Interesting statistics
Game theory analyzes the strategic interactions of players through mathematics. "Players" can be individuals, groups, or corporations. The result for each player depends on the strategy chosen by everyone.
Elements of game theory
Players: Participants who make strategic decisions. These can be project stakeholders such as clients, managers, or team members.
Strategies: Options that each player can choose from. For example, project managers may use different methods of task distribution or communication.
Payoff: The outcome or outcome of a strategy. It can be completion, cost savings, and reputation.
Types of Games in game theory
Co-op vs. non-co-op: Co-op games allow players to enter into binding agreements, while non-co-op games do not. Many project situations are not cooperative.
Symmetric and Asymmetric: Symmetric games have the same strategies. Asymmetric games have different strategies. Because stakeholder options vary, projects often include asymmetrical games.
Simultaneous and Sequential: Players make decisions at the same time in simultaneous games and one at a time in consecutive games. Project decision-making can involve both types.
Nash equilibrium
A key concept in game theory was named after the mathematician John Nash.
No player can benefit from a unilateral change in their strategy if the other players keep their strategies unchanged.
It is a point of stability and can help managers anticipate strategic decisions and reactions.
Game theory in everyday life
Used not only in project management or mathematics. Its guidelines offer a methodological understanding of everyday situations.
Shopping strategies. When a popular product goes on sale, buyers must make strategic choices. They can buy it at a discounted price or hope it doesn't sell out. In a non-cooperative game, each player (customer) decides to buy now or later, which affects the chances of others getting the item at a discount.
Road navigation. Choosing a route during peak hours requires strategy. All drivers (players) want the fastest route, but avoiding traffic can save time. This situation is reminiscent of the Prisoner's Dilemma, a game theory model in which cooperating players can get more.
Work negotiations. The candidate (player) must decide whether to accept the initial job offer or negotiate better terms. Each player's turn in this process is sequential. The candidate's initial response influences the employer's response to negotiations.
Auction sales. Auctioneers must decide whether to bid early to scare others off or bid later. In this scenario, all bidders make decisions simultaneously, which can affect the strategies of others.
Tragedy of the Commons. Community parks illustrate the Tragedy of the Commons game theory scenario. The park can go bad if all players act selfishly and abuse it. The park will remain clean if the participants cooperate and use it responsibly.
Game Theory and Project Management
Game theory and project management intersect when strategic decision making occurs between multiple stakeholders.
Making strategic decisions. Project decisions affect team members, managers, clients, and others. Each decision is a move in a strategic game in which each stakeholder, as a player, has certain interests, points of view, and opportunities.
Game theory helps project managers make more informed decisions by predicting how stakeholders will react.
Conflict resolution. Project conflicts often arise from stakeholder interests. These conflicts can be understood and managed through game theory. Project managers can find more balanced and effective solutions by modeling conflicts as games and taking into account the point of view of each stakeholder.
Example 1
Imagine that you are in charge of a software update project. The customer service team is one of the stakeholders. You model two methods using game theory:
(a) Involvement of support staff during the beta testing phase
(b) no.
If they are involved, they can actively create self-help materials for clients, resulting in a smoother rollout (positive outcome value). Otherwise, they may be overwhelmed by consumer requests after launch, leading to dissatisfied customers (assigning a negative value).
Project planning
Project planning can benefit from the strategic framework of game theory for stakeholder decision-making.
Stakeholder analysis. Understanding stakeholders as players in the game will help you understand their potential decisions and how they can affect the project. Stakeholder engagement planning is critical to the success of a project.
Distribution of tasks. Project assignments can be a complex strategy game. The skills of each player affect the results of the project. Game theory can help distribute tasks by looking at the actions and reactions of team members.
Project planning is a sequential game. Delays in one task can affect subsequent tasks. Game theory can predict and plan for these delays.
Resource management. Resource allocation decisions can decide the fate of a project or destroy it. Project managers can optimize the use of resources in conflict resolution using game theory.
Identification and reduction of risks. Risk management is essential to project planning. Risks can be modeled as strategic games. This method improves risk assessment and mitigation.
Example 2
Suppose the R&D and marketing departments disagree on the project's budget. You can design a "game" using game theory, in which each department has two options: agree to a compromise budget or raise the issue with senior management.
You distribute the potential reward for each event, considering project delays, the likelihood of budget increases, and damage to reputation.
You can use this information to mediate and propose a solution with the greatest overall benefit (for example, a compromise to avoid escalation).
