# Leadership scenarios in prisoner's dilemma game

**Authors:** S. G. Babajanyan, A. V. Melkikh, A. E. Allahverdyan  
**arXiv:** [1910.08929](https://arxiv.org/abs/1910.08929)  
**Date:** 2019-10-20  
**Summary page:** https://www.summarizepaper.com/en/paper/1910.08929v1/

## Key points

- The paper explores the implications of the prisoner's dilemma game for transactional and transformative leadership.
- The authors discuss a Pareto-optimal scenario where the leader commits to react probabilistically to pure strategies of the follower, who is free to make the first move.
- By offering F an opportunity to resolve the dilemma, L can get a larger average payoff than under an autocratic leadership model that is inefficient for this game.
- This exploitation can be stabilized via repeated interaction between L and F and turns out to be more stable than an egalitarian regime where both parties receive equal payoffs.
- Total payoff of exploiting regime is never larger than in egalitarian case.
- The authors also discuss applications of this solution to fighting corruption through soft methods and modeling Machiavellian leadership when defection benefit is large.
- Optimal strategies of F are mixed while summary payoff is maximal - one mechanism for sustaining this solution being that L recognizes intentions of F.
- Overall, this study provides new insights into how leaders can navigate situations involving cooperation and competition with followers in order to achieve better outcomes for all parties involved.

## Summary

In their paper "Leadership scenarios in prisoner's dilemma game," authors S. G. Babajanyan, A. V. Melkikh, and A. E. Allahverdyan explore the implications of the prisoner's dilemma game for transactional and transformative leadership. The prisoner's dilemma is a well-known contribution of game theory to social sciences, wherein two players face a situation where they can either cooperate or defect with payoffs depending on the other player's choice. The authors discuss a Pareto-optimal scenario where the leader (L) commits to react probabilistically to pure strategies of the follower (F), who is free to make the first move. By offering F an opportunity to resolve the dilemma, L can get a larger average payoff than under an autocratic (Stackelberg's) leadership model that is inefficient for this game. This exploitation can be stabilized via repeated interaction between L and F and turns out to be more stable than an egalitarian regime where both parties receive equal payoffs; however, it should be noted that total payoff of exploiting regime is never larger than in egalitarian case. The authors also discuss applications of this solution to fighting corruption through soft methods and modeling Machiavellian leadership when defection benefit is large; optimal strategies of F are mixed while summary payoff is maximal - one mechanism for sustaining this solution being that L recognizes intentions of F. Overall, this study provides new insights into how leaders can navigate situations involving cooperation and competition with followers in order to achieve better outcomes for all parties involved.