IEEE Computational Intelligence Magazine - February 2022 - 69

tell if agents are obtaining their reward continuously (i.e., displaying
a sustainable behavior). Contrarily to the social outcome
metrics, Shapley values can be computed even though
the reward is globally shared among agents. This is a huge
advantage when the environment does not allow precise
credit assignment.
120
100
80
60
40
1,000 2,000 3,000 4,000 5,000
Episode
(a)
110
105
100
95
90
85
1,000 2,000 3,000 4,000 5,000
Episode
(b)
0.88
0.86
0.84
0.82
0.80
0.78
1,000 2,000 3,000 4,000 5,000
Episode
(d)
6,000 7,000 8,000
6,000 7,000 8,000
110
115
105
100
95
90
85
1,000 2,000 3,000 4,000 5,000
Episode
(c)
500
495
490
485
480
475
470
460
465
1,000 2,000 3,000 4,000 5,000
Episode
(e)
6,000 7,000 8,000
FIGURE 8 Harvest environment: Evolution of the Shapley values and social metrics from [18] over different training episodes with A3C model.
From top to bottom are displayed (a) the Shapley values (noop action selection method; MC estimation with M = 500), (b) the mean of those
Shapley values of all agents, (c) the efficiency, (d) equality, and (e) sustainability metrics.
6,000 7,000 8,000
E. Choosing a Player Exclusion Method
In this subsection, results gathered using the different player
exclusion options (defined in Section IV) during the three
experiments above are analyzed in order to answer RQ3.
When looking at Figures 2, 5 and 7, it becomes clear that
the three player exclusion mechanisms lead to Shapley values
Player
Agent-0
Agent-1
Agent-2
Agent-3
Agent-4
6,000 7,000 8,000
FEBRUARY 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 69
Equality
Mean of Shapley Values of All Agents
Shapley Value
Sustainability
Efficiency

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