Risk and uncertainty
The methodology offers a new approach to understanding and managing project risks by considering potential outcomes under uncertain conditions.
Risk identification. Understanding the actions of project elements helps identify risks. Theory can help identify risks by analyzing players and how their actions can influence the outcome by creating risky events.
Risk assessment. Includes impact and likelihood assessment. The approach can improve risk assessment by estimating probabilities by modeling risks through strategy games.
Response planning. The methodology can help planners understand how players will respond to mitigation strategies.
Monitoring and control. Risk management requires monitoring. Game theory can predict risky behavior and help adjust strategy.
Uncertainty. Often leads to unexpected results. Project managers can use the method to predict strategic game outcomes in various scenarios and their probabilities.
Example 3
Imagine a situation where there is a chance that the project will exceed its budget. One tactic is to ask for more money upfront (which stakeholders may view negatively), and another is to use the money you already have (at the risk of losing).
Using game theory, you can develop a risk mitigation strategy that best contributes to project success. Model the scenario and assign values to each potential outcome (including stakeholder response, project delay, and opportunity for additional funds).
For example, by planning tighter budgetary controls or putting forward a business case for additional funding.
Conflicts
Understanding conflicts as games with different strategies can reveal the causes of conflicts and ways to resolve them.
The parties to the conflict pursue different goals. Game theory can identify potential conflict points, providing proactive conflict management.
The conflicting parties have different strategies. Understanding these strategies helps predict outcomes and create solutions. Game theory can evaluate the effects of these strategies.
Parties can intensify or weaken conflicts. Game theory can help guide conflict resolution tactics by identifying which strategies lead to escalation or de-escalation.
Game theory can play a crucial role in negotiations, a common method of conflict resolution. The method can help develop negotiation strategies that consider the potential moves and countermoves of all parties involved, leading to more effective negotiations.
Example 4
Let's say one of your project's important stakeholders opposes the project. In your game model, stakeholders can support or oppose the project, and you can improve or maintain contact levels with them.
Each outcome is assigned a potential reward score after considering the impact of the stakeholder, the resources to improve communication, and their support's impact on the project's success.
From this analysis, you can conclude that improving communication will produce the best results.
Negotiation
Game theory facilitates project discussion, decision making, and optimal outcomes.
Negotiation as a game. Project negotiations often involve several players with different interests and points of view. Viewing negotiations as strategic games makes predicting outcomes and creating effective strategies possible.
Evaluation of stakeholder strategies. Every negotiator has strategies. The methodology can reveal the negotiation path and other parties' reactions.
Consecutive negotiations. Negotiations are sometimes like sequential games of game theory. Knowing this sequence can help to agree on the time and content of the moves.
Simultaneous negotiations. In simultaneous negotiations, anticipating the strategies of others is crucial. In such situations, game theory can help choose a negotiation strategy by evaluating possible outcomes.
Joint negotiations. Game theory helps parties reach binding agreements in cooperation negotiations. The "joint games" of game theory can help create strategies that benefit both parties and build trust.
Example 5
Suppose you are a project manager negotiating the terms of a contract with a supplier. Price and delivery time are the two main issues. Compromise or perseverance are the two main options available to both parties.
You can create a reward matrix that ranks each potential outcome according to advantages and disadvantages. For example, keeping prices lower by a company may result in cost savings (benefit) but poses a risk of delivery delays (cost). A large price concession may guarantee timely delivery, but it will increase the project's cost.
Below is a simplified matrix:
Supplier: Compromise | Supplier: Don't give up | |
|---|---|---|
Manager: Compromise | Manager = -1, Supplier = 1 | Manager = -2, Supplier = 2 |
Manager: Don't give up | Manager = 1, Supplier = -1 | Manager = -3, Supplier = -3 |
The numbers show the net value of each outcome for each side (positive is good, negative is bad). If both parties agree to a compromise in this matrix, the supplier is happy with the result, but the project manager suffers a slight setback due to the higher cost. Both will suffer heavy losses if both sides do not make concessions.
Using this matrix, the project manager can determine the most beneficial method. This may entail choosing specific parameters or persuading the supplier to compromise regarding the possible outcomes.
Stimulating structures
Game theory provides a solid foundation for designing incentive structures, strategic behavior, and decision-making.
Rewards as games. Behavior is easier to understand when incentive structures are viewed as games where players make strategic decisions. From this perspective, changes in incentives can be predicted.
Understanding player strategies. Rewards affect players differently depending on their preferences and goals. Game theory can help tailor incentives to individual motivation and desired behavior.
