Analyzing the Publish-or-Perish Paradigm with Game Theory: The Prisoner’s Dilemma and a Possible Escape

Abstract

The publish-or-perish paradigm is a prevailing facet of science. We apply game theory to show that, under rather weak assumptions, this publication scenario takes the form of a prisoner’s dilemma, which constitutes a substantial obstacle to beneficial delayed publication of more complete results. One way of avoiding this obstacle while allowing researchers to establish priority of discoveries would be an updated “pli cacheté”, a sealed envelope concept from the 1700s. We describe institutional rules that could additionally favour high-quality work and publications and provide examples of such policies that are already in place. Our analysis should be extended to other publication scenarios and the role of other stakeholders such as scientific journals or sponsors.

Appendix

In “A Formal Application of Game Theory with Regard to Early or Late Publications: The Usual Publication Scenario and the Strong Publish-or-Perish Scenario”, we formally define a game theory basis of publishing early or late, define the usual publication scenario and introduce the strong publish-or-perish scenario. In “The Weak Publish-or-Perish Scenario in Terms of the Prisoners’ Dilemma”, we introduce the weak publish-or-perish scenario in terms of the prisoners’ dilemma; In “A Possible Option to Overcome the Publication Dilemma: Conditions Altered Appreciating Establishing Priority via the Pli Cacheté”, we introduce a possible option to overcome the dilemma by altering conditions to both appreciate quality and to establish priority.

A Formal Application of Game Theory with Regard to Early or Late Publications: The Usual Publication Scenario and the Strong Publish-or-Perish Scenario

For the sake of simplicity we restrict the discussion to only two competing researchers (or two competing research teams). In addition, we only consider two (pure) strategies: publishing early or publishing late. And we assume that the researchers are aware of the structure of the game as developed below and behave rationally, i.e., they strive for the largest payoffs. The basic structure of this publication scenario can be formally presented in terms of a symmetric two-players two-strategies no zero-sum game (Fudenberg and Tirole 1991).

Two researchers or research teams rival and work towards related discoveries. We assume that these scientists are at the same career stage, have attracted very similar amounts of grant money, and have comparable publication records. They can be interpreted as players in a game:

Player P₁ :

the first researcher or research team (denoted Researcher A in the main text)

Player P₂ :

the second researcher or research team (denoted Researcher B in the main text)

Both players have two options regarding how to act. Each player can arbitrarily choose one of both strategies.

Strategy s₁ :

early but incomplete publication, with other important pieces of work being published later

Strategy s₂ :

no early but only late publication after a full and convincing development of the issue

We assume that both strategies lead to a publication of an identical scientific content but s₁ leads to two pieces of publication (two chapters) whereas s₂ to only one piece. Given s₁ we assume additionally that the first chapter is suffering from minor errors and/or some confusing terminology and that these issues are successfully settled with publication of the second chapter. Given s₂ we assume that the work published in one piece is consolidated and free of errors. In the following we use “early publication” or “late publication” as short narratives when we refer to s₁ or s₂, respectively.

Both players will receive an academic reward as payoff (utility) depending on the strategies that are chosen.

Utility u_ijk :

payoff (a real number) that player P_k would receive if player P₁ chose strategy s_i and player P₂ chose strategy s_j, 1 ≤ i, j, k ≤ 2.

The game can be summarized as a bi-matrix (Table 3).

Table 3 Bi-matrix summarizing the formalized game of two players P_k, 1 ≤ k ≤ 2, who may play different combinations of two strategies, s₁ and s₂, to receive awards u_ijk, 1 ≤ i, j, k ≤ 2

Two intra-cell conditions and one inter-cell condition seem to be obvious in order to match the usual publication scenario (we note that these conditions do not hold in “A Possible Option to Overcome the Publication Dilemma: Conditions Altered Appreciating Establishing Priority via the Pli Cacheté”, pli cacheté):

1):

If P₁ and P₂ published simultaneously and early, both would receive the same award: u₁₁₁ = u₁₁₂ = a.

2):

If P₁ and P₂ published simultaneously and late, both would receive the same award: u₂₂₁ = u₂₂₂ = d.

3):

The scenario is assumed to be symmetric: u₁₂₁ = u₂₁₂ = b, u₁₂₂ = u₂₁₁ = c.

The usual publication scenario is presented in Table 4.

Table 4 Bi-matrix summarizing the formalized game of two researchers P₁ and P₂, who may choose different combinations of two publication strategies, s₁ and s₂, to receive awards a, b, c, or d

If early publication is favorable one additional intra-cell condition will hold:

4):

If P₁ published early but P₂ late, P₁ would receive a higher payoff than P₂: u₁₂₁ = b > u₁₂₂ = c.

