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Expected Dynamics of an Intra-Population Imitation Model for Inter-Population 2x2 Symmetric Games

payoffs
HH
0
HD
2
DH
1
DD
0
H
D
H
0 , 0
2 , 1
D
1 , 2
0 , 0
simulation parameters
players: N
100
time
5
run a simulation
Consider two distinct populations with the same number of individuals
N
. At each iteration (of time length
1/N
), all individuals are randomly matched in pairs made up of one individual from each population to play a symmetric 2×2 game. The two possible actions (or pure strategies) in the game are labeled
H
and
D
. Thus, each individual (regardless of the population to which it belongs) is either an
H
-strategist or a
D
-strategist. The payoffs of the game are
HH
,
HD
,
DH
, and
DD
(parameters), where, for instance,
HD
denotes the payoff obtained by an
H
-strategist when he plays with a
D
-strategist.
At the end of each iteration, after all individuals have played the game, one randomly selected player from each population revises her strategy
H
or
D
according to the following rule: "I look at another (randomly selected) individual in my population; if and only if she got a payoff higher than mine, I adopt her strategy". Thus, the game is played between individuals of different populations, but imitation takes place within each population.
The figure shows a simulation of the proportion of
H
-strategists in each population (in white), its expected dynamics (in dashed red), and the phase plane of the expected dynamics (mean field) in the background.
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