Networks and Cooperation

John T. Scholz Florida State University Political Networks Workshop May 19, 2009

Background: Why Networks?

• • •

Local Institutions develop to coordinate policies where environmental problems are most acute.

– Mark Lubell, John Scholz, Mark Schneider, and Mihriye Mete. 2002. “Watershed Partnerships and the Emergence of Collective Action Institutions” American Journal of Political Science 46: 148-163.

Federal policies can enhance the capacities of local policy networks to integrate policies within these institutions

Mark Schneider, Mark Lubell, John T. Scholz, Denisa Midruta, and Matt Edwards. 2003. “Building Consensual Institutions: Networks and the National Estuary Program” American Journal of Political Science 47:143-158.

Background: Why Networks?

•

Local institutions and policy networks transform interests and strongly influence independent federal policies

– John T. Scholz and Cheng-Lung Wang. 2006. “Cooptation or Transformation? Local Policy Networks and Federal Regulatory Enforcement” American Journal of Political Science 50(1): 81-97

Bonding Social Capital Bridging Social Capital A’s Network Position Measures Degree 3 Clustering Centrality 1 0 B’s Network Position Measures Degree 3 Clustering Centrality 0 0.8

The Risk Hypothesis

• • Bridging relationships most effective for low risk coordination/assurance games.

– Efficient information transmission Bonding relationships most effective for higher risk dilemmas, like prisoners dilemmas – Norms and 3 rd party punishment

Two questions for networks

• • The impact of networks on cooperative behavior (performance) – Network structures and general level of cooperation – Network positions and propensity to cooperate.

The dynamics of network selection in dilemmas – When do actors seek bridging, when bonding?

Bridging in Estuary Policy Arenas

• •

Betweenness centrality of ego, not clustering, enhances level of collaboration

– John T. Scholz, Ramiro Berardo, and Brad Kile. 2008.“Do Networks Solve Collective Action Problems? Credibility, Search, and Collaboration” Journal of Politics 70(2):393-406

Actors seek central coordinators, not transitivity

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Different organizations are central

– –

Indicates dynamic preference for popular actors

Ramiro Berardo and John T. Scholz, “Self-Organizing Policy Networks: Risk, Partner Selection and Cooperation in Estuaries” 2009?

Bonding Capital: 3 Studies

• • Learning Networks – Evolution of cooperation on fixed networks – Agent-based computational model Game Networks: Repeated Prisoners Dilemma – Experiment 1: Network impact on performance: • Bridging vs Bonding Capital, fixed networks – Experiment 2: Endogenous networks and performance

Learning Networks and Cooperation

• • Evolution transforms dilemma into coordination game of strategy selection TFT replaces AllD in finite populations, if – cooperative payoffs and repetitions before updating favor cooperation when p TFT >1/3 – : ρ TFT > 1/N >ρ AllD – ρ depends on • types of strategies (retaliatory, altruistic, exploitative) • clustering of contact types (replaces N) • Learning/updating algorithm and learning network

From: Nowak et al. 2004. Emergence of cooperation and evolutionary stability in finite populations

Nature

428: 646-50

Learning Networks and Cooperation • “Five Rules for the Evolution of Cooperation” – Kinship – Direct Reciprocity (Repetition) – – Indirect Reciprocity (Reputation) Network Reciprocity (Structure of Relationships) – Group Selection Martin A. Nowak, 2006; Science 314: 1560

Learning Networks and Cooperation • • Graph game (overlapping k-person public goods game): – – Cooperators give benefit b to all k neighbors, at cost c Defectors get benefits, do not give, and incur no cost.

Selection favors Cooperation if b/c > k (Ohtsuki et al Nature 2006)

Learning Networks and Cooperation • • • • • Fixed game structure (10 regulators play all firms) Vary learning structures • Ring, random, small world, and village • • Size: N ={25, 50, 100, 200 } Connectivity: Degree= {2,4,8} and {5,10} Proportionate Learning algorithm • Copy best response among friends, with innovation All 1-period strategies Together, they define a Markov chain • Invariant distribution determines cooperation

Learning Networks and Cooperation

Learning Networks and Cooperation

Learning Networks and Cooperation

Learning Networks and Cooperation

• Testable Hypotheses: Cooperation increases with: – Bridging Capital (faster exploitation of TFT): • Larger networks (to some threshold) • More connected (higher degree) – Bonding Capital (better defense against AllD) • Higher clustering – Greatest impact in small, less connected networks – Particularly effective in concentrated village structure

II. Do Closed Triads Increase Cooperation?

• Experimental Design – 66 subjects (in 3 separate sessions) – complete survey first (measure trust and trusting behavior) – assigned randomly in groups of 3 – Play 20 periods of PD (end known in advance) • Payoffs: 0, 25, 75, 100 – Reassign, repeat for 4 complete rounds of 20 periods each

