Leadership scenarios in prisoner’s dilemma game

Abstract

The prisoner's dilemma game is the most known contribution of game theory into social sciences. Here we describe new implications of this game for transactional and transformative leadership. While the autocratic (Stackelberg's) leadership is inefficient for this game, we discuss a Paretooptimal scenario, where the leader L commits to react probabilistically to pure strategies of the follower F, which is free to make the first move. Offering F to resolve the dilemma, L is able to get a larger average pay-off. The exploitation can be stabilized via repeated interaction of L and F, and turns to be more stable than the egalitarian regime, where the pay-offs of L and F are equal. The total (summary) pay-off of the exploiting regime is never larger than in the egalitarian case. We discuss applications of this solution to a soft method of fighting corruption and to modeling the Machiavellian leadership. Whenever the defection benefit is large, the optimal strategies of F are mixed, while the summary pay-off is maximal. One mechanism for sustaining this solution is that L recognizes intentions of F.

Thermodynamic selection: mechanisms and scenarios

“…Competition for the fixed energy current is considered under two known set-ups of game theory: Stackelberg equilibrium [53,55,57] and Pareto optimality [54][55][56]. Once photosynthesis is a heat engine operating between a hot thermal bath (photons generated by Sun) and the cold thermal bath (Earth environment), these set-ups are relevant for plants competing for light.…”

“…Now 2 responds to this switch in the best way, and the agents find themselves within actions (45) that are worst than 1 − √ ϑ 0 , 1 − √ ϑ 0 due to (46). This situation does resemble the prisoner's dilemma [31,34,53,55,82], where the agents following by best response strategies end up in the worse situation compared with the cooperative behavior, which for our case refers to (46). We emphasize that, in contrast to the standard prisoner's dilemma, here the best-response strategies are not unique and amount to 4-cycle (43); see rectangles in Fig.…”

Thermodynamic selection: mechanisms and scenarios

“…Now 2 responds to this switch in the best way, and the agents find themselves within actions (45) that are worst than 1 − √ ϑ 0 , 1 − √ ϑ 0 due to (46). This situation does resemble the prisoner's dilemma [31,34,53,55,82], where the agents following by best response strategies end up in the worse situation compared with the cooperative behavior, which for our case refers to (46). We emphasize that, in contrast to the standard prisoner's dilemma, here the best-response strategies are not unique and amount to four-cycle (43); see rectangles in figure 4.…”

“…Stackelberg's competition model [53,55,57] is a sequential solution of the above game: the first agent (1) is the leader, since it has the advantage of the first move. The second agent (2) is the follower that responds to the first move by 1.…”

Cooperate or Not Cooperate in Predictable but Periodically Varying Situations? Cooperation in Fast Oscillating Environment

“…This problem has produced a vast literature, and remains one of the major focuses of different scientific paradigms. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] Cooperation of agents generates a common good for all interacting agents, including those who do not cooperate. However, cooperative behavior is associated with a cost of cooperation, and so cooperative behavior is assumed to be unfavorable for interacting agents in the absence of supporting mechanisms.…”