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Hawk-Dove and “Rights”

Hawk-Dove and “Rights”. Recall our puzzle from intro lecture: Where do “ rights “ come from? . Self evident? The creator?. “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights…”. Might?.

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Hawk-Dove and “Rights”

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  1. Hawk-Dove and “Rights”

  2. Recall our puzzle from intro lecture: Where do “rights“ come from?

  3. Self evident? The creator? “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights…”

  4. Might?

  5. The “state of nature”?

  6. A “social contract”?

  7. What does this mean?

  8. Today’s lecture is motivated by larger goal of understanding where human rights like those in the Declaration of Independence come from We’ll develop a foundation for thinking about this puzzle

  9. … using the Hawk-Dove game

  10. First, let us discuss a related phenomena in animals (Recall, our “parsimony” argument: if we see similar phenomena in animals, probably same cause)

  11. Animal territoriality

  12. Territoriality: Animal more likely to behave aggressively to defend a resource (land, mate, food) if arrived at first

  13. Even against larger intruder

  14. Even if arriving firstdoesn’t affect value of resource, or likelihood of winning combat

  15. Why would it matter if got there first?

  16. Will explain using (extension of) Hawk-Dove Game Recall…

  17. H D Hawk-Dove H v/2-c v D 0 v/2 Object worth v>0 Cost of fighting c>v Get object if only H, o/w split

  18. Now extend this game as follows: Assume that can play “hawk if arrived first” (bourgeois) Assume that randomly determined before each encounter who “arrived first”

  19. Dove Hawk Bourgeois Hawk v/2-c v, 0 ½(v/2-c)+½v Dove 0 v/2 v/4 Bourgeois 3/4v v/2 ½(v/2-c) If play B and other plays H, half the time you arrive first, and both play hawk And get (v-c)/2, otherwise he arrives first and you play dove and he plays hawk, So get 0.

  20. Dove Hawk Bourgeois Hawk v/2-c 20, 0 ½(v/2-c)+½v Dove 0 v/2 v/4 Bourgeois 3/4v v/2 ½(v/2-c) -(B, B) is only “symmetric” (“pure”) Nash (will prove in homework) -Symmetric = where both players do same (makes sense when both drawn from single population)

  21. In HW, you’ll also show that this Nash Equilibrium emerges in dynamics

  22. Thus, we expect animals to pay attention to who arrived first! Even if arriving first has NO impact on value of resource or likelihood of winning combat

  23. Note: We could have written model where play Hawk if arrive second Play Hawk if second would be unique symmetric equilibrium in that game as well But we don’t ever observeHawk if arrive second. Why not? We’ll find out later in the semester!

  24. “Who arrived first?” or “who arrived second?” are examples of…

  25. Uncorrelated asymmetry: Difference between the two players that doesn’t (directly) impact payoffs Another example: “who has darker skin?”

  26. Questions to keep in mind as today’s class progresses: Which uncorrelated asymmetries can (in theory) dictate who plays hawk? Which uncorrelated asymmetries in practice do(empirically) dictate who plays hawk? We’ll start to address later today, and will have more insight at the end of the semester. But plenty more work can be done!

  27. Now we will present evidence that H-D-B game explains animal territoriality

  28. Wood speckled butterflies mate in sunspots in the forest

  29. Males patrol these sunspots

  30. And wait for females to come by

  31. Source: Davies 1978

  32. Spiral flight is symbolic: Lasts <5 secs Neither male is hurt Original owner always wins

  33. Why don’t the butterflies actually fight over spots?

  34. Life is short (c is high) and spots are abundant (v is low) So v < c B is equilibrium of this H-D-B game

  35. How can we be sure this isn’t driven by some kind of home court advantage?

  36. What does this have to do with humans?

  37. In an experiment, humans did the same thing as the butterflies

  38. Multiple players simultaneously played a computer game To stay alive, had to find berries in bushes

  39. When arrived at same bush, had to decide whether to fight or flee:

  40. Dove Hawk Bourgeois Hawk v/2-c 20, 0 ½(v/2-c)+½v Dove 0 v/2 v/4 Bourgeois 3/4v v/2 ½(v/2-c)

  41. Some players were healthier Some players were bigger

  42. And some simply arrived first

  43. Turns out, arriving first matters a lot (And matters more than being large or healthy)

  44. But arriving first stops mattering as much when lose H-D necessary condition for bourgeois equilibrium: v < c

  45. As H-D-B predicts, humans, like butterflies, attend to who arrived first even with size difference

  46. “Who got there first?” is just one example of an uncorrelated asymmetry

  47. What about in this real-world situation?

  48. Why do you pay? Why not just leave? If the cabby complains to a cop you can claim you paid in cash? No evidence that you didn’t

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