Treatment: Closed vs Open Triad

Bridging Bonding Open Leader= A Open Follower = B, C

Experimental Design

Variable

Logit analysis of cooperation

Coefficient Std. Error

Constant:OpenNonleader Closed

Open Leader

Trust: Behavior Attitude

Trust Behavior X Closed T rustEnvironment

Closedfirst round2 round3 round4 Last 3 periods 0.88

0.11

0.27**

0.09

0.07

0.20** 0.20**

0.00

0.77* 0.82* 0.33* -1.46

0.19

0.07

0.10

0.11

0.11

0.05

0.02

0.25

0.08

0.08

0.08

0.07

Predicted Probability of Cooperation

Predicted Probability of Cooperation

Do Closed Triads Increase Coordination?

• What comparable game can represent the coordination problem?

– Symmetric: Pick same alternative from multiple choices • Follow the leader: Open will coordinate in 2 periods – Asymmetric: • Open leader can exploit, but how much?

• Closed will do better if compromise (focal) solution exists?

III. Do Cooperators Cluster?

Does Clustering Increase Cooperation

• Market for Lemons: – Low value exchanges replace high value when information asymmetry induces opportunism • Exchange: baubles replace diamonds • Collaboration: low risk replaces high risk, high gains – Represented by PD payoffs, where • CC= high value exchange (diamonds for diamonds) • DD= low value exchange (glass beads for beads) • CD, DC = opportunism (beads for diamonds)

Market for Lemons

• Voluntary exchanges: – Select partner only when both agree – Execute the exchange – Drop partner whenever dissatisfied

Lemons Experiment

• • • • • 14 subjects per session, computer assisted.

Subjects propose, When proposals match, play pd with each partner. (Increasing costs for multiple matches) Repeat for 20 rounds (known in advance).

Reputation mechanism manipulation: – Experiential – Local – global

Benchmarks and Conjectures

• • • Pessimists: Stage game payoff dominant Nash equilibrium – 4 links per person, Defect in all games – Earning: 60.4 ECU’s Optimists: Social Optimum – 10 links per person, Cooperate in all games – Earning: 393.6 ECU’s.

Behavioral Conjectures – Selection: Optimists will cluster – Influence: Clustered player will learn to cooperate

Average % of C Plays

Baseline Central Local

Average Earnings

5 10 Period 15

Average # CC Links

20 5 10 Period 15

Average # of Links

20 5 10 Period 15 20 5 10 Period 15 20

Optimists Banish Pessimists to Nashville

• A movie is worth 10000 words

The Optimists’ Advantage

• • • Optimists play Quit-for-Tat (QFT) – Voluntary dilemma extension of TFT – Cooperate with all new links – Don’t associate with any defectors (cut link) In good context (many QFT) optimists cluster together to trade diamonds, not beads – all earn socially optimal payoff As context deteriorates, QFT becomes more generous – Maintain links, play TFT before cutting tie

The Pessimists’ Disadvantage

• Pessimists play Defect, don’t quit (DnoQ) – Cluster of DnoQ maintains trade in beads, not diamonds – Cut off from QnoT at first encounter – Earn “nash” payoff with lower earning (25 vs 75) – Supports fewer links (optimal at 4 links) – Expected payoff per period in experiment • • QFT vs QFT= ???? 100 DnoQ vs DnoQ= 400

Strategy

QFT Other DnoQ All

QFT versus DnoQ

Number observed

8 42 6 56 Strategies categorized by actions in first 3 periods

Total Earning

5967 3970 3276 4181

Comparison of cooperation decisions between top and bottom earners (local)

Cooperate After No link CC DD CD DC Periods 1-3 Bottom 25% Top 25%

0.38 0.69 0.11 0.33 0.33 0.92 1.00 0.00 0.71 1.00

Periods 15-17 Bottom 25% Top 25%

0.29 0.87 0.08 0.42 0.13 0.30 1.00 0.00 0.00 .

Comparison of linking decisions between top and bottom earners (local)

Link After No link CC DD CD DC Periods 1-3 Bottom 25% Top 25%

0.36 0.93 0.71 0.64 0.67 0.46 0.97 0.75 0.39 0.83

Periods 15-17 Bottom 25% Top 25%

0.46 1.00 0.79 0.88 0.89 0.15 1.00 0.38 0.33 0.00

Conclusion: Self-organizing resolution of the market for lemons

• • Optimists ban pessimists to Nashville – Self-organizing diamond exchange: cooperators cluster together and earn more.

– Bead exchange banished to “Nashville”.

Explanation: optimists play QFT and pessimists play DnoQ.

– Subjects playing QFT earn much more than those playing DnoQ – Top earners tend to play QFT