Because the scenario is symmetric we also have: u₂₁₂ = b > u₂₁₁ = c. We believe that the additional assumption 4) is almost evident because we assumed that the strategies s₁ and s₂ do not lead to different scientific contents published.

The following six inter-cell conditions are assumed additionally to match a strong publish-or-perish scenario:

5):

If P₁ and P₂ both published early, each would receive less than P₁ given that P₁ published early but P₂ late: b > a.

6):

If P₁ and P₂ published early, each would receive more than P₂ given that P₁ published early but P₂ late: a > c.

7):

If P₁ and P₂ both published late, each would receive less than P₁ given that P₁ published early but P₂ late: b > d.

8):

If P₁ and P₂ both published late, each would receive more than P₂ given that P₁ published early but P₂ late: d > c.

9):

If P₁ and P₂ both published late, each would receive less than P₁ and P₂ given that P₁ published early: a > d.

10):

If P₁ and P₂ both published late, both would receive in sum less than P₁ and P₂ given that P₁ published early but P₂ published late: b + c > d + d.

Given conditions 5)–10) we have b > a > d > c and b + c > 2d.

Given the strict publish-or-perish scenario we have one and only one Nash equilibrium in pure strategies: (s1, s1) with utilities (a, a). A Nash equilibrium is an outcome from which each player could only do worse by unilaterally changing the strategy. Illustrative examples of Nash equilibria are presented in Chapter 1.2; the existence and properties of such equilibria are discussed by applying powerful mathematics in Chapter 1.3 of the textbook by Fudenberg and Tirole (1991). We conclude that, given this strong scenario and that both players behave rationally, each researcher will publish as early as he/she can.

The Weak Publish-or-Perish Scenario in Terms of the Prisoners’ Dilemma

“A Formal Application of Game Theory with Regard to Early or Late Publications: The Usual Publication Scenario and the Strong Publish-or-Perish Scenario” introduced the strong publish-or-perish scenario. We believe that conditions 1)–8) are evident because we assumed that the strategies s₁ and s₂ do not lead to different scientific contents published. Next, we will relax the other two conditions to analyse whether this has impact on the decisions of the researchers and define the weak publish-or-perish scenario:

1) through 8):

These conditions remain unchanged.

9*):

If P₁ and P₂ both published late, each would receive more than P₁ and P₂ given that P₁ and P₂ published early: d > a. (changed)

10*):

If P₁ and P₂ both published late, both would receive in sum more than P₁ and P₂ given that P₁ published early but P₂ published late: d + d ≥ b + c. (changed)

Because conditions 9) and 10) are changed into 9*) and 10*) a higher value is given to a late publication. This is a rather strong modification because both conditions were changed into strict inequalities of opposite direction. The order of utilites is now b > d > a > c, and we have 2d > b + c. We note that the game has now been specified to a “prisoners’ dilemma” (Fudenberg and Tirole 1991). To see why we have to identify strategy s₁ with betraying (“defecting = confessing”) and s₂ with cooperating (“remaining silent = denying”).

The prisoner’s dilemma is an example of a game that shows why two individuals might not cooperate, even if it appears that it is in their best interests to do so. For further discussions see, e.g., http://www.prisoners-dilemma.com.

Thus, as rational players the scientists will publish as early as possible although our modification of the awards was clearly in favor of a late publication. In this analysis we maximized the absolute payoffs as it is usual in game theory (Fudenberg and Tirole 1991). Note that our conclusion is also true if we change the metric to measure the difference in awards between players: both assure to have no deficit in comparison to the competitor’s award if they publish early [strategy of minimizing the maximum possible loss relative to the competitor (Kahneman and Tversky 1979)]. Publishing early is the dominant strategy for both researchers.

In conclusion, simultaneous early publication is the only Nash equilibrium in the game: (s₁, s₁) with utilities (a, a). The dilemma then is that simultaneous late publication yields a better outcome than simultaneous early publication, but if the researchers behave rationally both will publish early although they know that this is not optimal. And this is so although we modified conditions 9) and 10) into 9*) and 10*) to reflect the higher value of a later and more developed publication. This weak publish-or-perish scenario is shown to be a publication dilemma equivalent to the prisoners’ dilemma.

A Possible Option to Overcome the Publication Dilemma: Conditions Altered Appreciating Establishing Priority via the Pli Cacheté

Obviously, we have to change the conditions more substantially to affect the rational strategy of both players. To do so we go back to Table 3 and introduce conditions to reflect pli cacheté (Erren 2009). The ‘‘pli cacheté” (deposition of a sealed envelope) approach could allow to establish priority of thinking and doing a posteriori, i.e., when the envelope is opened.

