently, do not form alliances among parties, as they consider their own interest (Ahmad & Al-Fagih, 2.
Conversely, cooperative game theory main paradigm is about how agents could bond coalitions to mutual objectives.
Coalitions and collaborations form a binding agreement that explains how the total gain would be distributed.
(Chalkiadakis et al.
, 2.
Cooperative games paradigm is especially relevant in business contexts where joint ventures, partnerships, or contractual relationships necessitate collaboration and surplus In cooperative game theory, the collective benefit that would be portioned over the cooperating agents is often termed as social surplus.
Social surplus refers to the total value created by cooperation, typically conceptualized as the sum of the agents' utilities or payoffs (Otaki et al.
, 2.
However, achieving optimal surplus distribution often hinges on addressing challenges related to moral hazard and information asymmetry.
Moral hazard is an effect that arises when one party in a transaction has the incentive to act in a way that is hidden from the other party and potentially detrimental to them (Dionne.
This often occurs in settings of asymmetric information, where one agent has more or better information than the other.
To mitigate the inefficiencies caused by moral hazard, studies have emphasized the importance of reputation and trust.
Reputation has been a feature which represents public measure of an agent .
articularly seller or service provide.
reliability based on the assessment of the agent historical behaviour and past interactions (Mui & Halberstadt, 2.
Despite the urgency of reputation in bridging ideal outcome transaction among agents.
Chen .
examines how establishing reputation is not necessarily always the case for optimal outcome to Chen .
provides an example of tipping culture in restaurants in the United States.
This phenomenon can be described using the standard economic model with two players moving sequentially.
This situation leads to an example of an inefficiency problem under incomplete contract.
The waiter will provide a service according to their belief on the amount of the tip that will be given by the customer.
Simultaneously, the customer will decide the tip amount based on the service level given.
Nevertheless.
Chen .
studies how in many other experiences, the situation is not captured exactly the same as earlier example.
Instead, a customer tends to leave a good tip even though the service level might not be adequate.
This introduces the hypothesis of agentAos quality and tendency to keep promise as a product of social convention and norms.
This quality has to be matched also with the waiterAos attitude to build trust, taking for granted that the customer will behave honestly even when it is not in their monetary interest, hence trustworthiness has led the waiter to provide top quality service.
Back to the insurance example, moral hazard would present because of the nature of Asymmetric information becomes a root of problem for dishonest, opportunistic insured.
Knowing that the insurer would not know about their insured health condition, circumstances like adverse selection & moral hazard problem are bound to happen (Xiang & Wang, 2.
Looking at insurance company case, relying only on promise and trust would be naive considering opportunistic customer would be highly probable to present.
This is where the presence of contract is crucial as it creates a system of incentives that encourages both parties to act in a mutually beneficial way and ensures that each party is held accountable for their This helps to protect against fraud, abuse, and other forms of moral hazard and helps to ensure that insurance remains affordable and available to those who need it.
Evidence of usefulness of contracts was studied on how to design optimal insurance contracts (Asimit & Boonen, 2.
Contract is then divided by two types, complete and incomplete contract (Baker & Krawiec, 2.
Complete contracts specify every possible detail and outcome related to a transaction, leaving no room for ambiguity or interpretation.
In contrast, incomplete contracts do not specify every possible detail and therefore may be subject to interpretation and negotiation between the parties involved.
Chen .
discusses how verifiability differs for each type of contract where complete contract means provision of quality being agreed is verifiable, but if the agreed upon quality is higher than what can be verified, then it is incomplete Describing contracts that way, develops follow-up question about residual right that explains which agent has the right to define whether the quality that goes beyond what can be verified is actually delivered.
Following this.
Chen .
develops two models that account for arrangements that assign the residual right to buyer .
enoted as BP, or buyer act as the promiso.
and as well as to seller .
enoted as SP, or seller act as the promiso.
and examines situation where social surplus is maximized.
Cooperative Game TheoryA Research Methods Model Formulation and Study Case: Cooperative Game of Local Government and Contractor in Bridge Infrastructure Project Cooperative games between buyer and seller are modelled where a transactional relationship takes place.
The study case used here is about a contractor as seller/service provider, and local government as buyer/client in a project where the contractor is hired to build a new bridge for a city.
Model formulation will be illustrated for the remaining section of this study and also how it is applied in the context of our case study.
yc yun .
cEa , ycyco } ycEa > ycyco Ou 0 In building a bridge, the quality of the bridge is measured by the materials used, design, and structural integrity.
The quality here is measured in real numbers suppose ycEa represent the highest quality that is 10, and ycyco is a measure of lowest quality which is 6.
yc tells the actual quality of the built bridge.
= ycayc ycO.
= ycyc yc>yca>0 .
here represents the contractor cost and expense in building the bridge, and ycO.
serves as the value of the service to local government.
In later case, the actual quality yc is observed by both parties after the project is done.
A term called recording device is used to record the actual quality, making it verifiable at the end.
Recording device arrangement is generated for the provision of this tool, denoted as ycN .
c, ycyc ).
