An application of evolutionary game theory to social dilemmas: the traveler's dilemma and the minimum effort coordination game

Abstract

The Traveler's Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler's Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games.

Figure 1. Results from playing the TD and MEC games with human subjects, adapted from .

(a) TD game: individuals make higher claims when the reward/punishment parameter is low, and make lower claims when is high. (b) MEC game: individuals expend more effort when the effort cost is low, and less effort when is high.

Figure 2. Results from simulating the TD game.

(a)(c)(d)(e)(f) Average claims in the smoothed TD game over the last of generations versus the reward/punishment parameter for different values of the smoothing parameter , on a complete graph (a), a random regular graph with degree 10 (c), a scale-free graph with mean degree 10 (d), 2D lattice graph with 4 neighbors (e), and 2D lattice graph with 8 neighbors (f). Parameter values: for lattice networks and for other networks, , and . (b) Number of individuals versus their claims , when and , on a complete graph with parameter values: , and .

Figure 3. Results from simulating the MEC game.

(a)(c)(d)(e)(f) Average effort levels in the smoothed MEC game over the last of generations versus the effort cost parameter for different values of the smoothing parameter , on a complete graph (a), a random regular graph with degree 10 (c), a scale-free graph with mean degree 10 (d), 2D lattice graph with 4 neighbors (e), and 2D lattice graph with 8 neighbors (f). Parameter values: for lattice graphs and for other graphs, , and . (b) Number of individuals versus their effort levels , when and , on a complete graph with parameter values: , and .