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Ingroup favoritism under indirect reciprocity

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Nakamura and Masuda, BMC Evolutionary Biology, 12, 213 (2012).

Nakamura and Masuda, BMC Evolutionary Biology, 12, 213 (2012).

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Ingroup favoritism under indirect reciprocity

  1. 1. Groupwise information sharing promotes ingroup favoritism in indirect reciprocity Mitsuhiro Nakamura & Naoki Masuda Department of Mathematical Informatics The University of Tokyo, Japan M. Nakamura & N. Masuda. BMC Evol Biol 2012, 12:213 http:/www.biomedcentral.com/1471-2148/12/213 1
  2. 2. Indirect reciprocity Alexander, Hamilton, Nowak & Sigmund ▶ A mechanism for sustaining cooperation Cost of help Benefit !! "# "# Later, the cost of help is compensated by others’ help 2
  3. 3. What stabilizes cooperation in indirect reciprocity? 1. Apposite reputation assignment rules 2. Apposite sharing of reputation information in the population 3
  4. 4. Reputation assignment rules Image scoring (IM) Donor’s action: Recipient’s cooperation (C) G B reputation: or defection (D) good (G) or bad (B) C G G D B B ▶ C is good and D is bad ▶ Not ESS (Leimar & Hammerstein, Proc R Soc B 2001) 4
  5. 5. Reputation assignment rules Simple standing (ST) Stern judging (JG) G B G B C toward a B player is B! C G G C G B D B G D B G D against a B D against a B player is G player is G ▶ ESS (e.g., Ohtsuki & Iwasa, JTB 2004) 5
  6. 6. What stabilizes cooperation in indirect reciprocity? 1. Apposite reputation assignment rules 2. Apposite sharing of reputation information in the population Incomplete Group structure information sharing (not well-mixed) ignored ignored ▶ We assumed groupwise information sharing and (unexpectedly) found the emergence of ingroup favoritism in indirect reciprocity 6
  7. 7. Ingroup favoritism Tajfel et al., 1971 ▶ Humans help members in the same group (ingroup) more often than those in the other group (outgroup). ▶ Connection between ingroup favoritism and indirect reciprocity has been suggested by social psychologists (Mifune, Hashimoto & Yamagishi, Evol Hum Behav 2010) 7
  8. 8. Explanations for ingroup favoritism ▶ Green-beard effect (e.g., Jansen & van Baalen, Nature 2006) ▶ Tag mutation and limited dispersal (Fu et al., Sci Rep 2012) ▶ Gene-culture co-evolution (Ihara, Proc R Soc B 2007) ▶ Intergroup conflict (e.g., Choi & Bowles, Science 2007) ▶ Disease aversion (Faulkner et al., Group Proc Int Rel 2004) ▶ Direct reciprocity (Cosmides & Toobey, Ethol Sociobiol 1989) ▶ Indirect Reciprocity (Yamagishi et al., Adv Group Proc 1999) 8
  9. 9. Model ▶ Donation game in a group- structured population (ingroup game occurs with prob. θ) "$ ▶ Observers in each group assign reputations to players based on a common !! "# assignment rule "# "# ▶ Observers assign wrong reputations with prob. µ << 1 9