O , ycnyce yc = ycyco , ycyc = ycEa ycN , ycnyce yc = ycyc = ycEa ycN .
c, ycyc ) = { yc = ycyc = ycyco ycuyc 0 , ycnyce { yc = yc ycaycuycc yc = yc ycN .
c, ycyc ) is the cost of installing recording device with ycyc being the minimum quality value to make the assessment of quality verifiable.
In our case, the recording device could be hiring third-party assessor that would collect documentation and assessment of material used, design and structural integrity.
Suppose that actual yc is 6 .
c = ycyco ), there will be no need to hire an assessor because it will be obvious that an assessment cannot be conducted if ycyc = ycEa .
By assigning value of infinity, the model illustrates the impossibility of initiating recording device.
And if actual yc is 10, the use of assessor is effective as he can confirm that the quality of the bridge is indeed matching the requirement of ycyc which also happen to be the highest quality for the bridge .
cEa ).
Furthermore, if the government only requires the bridge is built in bare minimum standard, then recording device will be 0 denoting it will not be needed as it does not matter anymore whether the contractor delivers even highest quality bridge.
c O , ycyc O ) = ycyc O Oe ycayc O Oe ycN.
c O , ycyc O ) .
Formula above explains how much the social surplus is generated from the bridge project transaction, here denoted as ycO.
c O , ycyc O ).
We have yc O as qualities that is delivered, and ycyc O being quality that is recorded.
In the case of building a bridge, it is difficult to fully specify or verify the quality of the service provided, as there may be unforeseen issues that arise during construction, such as inclement weather or unforeseen geological features.
Additionally, there may be ongoing negotiations and adjustments required throughout the project to ensure the quality of the service Therefore, incomplete contract would be more realistic to be made.
Moreover, assigning the residual right to the service provider is more suitable in the case of building a bridge, as it allows for flexibility and negotiation between the parties involved.
The service provider, in this case, the contractor, is better positioned to make the necessary adjustments and define the quality of the service beyond what can be verified .
cyc < y.
Additionally, the contractor has the necessary expertise and resources to deliver the service, making it more efficient to assign the residual right to them.
Building a bridge is also considered as an SP because it requires a high level of expertise and specialized knowledge, which the contractor is better positioned to provide.
For example, the contractor must have a deep understanding of civil engineering, structural design, and construction management, as well as the ability to manage and coordinate multiple teams and The contractor must also ensure that the bridge meets safety and regulatory requirements and is built to withstand the expected usage and environmental conditions.
The fees charged to the local government then are often decided upfront, while the quality of the service may depend on the efforts of the contractor.
Furthermore, infrastructure projects often involve complex and unpredictable situations such as when availability of materials, equipment, and labor may be affected by external factors, such as supply chain disruptions or labor strikes.
An agent in this model study case has tendency to maximize their monetary benefit.
this case, the contractor may be dishonest if they could gain large monetary gains.
This led to variable ycu being introduced, representing critical value at which the contractor would break a If the monetary gains have lower value than ycu, they will not cheat.
It can be seen as explicit utility .
ood feelin.
for contractor in keeping promises.
Given this situation, the payoff of the contractor can be calculated as below ycOyc .
c, ycyc , yc.
= { ycy Oe ycayc ycu, ycnyce ycaycuycuycycycaycaycycuyc ycayce Eaycuycuyceycyc ycy Oe ycaycyc , ycnyce ycaycuycuycycycaycaycycuyc ycaEayceycaycyc ycOyc explains contractor utility in an agreed contract of .
c, ycyc , yc.
with yc being the agreed quality to be delivered.
ycyc represents the quality that will be recorded.
And ycy defines the payment contractor will receive from their client.
Contractor will cheat only if ycy Oe ycayc ycu > ycy Oe ycaycyc .
For instance if cost of delivering agreed quality .
would be 10,000 and contractor know that providing certain quality with cost of 4000 .
caycyc ) would be sufficient to make it verifiable, as long as their good feeling of being honest has value of 6000, the contractor will be honest.
Cooperative Game TheoryA Similarly, utility for local government as client denoted as ycOyca will be ycOyca .
c, ycyc , yc.
= { ycyc Oe ycy, ycnyce ycaycuycuycycycaycaycycuyc ycayce Eaycuycuyceycyc ycycyc Oe ycy, ycnyce ycaycuycuycycycaycaycycuyc ycaEayceycaycyc Results and Discussion To illustrate the behavioral dynamics embedded in the model, a numerical simulation is conducted using hypothetical values.
The simulation explores how a contractor's internal motivation to honor a promise, or critical value, denoted by ycu influences the decision to either fulfil or cheat on the quality agreed upon in an incomplete contract setting.
Simulation Setup The model assumes a contractual relationship between a local government and a contractor tasked with building a bridge.
The quality of the bridge is quantified on a scale from 6 .
inimum verifiable qualit.
to 10 .
aximum desirable qualit.
