section, we use this consequence to have some discussion about a related 2-defender-interpreter game.

**Multi-agent invasion game** {#sectionmmultii}
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In this section, we consider an invasion including two agents $ i $ and $ j $ such as illustrated in Fig. \[fig:1\] and then, for every agent, $ i $, there is a forgetting factor $ \gamma_{i} $. Due to the fact that every agent has two different tasks of blocking and teaching, we consider $ \gamma_{i} = \gamma_{1i}  + \gamma_{2i} $ according to Eq. \[gamasamam\], where the first Gamma $ \gamma_{1i} $ stands for a forgetting factor in a blocking task belonging to the agent $ i $ and the second Gamma $ \gamma_{2i} $ stands for its forgetting factor in a teaching (helping) task. Furthermore, it assumed that every agent can select to be absolutely selfish ($ \gamma_{1i} =0 , \gamma_{2i} = \gamma_{i}  $) as a defender, sacrifice its blocking task ($ \gamma_{1i} = \gamma_{i} , \gamma_{2i} = 0  $) to be more helpful in teaching, or having every other selection among these two border options, namely, $ \gamma_{i} = ( \gamma_{1i} , \gamma_{2i} ) $, $ \gamma_{1i} + \gamma_{2i} = \gamma_{i} $.

![image](two_defender){width="75.00000%"}

Then we can have 