Modeling Collaboration in Academia:
A Game Theoretic Approach
Graham Cormode, Qiang Ma,
S. Muthukrishnan, and Brian Thompson
1
Outline
 Goal: Explore the use of Game Theory as a tool for modeling
and understanding the dynamics of collaborative behavior
 Contributions:
 A model of academic collaboration supported by real-world
publication data
 The Academic Collaboration game, where researchers
collaborate to maximize their academic success
 Analysis of collaboration strategies and game equilibria
Modeling Collaboration in Academia: A Game Theoretic Approach
2
Related Work
 Model one researcher’s papers and citations over time [Hirsch’ 05]
+6
+3
+6 +9
+9
+3
+3
+6
+3 +6
+3 +3
 Analyze the coauthorship graph [AAH’ 10, KPMVD’ 10]
Modeling Collaboration in Academia: A Game Theoretic Approach
3
Our Approach
 We present the first generative model to describe the
formation of academic collaborations, the resulting
papers, and the citations they receive
 We model the system as a repeated game, where
researchers choose collaborators each year in an
attempt to maximize their long-term academic success
Modeling Collaboration in Academia: A Game Theoretic Approach
4
Model Design and Validation
 Hypothesis: 𝑐𝑖𝑡(𝑝) is correlated with the academic
success of its authors up to that point and the amount
of effort they put into the paper
 Dataset: DBLP + Google Scholar, 1M researchers,
2M publications
 Experimental set-up: We consider three scenarios:
1. single-author paper, his/her only paper that year
2. two-author paper, their only paper that year
3. multiple papers by an author in the same year
Modeling Collaboration in Academia: A Game Theoretic Approach
5
Model Design and Validation
1. Single-author, no other publications that year
Observation: # of citations grows linearly with h-index
Modeling Collaboration in Academia: A Game Theoretic Approach
6
Model Design and Validation
2. Two-author, no other publications that year
Observation: # of citations received by a paper is
additive over the h-indices of the co-authors
Modeling Collaboration in Academia: A Game Theoretic Approach
7
Model Design and Validation
3. Multiple publications in the same year
Observation: # of citations received by an author is
additive over multiple publications
Modeling Collaboration in Academia: A Game Theoretic Approach
8
The Academic Collaboration Game
 Players: A set of researchers 𝐴
 Utility: Each researcher wants to maximize his/her
academic success ℎ𝑦 𝑎 as 𝑦 → ∞
 Actions: In year 𝑦, each researcher 𝑎 ∈ 𝐴 can
distribute ℎ𝑦−1 𝑎 + 1 units of “research potential”
between individual and collaborative projects
 Outcome: Each project produces a paper that will
receive citations equal to the total research potential
invested by the authors
Modeling Collaboration in Academia: A Game Theoretic Approach
9
Main Results
 A researcher’s h-index grows asymptotically faster
when collaborating than when working independently
– 𝑂 𝑛 versus 𝑂 𝑛
 In the static multi-player game, each perfect matching
on the researchers is in equilibrium
 In the dynamic multi-player game, however, the
perfect matchings are not in equilibrium
Modeling Collaboration in Academia: A Game Theoretic Approach
10
Take-away Messages
 Use of static rather than dynamic collaboration models
may yield misleading predictions of people’s behavior
in collaborative environments
 Game Theory is a promising tool for studying the
dynamics of collaborative behavior
 The Academic Collaboration game can help study
which metrics of academic success encourage
behavior that benefits the academic community
Modeling Collaboration in Academia: A Game Theoretic Approach
11
Future Directions
 Open question: Do there exist equilibria in the
dynamic game?
 Extend the model to allow mixed strategies
 Analyze the game under other metrics of academic
success besides the h-index
 Study the price of anarchy and stability under each of
these scenarios
Modeling Collaboration in Academia: A Game Theoretic Approach
12