The following parameters were defined:
yc = 10 ycyc = 6 ycayc = 10,000 ycaycyc = 4,000 ycyc = 18,000 ycycyc = 10,0000 ycy = 12,000 ycu OO .
, 8.
The contractor chooses to deliver yc .
or ycyc .
based on whether the net benefit of honesty .
ritical value of ycu ) exceeds the profit from cheating.
Derived from previous equation which define the situation where contractor would cheat, the decision rule is simplified as:
Contractor cheats if ycu < ycayc Oe ycaycyc Simulation Outcomes The simulation is run using previously defined parameters to better understand how the behavioral variable ycu influences contractor decisions and social outcomes.
The simulation observes the dynamic of multiple variables of interest value namely ycOyc , ycOyca .
Social Surplus for both if the contractor cheats or being honest given different value of ycu from 0 to 8000 with increment value of 500.
The result is presented into tabular form below.
ycu (Critical Value until Chea.
Table 1.
Simulation outcomes .
abular recapitulatio.
Social Social ycOyc ycOyc ycOyca ycOyca Surplus Surplus .
f hones.
f chea.
Contractor Behavior Cheat Cheat Cheat Cheat Cheat Cheat Cheat Cheat Cheat Cheat Cheat Cheat Honest Honest Honest Honest Honest The table recapitulation of the simulation above clearly shows a behavioral tipping point of the contractor at ycu = 6000.
When ycu < 6000, contractor maximises utility .
cOyc ) by cheating, compensating government utility and overall social surplus.
However, once ycu Ou 6000, honest behaviour becomes utility-maximizing for contractor, resulting in improvement in both partiesAo The dynamics are further visualized in figures below.
Figure 1.
Contractor Utility vs Critical Value .
Cooperative Game TheoryA Figure 1 illustrates the contractorAos utility under both behavioral options across increasing values of ycu.
When ycu < 6000, contractor chooses to cheat as the utility is maximised at 8000.
The intersection at ycu = 6000 represents the point of behavioral change, where promise-keeping becomes as profitable as cheating.
When ycu > 6000, even to cheat will generate less utility now which make being trustworthy is rewarding more than just keeping promise.
Figure 2.
Social Surplus vs Critical Value .
Figure 2 depicts the corresponding dynamics in social surplus.
It basically affirms that in the perspective of overall social surplus, being honest would be the best thing to do for both of the parties.
As the contractor shifts from opportunism to honesty, reputation is more likely to be established.
Figure 3 below shows how honesty threshold value of ycu would shift decision between cheating and being honest.
Figure 3.
Contractor Behaviour vs Critical Value .
Behavioral Interpretation The simulation reveals several critical behavioral and policy-relevant insights:
A Trust as a Threshold Variable: Trust .
odeled critical value of yc.
does not incrementally improve outcomes.
instead, it acts as a threshold variable.
Below the critical point, opportunistic behavior dominates.
Above it, cooperating is preferred.
A Incentive-Compatible Design: If contractors are known to possess low ycu values, formal mechanisms .
, verifiable contracts, third-party monitorin.
may be necessary to prevent cheating.
However, if ycu is sufficiently highAidue to cultural norms, professional standards, or intrinsic ethicsAithen reliance on informal promise-keeping may be both efficient and cost-saving, since assessing third-party or recording device might not be A Social Surplus Maximization: The presence of a high ycu not only reflective on contractor having good moral stance, but also increases government utility, leading to a social surplus maximization.
This reinforces the theoretical claim that trust-enhancing mechanisms .
hrough reputatio.
are not merely ethical complements but economic A Policy Leverage Points: In public-private partnerships, strategies that boost intrinsic trustAisuch as long-term contractor relationships, reputation scoring, or community accountabilityAican substitute or supplement incomplete contracts, leading to better outcomes under uncertainty.
Conclusion This study case provides a practical comprehension on how promise, trust and contract put in ycu plays a huge role in affecting not only contractor utility .
cOyc ), but also local governmentAos .
cOyca ) and social surplus .
cO).
The higher the ycu would indicate a higher tendency of contractor in keeping their promise.
And at the same time, local government would expect their contractor to have large ycu as it will increase the chance for them being provided the agreed quality considering the verifiable quality that can be recorded is lower than what they expect.
Simulation results support this reasoning by showing a clear behavioral threshold at ycu = 6000, beyond which the contractorAos best response shifts from cheating to keeping the promise.
When ycu is below this point, delivering only the verifiable minimum quality becomes more but as ycu increases, the intrinsic value of honesty overtakes gains from opportunism.
This behavioral switch is mirrored in the resulting social surplus, which rises substantially once the contractor chooses to respect the agreement.
This concept of economical model is advantageous in assessing behaviour of an agent in cooperative game and could be used in determining the most optimal outcome for both parties in term of social surplus.
However, in reality, some parties would interpret and see promise as non-negotiable thing.
There is a situation when integrity and righteousness outweigh monetary Thus, ycu is indefinite and most likely makes contractor gaining less that they could, and perhaps as well as the social surplus generated.
This demeanour put the economical model in Cooperative Game TheoryA
References