Hi Arielle, Thank you very much for exposing your reflections. Note that your main model -without payoff 5- is a prisoner's dilemma. It is a good idea to think about using game theory, but obviously this model is simplistic. It would take much more work to get to actually nontrivial realistic results from a game model.
I think you made a typo: « The top-right corner is the Nash Equilibrium ». It is the top left.
Also you say that the attractivity of the unique equilibrium explains why people defect/accuse. I think in real life people do not react to others' accusations: people are self-righteous, they consider they are right, they often resent things and readily accuse others. It is often what leads to mutual abuse. Even if in a heated discussion people suddenly vent, tell things they resent and had so far kept to themselves, it is not consciously as a reaction to others' accusations; it is elicited by the situation, "it just explodes", rather than being -even subconscious- strategic behavior. Or if we want to see it as strategic behavior we probably have to see things globally: including a person's education -learning to behave defensively in general- or even a species evolution -learning to learn and/or evolving to behave defensively.
I do believe there are many useful ways to apply game theory or optimal control to such a interpersonal/social situation but the models probably have to be much more complex. I have not yet researched existing literature, i expect there are some interesting things, but the field is probably not much developed.
Hi Arielle, Thank you very much for exposing your reflections. Note that your main model -without payoff 5- is a prisoner's dilemma. It is a good idea to think about using game theory, but obviously this model is simplistic. It would take much more work to get to actually nontrivial realistic results from a game model.
I think you made a typo: « The top-right corner is the Nash Equilibrium ». It is the top left.
Also you say that the attractivity of the unique equilibrium explains why people defect/accuse. I think in real life people do not react to others' accusations: people are self-righteous, they consider they are right, they often resent things and readily accuse others. It is often what leads to mutual abuse. Even if in a heated discussion people suddenly vent, tell things they resent and had so far kept to themselves, it is not consciously as a reaction to others' accusations; it is elicited by the situation, "it just explodes", rather than being -even subconscious- strategic behavior. Or if we want to see it as strategic behavior we probably have to see things globally: including a person's education -learning to behave defensively in general- or even a species evolution -learning to learn and/or evolving to behave defensively.
I do believe there are many useful ways to apply game theory or optimal control to such a interpersonal/social situation but the models probably have to be much more complex. I have not yet researched existing literature, i expect there are some interesting things, but the field is probably not much developed.