Balance of individual and collective interests. Game theory emphasizes the conflict between individual and collective interests. Incentive structures must balance individual performance and group goals.
Compatibility with incentives. Incentives must match motives. Game theory stimulus compatibility is applied. It links incentives to individual motives, promoting fair and optimal decision-making.
Consistent incentives. In situations where incentives are distributed over time, as in sequential games, game theory can provide insight into how to structure these incentives to encourage sustained performance.
Joint incentives. Cooperative game theory can help design incentive structures where collaboration is essential. These structures can improve teamwork.
Example 6
By applying game theory concepts, incentive structures can be successfully created. On the example of the work of the project team:
Imagine that you are the project leader of a team with a specific goal. Team members can be given bonuses if the goal is achieved. However, you know that not all team members contribute equally and that there may be free riders (those who contribute less but still receive a bonus).
Using game theory in this situation would entail designing a "game" where each team member can work hard or rest, with the bonus dependent on the team's overall success.
The payout matrix is shown below:
Other members: Hard work | Other members: Free ride | |
|---|---|---|
Member: Hard work | Member = 5, Other members = 5 | Member = 2, Other members = 3 |
Member: Free ride | Member = 6, Other members = 4 | Member = 1, Other members = 1 |
The numbers in this matrix represent each team member's remuneration and the team's total remuneration. Everyone wins if they put in their best effort and work hard (5). However, any particular participant may be motivated to ride for free, in which case they will receive a slightly larger gain (6) while reducing value to others (4). The income will be the lowest if everyone chooses a free ride (1).
This simple game demonstrates that a team-based motivation structure can run into the problem of free riders. You can develop a peer review system to identify and punish them or change the reward structure to include individual performance criteria.
Recall that the remuneration matrix must consider many more variables in real-life scenarios, such as team dynamics, individual incentives, and the complexity of the project's tasks. Along with supporting overall project goals and team morale, incentive structures must be clear.
Example 7
Let's take a simplified business example of choosing two technology companies. The "payoff matrix" from game theory helps visualize this scenario's possible outcomes. Matrix numbers are arbitrary and are used for illustration.
Let's say AlphaTech and BetaTech are competing technology companies. Both companies are considering using new technologies to launch their next product. "Invest" or "Don't invest" are options for both companies. Each decision's success depends on another company's choice, which turns this interaction into a strategic one.
The payout matrix shows the potential outcomes and their projected profit in millions of dollars:
AlfaTech: Invest | AlfaTech: Do not invest | |
|---|---|---|
BetaTech: Invest | AlphaTech = 30, BetaTech = 30 | AlphaTech = 0, BetaTech = 50 |
BetaTech: Don't Invest | AlphaTech = 50, BetaTech = 0 | AlphaTech = 10, BetaTech = 10 |
Let's go through this matrix:
If both companies decide to invest, they will compete directly. Let's assume they both make a moderate profit of $30 million each.
If only one company chooses to invest, it will have a first-mover advantage and a $50 million profit, while the other company will not make any profit.
If neither company decides to invest, they will receive less than $10 million from their existing products.
Both companies can make strategic decisions by looking at the payout matrix. This simplified example shows how game theory can be applied to decision-making.
Example 8
The prisoner's dilemma is another example from game theory. This model is used to model conflicts between individual and collective interests.
For simplicity, let's take arbitrary numbers and a hypothetical scenario involving two company project teams, Team X and Team Y.
Both are working on separate but potentially complementary projects. Teams can "collaborate" and share resources or "non-cooperate" and work alone.
In the payout matrix, the success of the project is represented by numbers from 0 (failure) to 10 (complete success):
Team Х: Collaborate | Team Х: Don't collaborate | |
|---|---|---|
Team Y: Collaborate | Team Х = 8, Team Y = 8 | Team Х = 6, Team Y = 10 |
Team Y: Don't collaborate | Team Х = 10, Team Y = 6 | Team Х = 7, Team Y = 7 |
Here is how to read this matrix:
If both teams cooperate, they share resources and knowledge, achieving a high project success score of 8 each.
If one team decides to cooperate and the other does not, then it benefits from the resources of the second team and gets 10 points, while the second team gets only 6 points.
If neither team cooperates and works in isolation, both receive an average score of 7.
The prisoner's dilemma here is that while both teams would benefit from cooperation, the fear of the other team not reciprocating and taking advantage of their cooperation may cause them to refuse to cooperate.
This lowers the project success rates of both teams. This example shows how game theory can model strategic interactions and decision making.
