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Not really an answer to your question, but since you seem interested in modelling, I wanted to put some ideas to you. When trying to understand an idea, its good to start simple. Perhaps you may want to start with a simpler model of a dynamic $M$ as a function of $y$: $M(y):=\min\{\frac{a}{y},1\}\; 0<a$, which implies that people spend roughly ...
If $f(\succ')=b$, then $2$ is better off pretending to have $\succ_2'$ rather than the actual $\succ_2$: the outcome will then be $b$ instead of $a$, and $b\succ_2 a$.