Game Theory in HR: Applications and 3 Case Study Examples

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Game Theory in HR: Applications and 3 Case Study Examples

As an HR community, we’re obsessed with metrics. We depend on metrics to meet HR regulatory standards and monitor the process variation month-on-month.

But do metrics displayed on our dashboards give us a robust roadmap for how to improve them? Or do they provide information about the hidden root causes when we observe improving or declining data?

Most HR practitioners will probably say no. And yet, this information is critical for making improvements. This is where game theory can provide invaluable insights for HR.

How has HR traditionally mitigated metrics constraints?
The differences between game theory and simulation modeling
Game theory explained
The strategic benefits of game theory for HR 
Game theory case studies
Why is game theory not extensively used in operational HR?

“Measuring the impact of HR on bottom-line performance is the holy grail of HR Analytics.” Edward Lawler & John Boudreau, HR Metrics and Analytics: Use and Impact

How has HR traditionally mitigated metrics constraints?

There has been a lot of investment in big data predictive modeling for typical business areas like attrition, succession planning, and learning. Often, this has also involved many months (sometimes years) aggregating vast data, which often involves navigating complex data confidentiality, compliance, and integration hurdles. 

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In addition, as HR analysts, we have also built complex predictive models on R, python, Alteryx workflows, and the like. However, therein lies a fundamental problem. 

HRBPs and other HR function leaders have found that the impact of predictive modeling projects in practice is limited and sometimes even misleading because one fundamental flaw hasn’t been solved when applying predictive models to human behavior. 

Predictive modeling can, at best, reliably predict human behavior at the group/ team level, as there are too many unmappable, untrackable, unreliable variables about human beings to reliably predict personal behavior through predictive modeling.

As Albert Einstein famously said, “Not everything that can be counted counts, and not everything that counts can be counted.” 

What’s the answer? 

It doesn’t lie in reporting or predictive analytics but rather in analysis, which sits somewhere between these two. Rather, in our last 8 years of strategic HR analytics consulting for the US/ Europe/ Canada market, we have discovered two distinct analysis approaches that are most impactful for HR.

  1. Game theory
  2. Simulation modeling

The differences between game theory and simulation modeling

Game theory Simulation modeling
Can quickly be incorporated into almost any tactical/one-time day-to-day HR operational problem or project. It is best suited where a key tactical goal is clearly defined.   More intuitive, provides detailed, granular prescriptive insights for identifying and improving all root causes related to any HR process/sub-process problem and provides solutions to manage or eliminate it. 
Needs less data and, in some cases, no data at all. Very easy to grasp by businesses.
Can also combine problems relating to multiple sub-processes within the same model/project and give an integrated solution for a project. Does require a lot of detailed process data and nifty work for intuitive and interactive dashboarding.
Both are distinct disciplines for HR business analysis, although it may be possible to deploy them together.
Key Application Area of Game Theory in Operational HR

Game theory explained

Let’s use a simple analogy to explain game theory:

If you were to toss a coin, there is a 50% chance that the coin will land on ‘heads’ since a coin only has 2 sides. But what are the chances that a coin tossed twice will land on ‘heads’? Would there be a  25%, 10%, or 1% likelihood?

Next, consider the minimum amount of times needed to toss 3 coins simultaneously to guarantee that each coin lands on ‘heads’ in a single toss.

Let’s reverse the scenario. How many coins would you need to toss simultaneously to 100% guarantee that at least one of the coins lands on ‘heads’? When extrapolated to HR processes, game theory can help to answer complex What-If scenarios. 

Can game theory be applied to any out-of-the-box discipline?

Game theory has roots in probability and statistics and is a vast subject with about 20 subsets or subdisciplines. Two subsets relevant for HR operational insights that we will use for the case studies include:

  1. Combinatorial games
  2. Bayesian game

In this article, we will cover game theory in HR in detail, and we will share 3 day-to-day real-life scenarios for operational HR. Our aim is that, by the end of this article, your HR data science team will be ready to take the first steps in implementing game theory in your HR production environment.

Note: The classical game theory has been modified via joint conditional probability to suit its adoption for real-life strategic HR problems.

Solving gender diversity in top leadership via game theory

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An employee experience platform Humaxa researched gender and racial diversity in leadership in the United States. Based on a study from Maryville University, the split between men and women was 68%/32%.

This is typical problem that HR professionals have been trying to address for years. For example, how can we ensure a higher probability of women leaders being promoted to an SVP level?

The solution to this is via enabling scenarios in the corporate ladder wherein:

1. Sufficient number of men retire at VP/Director level, thereby increasing the probability of women getting promoted
2. Ensure an attractive voluntary retirement for men at senior management level 
3. Lateral hiring of talented women at VP level 

What is the precise route map and metrics for achieving this? Game theory has answers to such strategic HR problems.

The strategic benefits of game theory for HR

These strategic insights, as illustrated in the use cases below, can improve all project efficiencies by approximately 25% or more, which is highly beneficial for operational HR. 

