Silver Professor’s Dilemma

Faculty positions with tenure are allegedly protected until financial exigency goes into effect.

The following note illustrates a decision-making scenario involving termination of employment. Mostly inspired by frameworks from Game Theory.

This fascinating field has roots in economics, social sciences and evolutionary biology. In 1950, John Nash coined the concept of equilibria:

"An equilibrium is reached as soon as no party can increase its profit by unilaterally deciding differently."

In the words of Kyle Polich from the Data Skeptic podcast, “game theory is the study of perfectly rational agents that act in equilibria.”

Snapshot obtained with NetLogo model PD Basic Evolutionary.

Algorithmic game theory is a spinoff with substantial contributions by computer scientists.  In a recent interview, Michael Kearns conveys the predictive modeling nature of scalable theoretical games in the design of platforms.

NetLogo is an agent-based simulator with a user-friendly interface. The figure above is a static illustration of undoubtedly the best-known theoretical game: Prisoner’s Dilemma.

Game Ingredients

David Easley and Jon Kleinberg formulate three required ingredients for a decision-making scenario to be classified as a game.

• Players: those participating in interactions where their outcome satisfaction is conditional on decisions made by everybody as a whole.

• Strategies: alternatives for how to engage with each other.

• Payoffs: incentives received for each selected strategy.

The Players

Let’s consider a cartoon scenario involving an employer and an employee. Specifically, the ‘Employer’ will be a public university, partly funded by appropriations from a state government, and managed by a governing board appointed by the governor of the home state.  

The employee represents a subset of the tenured instructional personnel, someone with at least 20 years of service and 60+ years of age.  With all due respect, the employee will be dubbed the ‘Silver Professor’.  In part, because of a seasoned wisdom that yields from decades of service, which is commonly reflected in hair style evolving from salt-and-pepper into silver.

Financial Exigency

Financial exigency is an extreme protocol bearing similarities to chapter 11 bankruptcy, because the reorganization mechanisms often involve rejection/cancelation of contracts.

The American Association of University Professors (AAUP) defines financial exigency as an “imminent financial crisis which threatens the survival of the institution as a whole.” Circumstances would be such that "the [financial] crisis must be one that cannot be alleviated by less drastic means than the termination of faculty appointments."

There are 28 reports published by AAUP comprising terminations of tenured faculty appointments due to financial exigency, from 1974 through 2001. Moreover, AAUP published in 1937 a study based on a sample of 197 institutions of higher education while analyzing the impact of the Great Depression. It was then noted that "publicly supported institutions are the most vulnerable"… to faculty salary reductions of at least 50%, furloughs, and terminations.

The Strategies

We suppose the ‘Silver Professor’ has two strategies to play: Retirement and No Retirement. Based on a true story.

On the other hand, the ‘Employer’ may play one of three strategies: Severance, Healthcare, and Termination.

Severance is a strategy involving a lump-sum payout of 50% of one year’s salary, together with no health insurance coverage.

Typically, the percent cost distribution of health insurance premium is an 80-20 split, where the employer incurs most of the cost. The strategy Healthcare denotes an instance with 0% of one year’s salary and 100% of health insurance coverage for 2 years. Based on a true story.

Lastly, the Termination strategy would be enforced as a consequence of financial exigency. It represents 0% of one year’s salary and 0% health insurance coverage. Based on true stories.

Understanding Payoffs

Let’s suppose a prototype tenured faculty line has an annual salary of $90,000.00, and a total compounded cost adding up to $140,000.00 (i.e., salary plus benefits).  In this hypothetical case, the health insurance premium costs $17,000.00 per year.

Over a period of two years this faculty line would cost $280,000.00. For the ‘Employer’ its incentive in playing one out of the three strategies, i.e, Severance, Healthcare, or Termination, is to reduce costs.  Clearly, Termination induces the most savings.  However, the other two strategies generate cost reductions between 84% and 88%.

The Matrix

A theoretical game can be understood as a mathematical model, which is specified by information displayed in a two-dimensional array.  Commonly, a payoff matrix or table is the fingerprint of a game.  The three ingredients appear listed, and the quest to find dynamic outcomes sustained by the game ensues.

For example, one may read from this payoff matrix that when the ‘Silver Professor’ chooses Retirement and the ‘Employer’ plays Healthcare, then the payoff pair is (c,d).  Meaning, the former player would receive c while the latter would collect d units of payoff.

Strategies may be dominant or evolutionary stable. 

Another potential dynamic outcome is for a pair of strategies to be a Nash equilibrium.  According to Easley and Kleinberg under Nash equilibria, “if the players choose strategies that are best responses to each other, then no player has an incentive to deviate to an alternative strategy”.

To avoid stalemates between the ‘Employer’ and ‘Silver Professor’ the payoff values must be set to sustain Nash equilibria.  In other words, parameter values that induce optimal solutions.  Pareto-optimality comes to mind, where win-win scenarios are those mutually beneficial to all parties involved.