# Applications of Game Theory in Project Management: A Structured Review and Analysis

## Abstract

**:**

## 1. Introduction

- We follow a comprehensive and principled method for searching and filtering relevant papers.
- We review papers across several disciplines, such as construction, ICT and education, and highlight the similarities and differences between them in their application of game theory in project management.
- We present a detailed multidimensional classification of the papers that we have reviewed.
- We present and analyse the citation network of the papers we have reviewed, highlighting their interdependency and relative impact.
- We identify gaps in the literature that point to potentially fruitful future research directions.

## 2. Background

#### 2.1. Project Management

#### 2.2. Game Theory

#### 2.2.1. Non-Cooperative Games and Cooperative Games

#### 2.2.2. Nash Equilibrium

#### 2.2.3. Zero-Sum Games

#### 2.2.4. Common Interest Games

#### 2.2.5. Normal-Form Games and Extensive-Form Games

#### 2.2.6. Simultaneous Games and Sequential Games

#### 2.2.7. Subgames

#### 2.2.8. Subgame Perfect Nash Equilibrium

#### 2.2.9. Stackelberg Games

#### 2.2.10. Nash Bargaining

#### 2.2.11. Evolutionary Game Theory

- $E({S}_{1},{S}_{1})>E({S}_{2},{S}_{1})$: By unilaterally changing strategy to ${S}_{2}$, the player will lose out against another player who sticks with the ESS ${S}_{1}$.
- $E({S}_{1},{S}_{1})=E({S}_{2},{S}_{1})$ & $E({S}_{1},{S}_{2})>E({S}_{2},{S}_{2})$: a player, by converting to ${S}_{2}$, neither gains nor loses against another player who sticks with the ESS ${S}_{1}$, but playing against a player who has already “converted” to ${S}_{2}$, a player is better off playing the ESS ${S}_{1}$.

## 3. Selection Methodology

- Scopus database was searched for a number of key phrases, as elaborated below, and all papers deemed relevant in this search were downloaded. A total of 776 papers were downloaded and considered in this manner.
- A brief manual screening was conducted considering the title and abstract of the papers, selecting some papers for detailed inspection. A total of 72 papers remained at the end of this stage.
- After detailed reading of each paper, some papers were excluded from our review and classification, as described below. A total of 25 papers remained at the end of this stage.
- The reference list of each remaining paper was considered, and checked against the list of papers already excluded. If a paper was not already excluded or not in Scopus, then it went through steps 2 and 3 of the screening process, and included in our review and classification if selected. At the end of this step, 32 papers were selected for inclusion in this review.

#### 3.1. Step 1

- ( “game theo*”) and (“project management” or “construction management” or “*contract”)
- (“decision”) and (“project management” or “construction management” or “*contract”)
- (“games”) and (“project management” or “construction management” or “*contract”)

#### 3.2. Step 2

- Title: those papers having titles where the keywords have been used in a different context were omitted. For example, if the word “game” was used in the sense of video game, computer game or other simulated game, those papers were omitted. Similarly, papers with titles where the word “contract” was used in a context not related to project management were omitted.
- Abstract: Those papers which had abstracts that made it clear that the paper deals with ongoing operational issues, and not project management issues, were omitted.
- English language: only records written in English were further considered. Records nominally written in English where the quality of the narrative was so poor as to not make sense to a reasonable native English speaker, were also excluded. Papers which had their title and/or abstract in English, but the body of the paper in another language, were also excluded.
- Availability: Papers which were not publicly available (either freely, or for a fee) were excluded. Note, papers that were publicly available for a fee were not excluded. Only those papers which did not have the full content publicly available freely or for a fee were excluded.
- In cases where two very similar papers by the same authors were found, where one paper is an extension of the other but included all content of the previous paper, only the later (and thus the more ‘matured’) paper was considered. For example, if a conference publication was later developed into a journal paper by the inclusion of additional material, the conference paper was excluded and only the journal paper was considered.

