Game theory of academic effort and hiring in the age of AI

Saptarshi Pal; Peter S. Park

cs.AIOct 26, 2026

Game theory of academic effort and hiring in the age of AI

Authors: Saptarshi Pal, Peter S. Park

Organizations: Department of Mathematics, Harvard University · Department of Human Evolutionary Biology, Harvard University

Abstract

Many academic disciplines (in particular, mathematics and the theoretical sciences) face difficult questions about how to adapt their practices to the rise of highly capable artificial intelligence (AI). Before AI, a well-written research paper with a strong theoretical result acted as a reliable signal that its authors understood their field in depth. Now that AI is widely accessible, such signals have become cheaper to produce. As a result, they no longer reliably sort academics by their level of understanding. This has direct consequences for academic hiring. The age of AI raises a question for each side of the academic job market. Should an early-career researcher invest in a deep understanding of their field, or instead use AI to build a longer resume with many papers? Should a recruiter favor applicants with fewer papers who pass an interview aimed at probing understanding, or insist on both publication volume and a pass? In this paper, we develop a game-theoretic model of this two-sided dilemma. We classify all pure-strategy equilibria that can arise in this game and use learning simulations to identify the behaviors that populations of applicants and recruiters may learn to adopt. Our analysis provides a framework for reasoning about how academic hiring can adapt to AI and for evaluating practices that preserve the value of deep understanding.

Figures & tables

Figure 1: The effort-and-hiring game. In Section 2 , we describe the game in full detail. This figure illustrates the textual description. First, nature produces an applicant that is either high-potential, medium-potential, or low-potential, with probabilities $\pi_{H},\pi_{M}$ , and $\pi_{L}$ , respectively (each $>0$ ). The high and medium-potential applicants then choose between two strategies: deep and shallow + AI. Choosing Deep yields a deep understanding of the field ( $u=1$ ), and choosing shallow + AI produces a shallow understanding of the field ( $u=0$ ). In addition to determining the understanding of an applicant, a strategic trajectory (deep or shallow) also affects the volume of academic papers an applicant produces pre-interview. In the baseline model, the high-potential individual produces many papers regardless of their strategy ( $y=1$ ), but the medium-potential individual only produces many papers if they choose shallow + AI. By going deep, the medium-potential individual earns few or no papers ( $y=0$ ). The low-potential type is non-strategic: they have no understanding and they produce no papers $(y,u)=(0,0)$ . Recruiters receive the signal $y$ from an applicant’s resume. In addition, they conduct a hiring test (interview), which is meant to sort applicants based on their understanding. However, this test is prone to false positives. Individuals with no understanding (i.e., $u=0$ ) fail the test ( $t=\text{F}$ ) with probability $\tau\in(0,1)$ and pass it ( $t=\text{P}$ ) with probability $1-\tau>0$ . The recruiter makes a decision based on the joint variable $(y,t)$ coming from the candidate’s resume and interview performance. If hired, an applicant receives $W-c$ , and if rejected, $-c$ , where $c=\delta_{\theta}$ after deep study and $c=0$ after shallow study. If an applicant is hired, the recruiter gets payoff $Ay+Bu$ with $A,B>0$ representing how much the recruiter values the productivity and the understanding of their applicant, respectively. If an applicant is rejected, the recruiter earns an opting-out payoff $r>0$ .

Symbol	Meaning and values	Applicant knows?	Recruiter knows?
Applicant type (drawn by Nature)
$\theta$	high ( $H$ ), medium ( $M$ ), or low ( $L$ ) potential	✓ (private)	✗
$\pi_{H},\ \pi_{M},\ \pi_{L}$	Population shares of types, $\pi_{H}+\pi_{M}+\pi_{L}=1;\>\pi_{\theta}>0$	✓	✓
Applicant’s choice
$a$	Trajectory chosen by $H$ and $M$ :
	deep ( $\mathsf{D}$ ) or shallow+AI ( $\mathsf{S}$ ); $L$ does not choose	✓ (own)	✗

Table 1: Elements of the effort-and-hiring game . This table summarizes the variables and parameters in the effort-and-hiring game described in Section 2 . The applicant’s type

\theta

, trajectory

a

, and understanding

u

are private to the applicant. The recruiter observes only output

y

and the test outcome

t

(which may produce false positives by passing

u=0

players with probability

1-\tau>0

). All other parameters are common knowledge. A high-potential applicant produces papers

y=1

regardless of trajectory, but medium-potential applicants only get

y=1

with shallow+AI. If hired, the applicant receives

W-c

and the recruiter gets

Ay+Bu

; if rejected, the applicant receives

-c

and the recruiter,

r

, where

c=\delta_{\theta}

after deep work and

c=0

otherwise. In an extended model, we allow

y

to take three values,

y\in\{0,1,2\}

, representing different levels of research output. With AI, a high-potential individual achieves

y=2

(called a super-output), whereas a medium-potential individual achieves

y=1

. Without AI, a high-potential individual also achieves

y=1

Panel A. Notation
Symbol	Definition
$\sigma_{H},\ \sigma_{M}\in\{0,1\}$	Effort strategy of high-potential ( $H$ ) and medium-potential ( $M$ ) applicants:
	deep work ( $=1$ ) or shallow work with AI ( $=0$ ).
$\rho_{1\mathsf{P}},\rho_{1\mathsf{F}},\rho_{0\mathsf{P}},\rho_{0\mathsf{F}}$	Recruiter strategy; probability to accept after observing $y\in\{0,1\}$ and $t\in\{\mathsf{P},\mathsf{F}\}$
$\rho_{2}$	Probability of accepting super-output, $y=2$ (in extended model only).
$\mu_{1},\ \mu_{0}$	Recruiter belief that an applicant who passed the test with many papers ( $\mu_{1}$ ) or few papers ( $\mu_{0}$ ) truly understands.

