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Groupwise information sharing promotes ingroup favoritism in indirect reciprocity Mitsuhiro Nakamura & Naoki Masuda Department of Mathematical Informatics The University of Tokyo, JapanM. Nakamura & N. Masuda. BMC Evol Biol 2012, 12:213http:/www.biomedcentral.com/1471-2148/12/213 1

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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

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What stabilizes cooperation in indirect reciprocity?1. Apposite reputation assignment rules2. Apposite sharing of reputation information in the population 3

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Reputation assignment rules Image scoring (IM)Donor’s action: Recipient’scooperation (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

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Reputation assignment rulesSimple standing (ST) Stern judging (JG) G B G B C toward a B player is B!C G G C G BD 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

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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

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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

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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

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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

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Reputation dynamicsd 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

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Ingroup reputation dynamicsd M () = − () + θ ( ) + (1 − θ)− ( ) Φ (σ ( ) )d ∈{GB}M =1d in () = −in () + θin ( ) + (1 − θ)out ( ) Φ (σ ( ) ) d ∈{GB} 11

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Outgroup reputation dynamicsd M () = − () + θ ( ) + (1 − θ)− ( ) Φ (σ ( ) )d ∈{GB}M =1d out () = −out () +d ∈{GB} ∈{GB} 1 1 θin ( )out ( ) + (1 − θ) out ( )in ( ) + 1 − out ( )out ( ) Φ (σ ( ) ) M −1 M −1 12

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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

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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 0.8Player 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

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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

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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

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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

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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

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Conclusions▶ Indirect reciprocity with group-structured information sharing yields ingroup favoritism.▶ Ingroup bias is severer than under JG than under ST. 19