#### 3.3. Step 3

#### 3.4. Step 4

## 4. Classification of the Selected Papers

- Classification based on the application domain
- Classification based on the players of the game
- Classification based on the type of game played

#### 4.1. Classification Based on the Application Domain

- Papers focusing on project management in construction projects
- Papers focusing on project management in ICT (Information and Communications Technology) projects
- Papers focusing on project management in other fields or generic project management

#### 4.2. Classification Based on Players of the Games

- Papers focusing on contractor—contractor games (including investment decision games)
- Papers focusing on contractor—subcontractor games
- Papers focusing on contractor—government games (sometimes called Public–Private Partnerships, where the phrase ‘public’ represents the government and ‘private’ represents the private company which is the contractor)
- Papers focusing on subcontractor—subcontractor games
- Papers focusing on games with other player combinations

#### 4.3. Classification Based on the type of Game Played

## 5. Description of the Papers Reviewed

#### 5.1. Papers Using Normal-Form Games

#### 5.1.1. Papers Using Normal-Form Non-Cooperative Games

**Papers using normal-form non-cooperative zero-sum games**: In this section, we describe papers which exclusively use zero-sum games, or their primary modelling uses zero-sum games, within the normal-form non-cooperative game category. As shown in Figure 3, there are three such papers.

**Papers using normal-form non-cooperative non-zero-sum games**: There are five papers in our review, which exclusively or primarily use normal-form non-cooperative non-zero-sum games to model scenarios in project management, as shown in Figure 3.

#### 5.1.2. Papers Using Normal-form Cooperative Games

#### 5.2. Papers Using Extensive-Form Games

#### 5.2.1. Papers Using eXtensive-Form Non-Cooperative Games

**Papers using extensive-form non-cooperative zero-sum games**: We did not find any papers eligible for our review, as specified in Section 3, which use extensive-form non-cooperative zero-sum games.

**Papers using extensive-form non-cooperative non-zero-sum games**: Nine papers covered in this review use extensive-form non-cooperative non-zero sum games to model project management scenarios. Several of these papers model bargaining between competing entities (such as contractor and subcontractor, or private contractor and government), even though, assuming some solutions are better for all players on average compared to others, these games are not zero-sum.

#### 5.2.2. Papers Using Extensive-Form Cooperative Games

#### 5.3. Papers Relevant to Project Management but not Explicitly Set in Project Management Context

#### 5.4. Gaps in Literature

## 6. Citation Network of Reviewed Papers

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Some examples of papers which were not classified, as they were not project management-specific.

**Figure 6.**The citation network of papers reviewed—domain-based classification shown. Bright pink: construction domain; blue: ICT domain; brownish-pink: other domains or generic project management.

**Figure 7.**The citation network of papers reviewed—player-based classification shown. Blue: government sector—private sector game; pink: contractor—contractor game; red: contractor— subcontractor game; yellow: subcontractor—subcontractor game; green: other types of players.

**Figure 8.**The citation network of papers reviewed—game-based classification shown. Blue: normal-form non-cooperative game; yellow: normal-form cooperative game; red: extensive-form non-cooperative game; green: extensive-form cooperative game.

**Figure 9.**Citation counts of the papers classified according to Google scholar, as accessed on the 4 April 2019. The number of references in each paper is also shown; that is, the incoming citations and outgoing citations of each paper we reviewed are shown. The publication year of the paper is mentioned as part of the paper name.

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Piraveenan, M.
Applications of Game Theory in Project Management: A Structured Review and Analysis. *Mathematics* **2019**, *7*, 858.
https://doi.org/10.3390/math7090858

**AMA Style**

Piraveenan M.
Applications of Game Theory in Project Management: A Structured Review and Analysis. *Mathematics*. 2019; 7(9):858.
https://doi.org/10.3390/math7090858

**Chicago/Turabian Style**

Piraveenan, Mahendra.
2019. "Applications of Game Theory in Project Management: A Structured Review and Analysis" *Mathematics* 7, no. 9: 858.
https://doi.org/10.3390/math7090858