Table 2: Pure-strategy perfect Bayesian equilibria of the effort-and-hiring game. Panel A defines notation. Panel B lists every pure-strategy equilibrium outcome for

0\!<\!\tau\!<1

in the baseline (B1) and super-output (B2) models; outcomes not listed in a regime do not exist there. Each row gives the conditions under which its supporting profile is an ordinary perfect Bayesian equilibrium. Outcomes with several supporting profiles, such as

\mathbf{E}_{7}

, have one row per profile. We assume

0<\delta_{H}<\delta_{M}<W

and break ties in favor of acceptance. A dash (–) marks an observation impossible in the baseline. A dagger ( † ) in the strategy profile marks a decision after an observation that never occurs in equilibrium. These actions rest on some off-equilibrium beliefs. We discuss them in Section 3 .

Figure 2: Existence regions of pure-strategy perfect Bayesian equilibria. Each region of the

A

–

B

plane is labeled with the perfect Bayesian equilibrium outcomes that exist there, for the baseline model ( A ) and the super-output model ( B ). The red line is

B=\mathcal{B}_{1}

, the dashed line is

B=\mathcal{B}_{0}

, and the vertical lines mark

A=r

and, in B ,

A=r/2

. These are all defined in Table 2 A. As we see, several equilibrium outcomes can coexist for a particular parameter combination. The shade of blue in the parameter plane gives the number of distinct equilibrium outcomes for the underlying parameter (not strategy profiles). Parameters are

(\pi_{H},\pi_{M},\pi_{L})=(0.3,0.5,0.2)

\tau=0.9

\delta_{H}=0.2

\delta_{M}=0.4

, and

W=r=1

Eq.	Who is hired	Hire rate	$\mathbb{P}(u=1\mid\text{hired})$	Example
Panel A: Baseline model
$\mathbf{E}_{1}$	nobody	$0$	–	–
$\mathbf{E}_{2}$	H (deep); M (shallow) who pass	$\pi_{H}\!+\!(1-\tau)\pi_{M}$	$\dfrac{\pi_{H}}{\pi_{H}\!+\!(1-\tau)\pi_{M}}$	0.857
$\mathbf{E}_{3}$	H, M (deep); L who pass	$\pi_{H}\!+\!\pi_{M}\!+\!(1-\tau)\pi_{L}$	$\dfrac{\pi_{H}\!+\!\pi_{M}}{\pi_{H}\!+\!\pi_{M}\!+\!(1-\tau)\pi_{L}}$	0.976
$\mathbf{E}_{4}$	M (deep); L who pass	$\pi_{M}\!+\!(1-\tau)\pi_{L}$	$\dfrac{\pi_{M}}{\pi_{M}\!+\!(1-\tau)\pi_{L}}$	0.962
$\mathbf{E}_{5}$	H, M (shallow)	$\pi_{H}\!+\!\pi_{M}$	$0$	0

Table 3: Rate of hiring and the probability that a hired candidate understands in each listed pure-strategy equilibrium of the two models. Panel A reports the baseline results, and panel B the extended results. The last column gives values for

\pi_{H}=0.3

\pi_{M}=0.5

\pi_{L}=0.2

, and

\tau=0.9

Figure 3: Long-run behavior of applicants and recruiters in a learning process (baseline model). We study how strategies evolve in populations of high-potential applicants, medium-potential applicants, and recruiters as a result of imitation and rare exploration. For full details of the learning process, see Methods . In panel A , we plot the long-run likelihood that the high-potential and medium-potential populations use a deep (or shallow) trajectory. In panel B , we plot the long-run likelihood that recruiters accept after one of four possible outcomes of an evaluation $(y,t)\in\{(1,\mathsf{P}),(1,\mathsf{F}),(0,\mathsf{P}),(0,\mathsf{F})\}$ . We plot this as we vary the parameters $A$ and $B$ in the horizontal and vertical axes, respectively, and the accuracy of the test, $\tau$ , in rows. Game parameters are the same as those in Figure 2 . The population size is set at $N=30$ and the strength of imitation, at $\beta=5$ .

Figure 4: Long-run applicant and recruiter behavior in a learning process (extended model). We study the same process as the one in Figure 3 but for the super-output extension model. Panel A stays the same as Figure 3 . Here, in panel B , we plot the long-run likelihood that recruiters accept after one of five outcomes of an evaluation $(y,t)\in\{(1,\mathsf{P}),(1,\mathsf{F}),(0,\mathsf{P}),(0,\mathsf{F}),(2,x)\}$ , where $x$ can either be Pass or Fail. In our super-output extension model, we assume that recruiters do not pay attention to the test outcome if they see $y=2$ . This is because seeing this outcome automatically implies that the applicant is high-potential and shallow. We plot these likelihoods as we vary the parameters $A$ and $B$ in the horizontal and vertical axes, respectively, and the accuracy of the test, $\tau$ , in rows. Game parameters are the same as Figure 2 . The population size is set at $N=30$ and the strength of imitation, at $\beta=5$ .

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