Hi All, I have an equation that can't be evaluated, and I'm not sure what is causing it. Even if I try and let it run overnight, the evaluation is still running the next day. The equation that I'm trying to solve for is at the very bottom of all my mathematica script (I tried a few variations, all had to be aborted). I wasn't sure how to just add in the equation without the rest of the notebook, and I thought the other workings in the notebook might be useful to give context.
Just to give context. I have two players, X and Y, with two welfare functions, funx and funy. The variables are a1x, a1y, a2x, a2y, ix and iy. I also have some undefined parameters b, q, r, and c. It's a two period game, so player X chooses a1x and ix in the first round, then a2x in the second round. Similar for player Y. Using backwards induction, I was able to figure out what a2x and a2y would be in terms of ix and iy, and subbed them back into the welfare functions, then I also found a1x and a1y in terms of the parameters. However, when I have the welfare functions in terms of just ix and iy, and differentiate funx with respect to ix and try to solve for zero, thats when Solve or Reduce no longer works. Looking at the original welfare functions funx and funy, it's clear that ix and iy do make things more complex, but not to the point of making this unsolvable right? Figuring out ix and iy are the last step to figuring out the nash equilibrium for this game theoretic model, so i would really appreciate help in figuring out how to solve for them! Thanks in advance!
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