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Evolutionary Game Theory and Spontaneous Brain Activity

https://www.nature.com/articles/s41598-017-15865-w

 

Significant evidence in the past has shown that the brain is constantly firing and different regions are in communication even when the person is completely at rest. These spontaneous signals are also unique to each person, making them an area of great interest to researchers. Further research has shown that this firing is a complex and nonlinear system. This academic paper sought then to propose a complex model of this activity by analyzing graphical connectivity dynamics through the lens of evolutionary game theory.

 

This model called Evolutionary Games on Networks (EGN), describes the dynamic interactions of neurons arranged in a network, where each network differs in their location/area within the brain. In their system, each neural network is a player in an evolutionary game. A network/area may either take on an activating or inhibiting strategy dependent on what another network/area chooses to do. Furthermore, each area can take an emulative or non-emulative attitude towards another network and thus affect which strategy it will choose. That is, for example, if area one is activating and is non-emulated by area two, area two’s best strategy will be to become more inhibiting. If area one is activating and is emulated by area two, area two’s best strategy will be to become more activating. With many interacting networks and subnetworks, the hypothetical firing can become extremely complex and oscillating by way of continuous balancing between activation and inhibition . Though complex, the firing can accurately model and predict the rest-state fMRI data of a certain brain area about three seconds before it is recorded. In fact, the EGN model had significantly lower prediction errors than the linear model, which varied greatly between individuals.

 

The paper further goes on to explain why brain regions might follow the rules of game theory. First, it may be for metabolic needs in that there is not an infinite supply of resources like oxygen or glucose, so different regions must compete or cooperate with one another. Game theory may also allow for simultaneous firing of regions in a given network without causing complete firing all over the brain at one time, which could be detrimental.  Lastly, the researchers suggest that this approach may be so that the brain can optimize its information processing ability. They also propose that their study provides evidence for brain signals that not only indicate current regional activity, but also impending future activity. This would explain the constant shifting in activation and inhibition associated with a game theoretical situation.

 

This research overlaps with material from our class in many ways. First, the emulative and non-emulative attitudes of the interconnected areas could easily be compared to positive and negative ties respectively, as discussed in class. The interaction between two sites that is emulative can be seen as a positive relationship where one wants to be like the other, and the non-emulative can be seen as a negative relationship with one wanting to do the opposite of what the other one does. Second, these interactions between the brain regions are directed rather than undirected relationships. That is, region one will either emulate or not emulate region two, independent of how region two emulates region one. Just because region one, for example, emulates region two, does not mean that region two will emulate region one.

 

The most significant way that the above research relates to our class discussion is through the application of game theory. Though we have yet to extensively talk about it in class, this study utilizes evolutionary game theory, a modified form of what we have discussed so far, for their prediction model. In evolutionary game theory, individuals will act in such a way that makes them fit best within their population or environment. The game they are playing is for survival and reproduction, so they can have their genes passed down from generation to generation. Evolutionary game theory thus explains how strategies may evolve at the population level without explanation of what each individual member’s strategy is. Therefore the researchers chose to look at the interactions of entire brain regions. This EGN model allowed them to group neurons in together and find the best strategy for them all as one unit given a certain area.

 

Futhermore, we can apply our class lecture on payoff matrices to this study. Looking at Figure 1A, one can see how the interaction of the two areas v and w is extremely similar to the interaction of two players participating in a game as discussed in class. For the first image the two areas are both emulating one another. The payoff matrix may look as follows:

In this case, both activate-activate and inhibit-inhibit are mutual best responses, i.e. Nash equilibria with no dominant strategy present. In the second graph both areas are non-emulators. The payoff matrix may look as follows:


In this case, both activate-inhibit and inhibit-activate are mutual best responses, i.e. Nash equilibria with no dominant strategy present.  In the last graph area w is an emulator while area v is a non-emulator. The payoff matrix may look as follows:


This game has no Nash equilibrium, very similar to the pass attack/defense homework question. Just like in that question, the mixed equilibria are ((½,½),(½,½)) and consistent oscillation between activation and inactivation will occur between areas v and  w. This is a simplified oscillation that when grown to incorporate many other players/regions can correctly model and predict the spontaneous firing seen on fMRI scans.

 

 

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