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I've just read through part two of the Nash Equilibrium blog post (linked below) and I'd like a bit of clarification. Is the ultimate goal of modeling the IOTA-specific Nash Equilibrium scenarios to ensure that malefactors using non-default attachment selection won't gain an advantage in the tangle?

The blog post on iota.org.

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Here's my takeaway, and technical people please feel free to correct me:

This blog post is about how every node can pick their own tip selection algorithm, which is the method by which they decide which two transactions to attach a new transaction to (as each time you send a transaction to a node, you confirm two previous ones). As nodes can do whatever they want and can modify the code of the node server, there can be greedy nodes that build their own tip selection algorithm that is different than the default one, in order to benefit themselves (for example, making sure all their transactions are confirmed faster than everyone else).

Essentially, if the default tip selection algo is designed in such a way that it is very beneficial to all nodes, its unlikely for greedy nodes to resort to using inefficient selfish algos. Therefore, nash equilibrium is the criteria to be used to determine how efficient the current default tip selection algo is, in comparison to greedy non-conventional ones.

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In the Tangle randomness is important, if some portion of nodes are selsifh (try to choose the best two tips) we don't want a situation like Figure 1 from this blog post (here).

In other words, only few nodes get lucky, because there will be competition between the "best two tips". In this situation we'll have a thin Tangle and lots of transactions orphaned forever. The proof of the Nash Equilibrium and simulations scenarios shows that the Tangle will be fine under some hypotheses.

Note that all the selfish nodes adopt the same selfish strategy. We can assume that only the selfish nodes are "in the game". The reason for this is because the most players will using the recommended MCMC method for selecting tips. So the non-selfish nodes aren't actually part of the game, but their default behavior constitutes the rules of game that is being played.

Also it's possible to do some analysis to find out which strategy a node is using, for example: if a p_ player uses a selfish strategy, there is an additional risk that other players will detect and ban p_ from the game.

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