Additionally, this type of information can help HR with project perspective planning, budgeting, scheduling, and, most importantly, being able to calculate and commit to reliable timelines. 

These strategic insights can be computed relatively quickly (in an average timeframe of 4-5 working days) and don’t require big data or complex calculations as is needed for machine learning or AI. Enrolling in a people analytics certificate program will help you develop the skills and knowledge you need to work on people analytics-related projects.

Let’s unpack 3 case studies to illustrate the benefit of game theory for operational HR.

Game theory for HR case studies

Note: The complete calculation of the formulas cannot be given due to space limitations. However, sufficient guidelines are provided to build your own cases and calculate the formulas. Please consult with your data science team for production implementation.

Case study 1: Talent acquisition

  • Location: Conference room, People analytics department, a fortune 500 MNC
  • Host: VP People analytics
  • Client: VP talent acquisition 

HR Game problem statement:

Due to a combination of business factors,  VP Talent acquisition has the following mission-critical requirements: 

  1.  Need to hire 5 sales direct to head different zones to handle a new line of products about to be launched
  2. 2 of the hires need to be women
  3. The average hire’s experience should not be less than 4 years in a senior leadership role.
  • Question: Can game theory for HR provide insights to meet the below requirements?

Solution statement:

VP People analytics: Yes, the following is the route map for meeting the above requirements: 

  • You should interview a maximum of 14 male and 8 female candidates who fulfill the prerequisites for the job role of director. There is a 92% chance that you will find the required number of fitments. 
  • There is an 87% chance that the process will be completed in 84 days and an 80% chance it will be completed in 72 days.
  • It is advised not to include any candidate below 2 years of experience in a leadership role. If you do, there is a 90% chance that the average experience in a senior leadership role will be 4 years or above.

How to report this simplistically to HR leadership:

Up to 14 male and 8 female candidates should be interviewed. It will take 85 days to close all the positions.  The prerequisite for eligibility should be at least 3 years in a senior management role.

The calculations (non-technical overview)

Data used for analysis4 years of high-level recruitment data for director level (region-specific)
Game / Probability techniques usedOverall- Combinatorial and Bayesian game
Computation – Game theory for HR is essentially an HR adoption of the mathematical discipline of probability theory. 
– The approaches used to develop the game theory model were: 
— Separate binomial probability of men and women, multiplied by the number of applicants
— Poisson distribution for the number of days required to complete interviews 
— Normal distribution and anomaly testing of the selected directors over the last 3 years
Time to conduct analysis3 days
Tool usedAlteryx workflow OR Excel Macros OR Python
DeploymentThis can be deployed as a one-time analysis (before the start of a project) or as a CEP dashboard running continuously (updating every day) through the lifecycle of the project

Case study 2: Rewards

  • Client: VP Rewards

HR Game Problem Statement:

Due to a combination of business factors, VP Rewards has the following requirements:

  1. Business needs to ensure that exactly 8 directors accept voluntary retirement(VR)
  2. The average tenure of all the directors accepting VR should be 14 years
  3. The VR offer can only be given in sequence and after the initial 8 have received the offer. This means that the 9th director can only be given the option to retire voluntarily if 1 out of the 8 directors does not accept the offer. 
  4. The VP Rewards wants to know the minimum number of serving directors that should be given this option to ensure that 8 directors will accept VR.
  5. Additionally, the VP Rewards wants to know how to ensure that the average tenure will be at least 16 years.

Solution statement:

VP People analytics: Yes, here is the route map for meeting the above requirements

  • To meet the goal of 8 VRs, Rewards will need to give the VR option to 27 Directors to ensure an 99% chance.
  • It is not recommended to give the VR to directors with less than 12 years tenure. If so, there is a 95% chance that all the directors accepting the VR program will have an average tenure of at least 14 years.
  • The correct sequence in which potential directors must be given the VR can only be analyzed via machine learning, which is beyond the scope of game theory.

How to report this simplistically to HR leadership

Up to 27 directors may need to be given VR options. VR options should ideally be given to employees who have completed at least 12 years of service in the organization. The selection and sequence in which the directors are to be given VR have been computed through a support vector model (machine learning).

Data used for analysis6 years high-level VR data of director level (region-specific)
Hints on the calculations– Sequential hypergeometric distribution through looping
– Group loops were needed for computation because the VR is executed in phases.
Time to conduct analysis7 days
Tool usedAlteryx workflow OR Excel Macros OR Python

Case study 3: Learning & development

  • Client 3: VP Learning & Development (L&D)

Game problem statement:

Due to a combination of business factors, the VP L&D has the following requirements:

  1. L&D is organizing multiple online “remote working leadership training” sessions for senior leaders (such as directors and above) across all 5 global zones.
  2. L&D must ensure that at least 300 leaders from 5 regions attend one online session.
  3. VP L&D wants to know how many sessions must be conducted to ensure that 300 or more leaders attend. Also, whether the sessions should be conducted on specific days of the week and how many days can the entire program be completed (a session length will be 4 hours).

