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is selected uniformly at random). At each time-step, the chosen best-response is added
to a player's sequence, and her strategy sequence get extended.
Initialization
The initialization is limited to the creation of the agents and the initialization of the
game from simulation parameters. The history, as it has been implemented right now,
makes interactions with one agent totally independent from interactions with others: an
agent's expected utilities will be computed taking into account only the ratio of coop-
eration on total interactions with each other agents. We can thus create only one agent
per possible guilt aversion level in order to explore all the space of possible interactions
given all other parameters. We thus create one agent per guilt aversion level from 0
to a maximal chosen value of the guilt aversion parameter ('
guiltAversionInitMAx
),
for each discretization step (concretely each 0.1, in this case). Although establishing an
upper threshold for the guilt aversion parameter might seem arbitrary, in the following
section 3.2 we will see that, from a given degree of guilt aversion, results in terms of
agents' payoffs do not vary.
Model Dynamics
At each simulation time-step we randomly pair agents. For each pair, each agent will
first compute the expected utilities associated to each of the possible strategies (
C
and
D
), depending on the probability distribution (computed from the history) of their
mate's strategies. Note that agents choose blindly the first time the interact and then
select, according to the recorded history, the pure best response against the empirical
strategy distribution of their opponent (cf. paragraph 3.1); that is, the strategy that max-
imizes her expected utility. In case both strategies have the same expected utility, agents
choose randomly. After choosing, each agent is informed of the strategy the other agent
played, and computes her payoffs. Agents update their history: (1) they number of inter-
actions with that given opponent; (2) the number of interactions in which
j
cooperated,
if it is the case; and (3) they payoff won (cf. paragraph 3.1). This payoff represents the
real payoff of the game, without taking into account the guilt element; that is, indepen-
dently of the agent's ideality notion. The simulation is iterated until the limit time-step
chosen. The history is then registered to be analyzed afterwards.
3.2
Results: Harsanyi's and Rawls' Idealities Comparison
In Figures 1 and 2, we illustrate behaviors emerging from the interactions during the
game being played. Both axes represent the guilt aversion values from 0 to 10 (with a
step of 0.1). Each guilt aversion value represents also one single agent, as we have cho-
sen to create 1 agent per each guilt aversion value. Figures represent thus the behavior
that is emerging from the interactions of the agent on the vertical axe with the one on
the horizontal axe. Note that we stopped simulations after 5000 steps
7
. In both cases,
we launched 20 replications (without observing any variability in the results despite the
randomness of the first move).
7
This number should be big compared to the number of agents, to allow a high ehough number
of interactions with all other agents.
