hawk/dove: vary the payoffs

[jerielizabeth]

[MODIFIED ON 11/22]

Our current payoffs are 0, 1, 2.1, 3. We want to know what happens when these numbers are different. Since the actual numbers don’t matter, only the ratios between numbers, all of the relevant variation can be seen by varying the middle two numbers. In particular: pick two values, b and c, both between 0 and 1. Then:
Instead of “1”, let the payoff of “dove when your opponent plays hawk” be 3b.
Instead of “2.1”, let the payoff of “dove when your opponent plays dove” be 3b + c(3 - 3b). [this represent going “c of the way up the interval” between 3b and 3.]

E.d., b = ⅓ and c = ½ represent the payoff structure 0, 1, 2, 3.

If it’s too much to have two variables, we could just keep “1” and let our single variable be c, again between 0 and 1, where we define the payoff of “dove when your opponent plays dove” as 1 + 2c.

NOTE: This is replacing what I had previously listed as this issue, under lower-priority possibilities: Varying the payoffs of the game, in particular letting the sum of (D, H) + (H, D) > 2(D, D) [more of a robustness check than anything else

see also #44 (one of these is probably a duplicate)