Solution statement:

  • Conduct 12 sessions. 97% chance that 300 or more leaders will attend. Conduct the sessions on Friday afternoon, followed by Wednesday evenings.
  • There is an 85% chance that the 12 sessions will be spread over 4 months.
Data used for analysisNo actual data was available because there was no need for such an exercise in the pre-pandemic period. A small internal experiment was conducted, and the results were magnified to generate soft-simulated data.
Hints on the calculations– Extended Poisson model was employed based on the limited data available.
– Reclusion loop was used, and multiple Poisson computations were completed after each simulated session without replacement to arrive at a figure of 12 sessions.
– An ANOVA test was conducted on the pre-lunch and post-lunch sessions for all days of the week to find the optimal time slots.
Time to conduct analysis7 days
Tool usedAlteryx workflow OR Excel Macros OR Python
Deployment: This can be deployed as a one-time analysis before the start of a project or as a CEP dashboard that runs continuously through the lifecycle of the project.

Unique challenges:

Representative historical data for modeling was unavailable because there had never been such a unique business requirement in the pre-pandemic era. Most of the previous limited well-being sessions of leaders were smaller and non-virtual, with leaders often flying to venues in global locations.

The methodology used

The calculation steps are as follows: 

  1. The business case is transformed into game theory
  2. Historical data was taken ( 3 or 4 years of data )
  3. Distribution type observed ( this can be done in-house by Minitab statistical software or via taking an obfuscated sample and parsing it via an online tool )
  4. The data is then parsed through the identified CDF (cumulative density function) specific to each distribution (as identified in point 3). For example, Step 4 can be calculated with the following:
  5. The probabilities are multiplied together for joint probability (as required)
  6. Compounding reclusive looping has to be done if required (like in the rewards use case) via python or R.
  7. The probability calculations use linear algebra and factorials. No one needs to do this in practice, as preconfigured statistical tools ( Minitab, Online sites ) are available to calculate this.
HR Game Theory Deployment Roadmap
This roadmap has been created by Humaxa.

Key technical snippets used in the examples

  • Some of the above HR-specific computations involve stretching applied probability functions to their limits but are all easily doable by a statistician.
  • The above examples represent only 1% of the possibilities of its application in HR. Game theory can be applied to almost every conceivable transactional HR process.
  • Most cases only need obfuscated high-level data, which takes care of the need for data confidentiality regulations like the EU GDPR etc. This is a significant advantage when compared to analytics and machine learning approaches.
  • Theoretically, these computations can even be executed on excel macros; however, a better idea might be to use platforms such as Alteryx or Python programming.
planning levels for hr game theory

Why is game theory not extensively used in operational HR?

Interestingly, we have not observed HR actively using game theory in operational planning, at least not in a productive environment. This is a lost opportunity, given game theory’s huge potential. 

Why has HR not better-leveraged game theory? Over the last decade or so, the data science application narrative in HR seems to have shifted from a static or dynamic reporting focus to AI, machine learning, and NLP or big data –  overlooking the potential that game theory has to offer in the process. 

Probability and game theory are part of an old discipline in its practical application that has been around for at least 100 years.

French mathematicians Pascal, Fermat, and Poisson ( pronounced as ‘poa – sohn’) are credited with pioneering research in this field, supplemented by many other European mathematicians. It is used in disciplines as diverse as insurance actuaries, criminal behavior tracking, equity portfolio macro balancing, even warGame, and estimating  COVID spread patterns.

Some machine learning routines, like Naive Bayes and KNN, even use a subset of probability and game theory in some form, for example, computing likelihood and probabilistic voting score.

It’s important to note that using probability and game theory in isolation with Baysen Game opens up a whole new dimension of tactical application, which is a game changer for HR and others. 

The case studies above illustrate how we can quickly calculate close approximate answers for any tactical business problem. Whereas advanced analytics projects only work on standard well-documented HR use-cases such as calculating attrition, succession planning, or predicting absenteeism. 

The pros and cons of HR gaming theory vs. HR machine learning and AI

HR gaming theoryHR machine learning & AI
Minimal and only high-level data required Big data and unobfuscated data required 
Can be computed using a regular PC or a smartphone, with Excel,Needs a powerful computer or distributed computing
Formula can be adapted to give immediate answers to any tactical, operational HR problemRigid in application possibilities. 90% of machine learning projects in HR are still centered around attrition, succession planning, and workforce optimization

To conclude

Functional HR doesn’t have to get into the finer details of the computations, as this will be the job of a statistician. However, to give you a brief overview of the maths, game theory is based on an estimate known as cdf (cumulative density function) with various documented distribution types such as normal, binomial, geometric, Poisson, etc. These distribution types approximate multiple types of HR processes and subprocesses.

For the adoption of game theory in HR, all factors are tweaked so that the probability of an occurrence of the desired event (tactical HR projects) is at least 85%. This is the essence of a Baysian Game.

Happy gaming, HR!

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