Abstract
Cooperation motives are traditionally elicited in experimental games where players have misaligned interests that yield noncooperation in equilibrium. Research finds a typology of behavioral types such as free riders and conditional cooperators. However, intrinsic motives in conflict settings such as appeasement, punishment, and greed are elusive in such games where noncooperation is the equilibrium prediction. To identify types in the dark side of human interaction, we apply hierarchical cluster analysis to data from the Vendetta Game, which has a payoff structure similar to public goods games but a dynamic move structure that yields cooperation in equilibrium. It allows us to observe diverse non-equilibrium conflict strategies, and to understand how feuds perpetuate. We relate our method and typology to other social dilemmas.
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Notes
We use session averages as the unit of independent observation for these non-parametric tests to control for the non-independence of observations within each session.
We do not use decisions when a player is disadvantaged but cannot steal more than the equilibrium amount (typically when the state of the game is one step away from the terminal point), or when one is equal/advantaged and the co-player has nothing left to steal (cannot play Greed). Four subjects were unclassifiable because they were either never disadvantaged or never equal/advantaged.
There are many alternatives to our method, which we have chosen because of its simplicity and transparency. In addition to pure data mining methods, clustering can be carried out with respect to the parameters of a game theoretic model (e.g., Bolle et al. 2012). Our analysis distinguishes between disadvantaged or equal/advantaged states which are derived from game theoretic equilibrium analysis and are equality oriented.
Comparisons between Sharks and Non-Sharks use independent session-level means, while comparisons between Sharks and other types match individual-level emotions. Table 3 shows no contradiction between the evaluation methods.
In experiments with a stranger design (random matching in every round), players may adapt to average behavior in the population but cannot reply to the behavior of a specific opponent as in the VG.
Analyzing decisions in the HDL and the HDH separately, only 30 and 32 of the 86 subjects can be characterized by applying a cluster analysis. Therefore, although behavior in the two games differ, we analyze them jointly.
This may be implemented by a mixed Markov strategy or by an algorithm of switching after a number of rounds. Such strategies are more sophisticated than the simple Markov strategies found in the VG.
We compute C-Lasso using the MATLAB code of Shi Zhentao (https://github.com/zhentaoshi/C-Lasso). Our linear probability model captures the sequence of moves with four Markov states, controls for HDH and round, and selects two groups. Group 2 estimates for S1–S4 (0.99, 0.50, 0.76, 0.48) are compatible with Stayers, and others including Meeks and TfTs are captured by Group 1 (0.92, 0.66, 0.44, 0.55); all coefficients are significant at p < 0.0001. Group 1 contains 8 of 11 Meeks and 8 of 9 TfTs while Group 2 contains 22 of 30 Stayers. Thus, 76.5% of hierarchical cluster types are consistently grouped by C-Lasso.
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Acknowledgements
The research assistance of Hue Jun Yu is much appreciated. We thank Maria Bigoni, Dirk Engelmann, and two anonymous referees for the invaluable comments. Thanks to Yves Breitmoser, Simon Gächter, Yohanes Eko Riyanto, and Wang Wenjie for the advice and encouragement, and to Nick Feltovich for providing his experimental data. Tan gratefully acknowledges the financial support of Nanyang Technological University through the Start-Up Grant and the Ministry of Education Singapore AcRF Tier 1 Grant RG126/20.
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Bolle, F., Tan, J.H.W. Behavioral types of the dark side: identifying heterogeneous conflict strategies. J Econ Sci Assoc 7, 49–63 (2021). https://doi.org/10.1007/s40881-021-00101-z
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DOI: https://doi.org/10.1007/s40881-021-00101-z
Keywords
- Conflict
- Vendetta game
- Experiment
- Hierarchical cluster analysis
- Types
JEL classifications
- C65
- C72
- D74