implement Hawk-Dove game with risk-attitudes

[rlskoeser]

Game setup from @LaraBuchak :

Hawk/Dove Game: https://en.wikipedia.org/wiki/Chicken_(game)

	H	D
H	0, 0	3, 1
D	1, 3	2, 2

BACKGROUND: Blessenohl (unpublished paper) shows that the equilibrium in this game is different for EU maximizers than for REU maximizers (all with the same risk-attitude), and that REU maximizers do better as a population (basically, play DOVE more often)

We want to know: what happens when different people have different risk-attitudes.

GAME: Hawk-Dove with risk-attitudes
Players arranged on a lattice [try both 4 neighbors (AYBD) and 8 neighbors (XYZABCDE)]

X	Y	Z
A	I	B
C	D	E

Each player on a lattice (grid in Mesa):

• Has parameter r [from 0 to 8] [or 0 to 4 on the 4 neighbors lattice]
• Let h be the number of neighbors who played HAWK during the previous round. If h > r, then play DOVE. Otherwise play HAWK.
  • [or reverse inequalities? - make sure we're defining risk attitude consistent with other simulations]
  • [first round: randomly determined? Something else? See how initial conditions matter?]
  • [OR VARY FIRST ROUND: what proportion starts as HAWK
    • [Who is a HAWK and who is a DOVE is randomly determined; proportion set at the beginning of each simulation. E.g. 30% are HAWKS; if we have 100 players, then each player has a 30% chance of being HAWK]
  • Call this initial parameter HAWK-ODDS
• Payoffs are determined as follows:
  • Look at what each neighbor did, then:
  • If I play HAWK and neighbor plays DOVE: 3
  • If I play DOVE and neighbor plays DOVE: 2
  • If I play DOVE and neighbor plays HAWK: 1
  • If I play HAWK and neighbor plays HAWK: 0

[could also change these, especially if we want negative payoffs to keep the total points manageable (e.g.: 2, 1, 0, -1). What makes it a HAWK/DOVE games is the order of the payoffs]

-Add all 8 of your payoffs

We want to see: do we end up with stable populations/regions playing HAWK/DOVE?
(e.g. for 90% of the population, the strategy each agent plays on round n is the same as it plays on n-1)
(e.g. distribution of HAWK to total population on each round stays within a 5% interval)

For 100 rounds: take max {hawks/total} minus min {hawks/total}, if that’s less than 0.05, stop (e.g., hawks at least 10% but no more than 15%)

QUESTION: do we meet either of these ending conditions?

(2) If so, what do these look like in terms both of risk attitudes and strategy played?

SPIT OUT: proportion of H vs. D
SPIT OUT: proportion of {H, r = 1}, {D, r = 1}, {H, r = 2} etc.

How does each risk attitude do in terms of points received over time?

Doesn’t depend on stopping
SPIT OUT: average cumulative payoff of r =1, average payoff of r = 2, etc.

VARIANT: After 10 rounds, each player looks at her neighborhood (4 or 8), and adopts the risk-attitude of the player with the most points.

---

updates:

• adjust to allow specifying a single configurable risk attitude for all agents
• customize display to use shapes to communicate choice of hawk/dove
• revise choice logic so we're consistent in how we define r

[LaraBuchak]

To match with how we're defining risk in the other simulations, this:

Let h be the number of neighbors who played HAWK during the previous round. If h > r, then play DOVE. Otherwise play HAWK.

Should be:

Let d be the number of neighbors who played DOVE during the previous round. If d > r, then play HAWK. Otherwise play DOVE.
[Intuitive idea: if I'm risk-avoidant, I only play HAWK if there are a lot of doves around me. More risk-avoidance requires a higher number of doves to get me to play HAWK. Our original text had said that large r means I require a lot of hawks to play DOVE, i.e., the higher the r the more I play HAWK.]

Or, if you want to keep it in terms of h = # of HAWKS:

Let h be the number of neighbors who played HAWK during the previous round. If 1 - h > r, then play HAWK. Otherwise play DOVE.

[rlskoeser]

implemented in #16; reviewed in meeting 9/13