We assume that both players P₁ and P₂ used a pli cacheté and, without loss of generality, that the sealed information revealed that P₂ had priority. Alternatively, we may have assumed that only P₂ used the pli cacheté and that P₂ had in fact priority according to the sealed information. We note that this version does not change the structure of the game. The third situation (only P₂ used pli cacheté but P₁ was proven to be first) means that pli cacheté had no effect on the outcome and we are back in a situation without pli cacheté as discussed before. Thus, it suffices to analyse the case that both players P₁ and P₂ used a pli cacheté and that the sealed information revealed that P₂ had priority.

In addition, we assume that P₂ did not know a priori whether P₂ had priority or not but P₂ believed/hoped so. Of course, we make the same assumption about P₁. Finally, we assume that the sealed letters will be opened in all four situations described by Table 3.

This situation is assumed to be known to the scientific community so that late publications are appreciated by Journals, Universities and other stake holders. Thus, we assume that pli cacheté is well established as a procedure within the scientific community. To exemplify, let us suppose P₁ published results in a leading journal. P₂, using the pli cacheté, claims to have obtained (a) identical or (b) extended results earlier. In case (a), the journal should publish a short communication authored by P₂. The journal should also publish a note clearly stating that P₂ was first. In case (b), the journal should publish the whole research of P₂. This will allow recognition of P₂ having been “first” within the scientific community.

The following four intra-cell conditions are used to describe the pli cacheté publication scenario:

1^pc):

If P₁ and P₂ published simultaneously and early, P₂ would receive a higher payoff than P₁: u₁₁₁ < u₁₁₂.

2^pc):

If P₁ published early but P₂ late, P₂ would receive a higher payoff than P₁: u₁₂₁ < u₁₂₂.

3^pc):

If P₁ published late but P₂ early, P₂ would receive a higher payoff than P₁: =u₂₁₁ < u₂₁₂ (P₂ was definitely the first)

4^pc):

If P₁ and P₂ published simultaneously and late, P₂ would receive a higher payoff than P₁: u₂₂₁ < u₂₂₂.

Furthermore, the following four inter-cell conditions are set to match the pli cacheté publication scenario (note that publishing in one piece is appreciated):

5^pc):

If P₁ and P₂ both published early, P₁ would receive the same but P₂ less given that P₁ published early but P₂ late: u₁₁₁ = u₁₂₁, u₁₁₂ < u₁₂₂.

6^pc):

If P₁ and P₂ published early P₁ would receive less but P₂ the same given that P₁ published later but P₂ early: u₁₁₁ < u₂₁₁, u₁₁₂ = u₂₁₂.

7^pc):

If P₁ and P₂ both published late, P₁ would receive more but P₂ the same given that P₁ published early but P₂ late: u₁₂₁ < u₂₂₁, u₁₂₂ = u₂₂₂.

8^pc):

If P₁ and P₂ both published late, each would receive more than P₂ given that P₁ published early but P₂ late: u₂₁₁ = u₂₂₁, u₂₁₂ < u₂₂₂.

It follows that

A):

If P₁ and P₂ both published early, each would receive less than given that P₁ and P₂ published late: u₁₁₁ < u₂₂₁ (because u₁₁₁ = u₁₂₁ < u₂₂₁), u₁₁₂ < u₂₂₂ (because u₁₁₂ < u₁₂₂ = u₂₂₂),

B):

If P₁ and P₂ both published late, both would receive in sum more than under all other scenarios: u₁₁₁ + u₁₁₂ < u₂₂₁ + u₂₂₂, u₁₂₁ + u₁₂₂ < u₂₂₁ + u₂₂₂,. and u₂₁₁ + u₂₁₂ < u₂₂₁ + u₂₂₂.

Obviously, P₁ is striving under all conditions to reach the maximum utility u₂₁₁ = u₂₂₁ (because u₁₁₁ < u₂₁₁ and u₁₂₁ < u₂₂₁), whereas P₂ is trying to receive u₁₂₂ = u₂₂₂ (because u₁₁₂ < u₁₂₂ and u₂₁₂ < u₂₂₂). Thus, both players will choose the strategy “late publication” to maximise the individual pay-off. We have one and only one Nash equilibrium in pure strategies (s₂, s₂) with utilities (u₂₂₁, u₂₂₂). This equilibrium leads to the maximum outcome for the group because of statement B).

Our main conclusion is that this rather simple and first-step analysis revealed pli cacheté as a possible option to achieve more high-quality publications.