  10. 10. Reputation dynamics d M () = − () + θ ( ) + (1 − θ)− ( ) Φ (σ ( ) ) d ∈{GB}M =1 ▶ where, r=(G,G,B) () Prob. that a player in group k has reputation vector r in the eyes of M observers Group 3 − () ≡ ()/(M − 1) $ Group 1 Group 2 = !! # σ () Donor’s action: σ (G) = C σ (B) = D # # Φ ( ) Prob. that an observer assigns r when the observer scalar observes action a toward recipient with reputation r’ 10
  11. 11. Ingroup reputation dynamics d M () = − () + θ ( ) + (1 − θ)− ( ) Φ (σ ( ) ) d ∈{GB}M =1 d in () = −in () + θin ( ) + (1 − θ)out ( ) Φ (σ ( ) ) d ∈{GB} 11
  12. 12. Outgroup reputation dynamics d M () = − () + θ ( ) + (1 − θ)− ( ) Φ (σ ( ) ) d ∈{GB}M =1 d out () = −out () + d ∈{GB} ∈{GB} 1 1 θin ( )out ( ) + (1 − θ) out ( )in ( ) + 1 − out ( )out ( ) Φ (σ ( ) ) M −1 M −1 12
  13. 13. Results: Cooperativeness and ingroup bias Frac. G Frac. G Ingroup (ingroup) (outgroup) Prob. C bias Rule ∗ (G) in ∗ (G) out ψ ρ 1 1 1 IM 2 2 2 0 1+θ µ µ ST 1−µ 1−µ 1− θ θ θ 1 1+θ 1 JG 1−µ − µθ −µ 2 2 2 ψ ≡ θ∗ (G) + (1 − θ)∗ (G) in out ρ ≡ ∗ (G) − ∗ (G) in out 13
  14. 14. Results: Individual-based simulations (a) 1 IM ST ψ ST, theory 1.0 1.0 0.5 ST, M = 2 ST, M = 10 0.8 0.8 Player Prob. C JG, theory 0.6 0.6 JG, M = 2 0.4 0.4 0 JG, M = 10 0.2 0.2 0 0.5 1 JG 0.0 0.0 Group −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 θ (b) 1.0 0.5 0.8 G 0.6 B ρ 0.4 0.25 Ingroup bias 0.2 0.0 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 N=300, µ=.01, N=103, µ=.01 0 M=3, θ=.6 0 0.5 1 14 θ
  15. 15. Results: Cases with error in actions (a) 1 ψ ▶ Donors fail in cooperation 0.5 ST, theory ST, = 0.01 with prob. ε Prob. C ST, = 0.1 JG, theory JG, = 0.01 0 JG, = 0.1 0 0.5 1 θ (b) 0.5 ρ 0.25 Ingroup bias N=103, µ=.01, M=10 0 0 0.5 1 15 θ
  16. 16. Results: Evolutionary stability ▶ Conditions under which players using reputations are stable against invasion by unconditional cooperators and defectors: ST 1 public reputation: θ = 1 1 1−θ private reputation: θ → 1/M, M → ∞ JG (M−1)(1+θ) M−1 1 1+(M−3)θ+Mθ 2 1−Mθ if 0 ≤ θ M (M−1)(1+θ) 1+(M−3)θ+Mθ 2 if 1 M ≤θ≤1 1 → (M → ∞) θ 16
  17. 17. Results: Mixed assignment rules ▶ Observers use JG with prob. α and ST with prob. 1-α a b c 1 0.5 5 M2 Θ 0.6 Ψ Ρ 4 bc 0.5 0.25 3 M 2, Θ 0.6 M , Θ 0.6 M 2, Θ 0.2 2 M , Θ 0.2 0 0 1 0 0.5 1 0 0.5 1 0 0.5 1 ST Α JG ST Α JG ST Α JG d e f 5 5 5 M M2 M Θ 0.6 Θ 0.2 Θ 0.2 4 4 4 bc bc bc 3 3 3 2 2 2 1 1 1 0 0.5 1 0 0.5 1 0 0.5 1 ST Α JG ST Α JG ST Α JG 17
  18. 18. Results: Heterogeneous assignment rules ▶ Different groups use different rules (either ST or JG) (a) (b) 1 1 ψST , ψJG , ρST , ρJG ψST ρST ψST ρST ψJG ρJG ψJG ρJG 0.5 0.5 0 0 0 2 4 6 8 0 5 10 15 20 (c) (d) 0.2 M=8 0.2 M=20 b=2 b=2 b=4 b=4 πJG − πST 0.1 b=6 0.1 b=6 0 0 Number of -0.1 -0.1 JG groups 0 2 4 6 8 0 5 10 15 20 18 m m
  19. 19. Conclusions ▶ Indirect reciprocity with group-structured information sharing yields ingroup favoritism. ▶ Ingroup bias is severer than under JG than under ST. 19

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