coordinating towards a common good

Transcription

1 coordinating towards a common good Jorge M. Pacheco (with Francisco C. Santos ) Math Department, U. Minho, Braga CFTC, Lisbon PORTUGAL Venice, IT, 19-oct-2009

2 the challenge of minimizing climate change saving the climate requires cooperation!

3 the challenge of minimizing climate change cooperation between individuals cooperation between countries cooperation between ALL & how about networked coordination towards a common good? per capita CO 2 emmisions france / sweden x UK / japan 2x USA 3x

4 the challenge of minimizing climate change cooperation between individuals cooperation between countries the cooperation we need to consider involves collective action cooperation between ALL public goods games? (N-person games) or networked coordination towards a common good? per capita CO 2 emmisions france / sweden x UK / japan 2x USA 3x

5 tragedy of the commons N-person gamestypify the theoretical framework to capture the tragedy of the commons how to escape it? yet, why do people contribute to public goods?

6 a game experiment on climate change [ Milinski et al., PNAS 195 (2008) players, 10 rounds each player : 40 contribution in each round : 0(selfish), 2(fair) or 4(altruistic) cost for saving the planet: 120 if Σcontributions 120, planet is saved and each gets away with money left if Σcontributions < 120, planet is saved with 10% prob., else all loose everything france / sweden UK / japan USA per capita CO 2 emissions strategy x altruistic 2x fair 3x selfish

7 a game experiment on climate change [ Milinski et al., PNAS 195 (2008) 2291 NASH equilibrium : each player contributes 2 per round RESULTS : 50% of times planet was saved!!! 50% of times average contribution = 113 < 120 example of a failed attempt : did altruists feel they had contributed enough? what was in the mind of the free riders?

8 a game experiment on climate change [ Milinski et al., PNAS 195 (2008) 2291 if : i. planet is saved with prob= 50% 1 /10 reached 120 ii. planet is saved with prob= 90% 0/10 reached 120 still : i. <contribution> = 92 ii. <contribution> = 73 these experiments portray, once more, among other things, the bounded rationality of human participants.

9 message from the game experiment on climate change perceived risk of disaster cooperation rationality of players is not an argument drawbacks from the game experiment on climate change small groups... and only 1 group size... repeated game with fixed number of rounds...

10 an evolutionary approach to climate change N-personCoordination game... with a risky twist b M = coordination threshold N M Z

11 an evolutionary approach to climate change N-personCoordination game... with a risky twist b M = coordination threshold N M Z Evolution REPLICATOR DYNAMICS Communities HOMOGENEOUS ANSATZ : WELL-MIXED populations

12 N-personCoordination game... with a risky twist Cooperatorscontribute an amount c(cost) to a public good which helps saving the planet. Defectors do not contribute. group size is N; everyone receives a benefit bwhenever: threshold (M) of number of Csis exceeded or,if not : with probability α the benefit is still obtained somehow P D [ 1 ( )] = b H ( k M ) + αb H k M P C = P D c Cs now may pay a cost in vain (1-α) perception of risk similar to N-person games, Cs are always worse off than Ds.

13 evolutionary dynamics of N-person coordination games JmP,F. C. Santos, Max Souza, B. Skyrms,Proc.Royal Society B276 (2009) 1655 Max Souza, F. C. Santos, JmP, J. Theor. Biol. 260(2009) x& = x ( 1 x )( f ( x ) f ( x C D )) for N-person games in well-mixed populations we have f D (x) = N 1 k= 0 N 1 x k (1 x) N 1 k P D (k) k N 1 N 1 f C (x) = x k (1 x) N 1 k P C (k +1) k k= 0 we are assuming infinite populations; whenever populations are finite, binomial samplingis replaced by hypergeometric samplingand the replicator dynamicsis also replaced by its finite population stochasticanalogue.

14 risk-dependence results Z ; N = 6 ; M = b = 4 ; c = 1

15 risk-dependence results Z ; N = 6 ; M = b = 4 ; c = 1 cordination coexistence

16 risk-dependence results Z ; N = 6 ; M = b = 4 ; c = 1 increasing the perception of risk boostscooperation cordination coexistence

17 risk-dependence results Z ; N = 6 ; M = b = 4 ; c = 1 increasing the perception of risk boostscooperation cordination coexistence in fact increasing the perception of risk may transform cooperation into a winning strategy

18 threshold-dependence results Z ; N = 6 ; b = 4 ; c = 1 (high risk)

19 threshold-dependence results Z ; N = 6 ; b = 4 ; c = 1 increasing the threshold can transform a game from pure coexistence into pure coordination (high risk)

20 results population-size dependence N = 6 ; M = b = 4 ; c = 1 (highest risk)

21 results population-size dependence N = 6 ; M = b = 4 ; c = 1 (highest risk) as Zapproaches N cooperation becomes less likely

22 summary cooperation when : perception of risk group size threshold population size

23 summary cooperation when : perception of risk group size threshold population size how to optimize these conditions in practice?

24 networked public goods games of cooperation

25 in networked public goods games of cooperation F. C. Santos, Marta Santos, JmP, Nature 454 (2008) we have shown that cooperation blooms under networked PGG is what matters is the act of contributing and not how much each contributes diversity of roles & contributions in networked PGGs promotes cooperation. this result was obtained in the absence of any enforcement mechanisms enforcement via social normswill render the emergence of global cooperation more likely

26 networked public goods games of cooperation how to define the networks? some ideas... maybe networks could defined based on groups of countriesbound by common interests alternative forms of energy similar means of managing CO 2 emmisions joint interest in local commons etc...

27 conclusions an evolutionary game theory perspective of public goods games suggests that coordinating for a common good should be attempted in many small groups with high perception of risk stringent thresholds to meet goals social norm enforcement would further help in managing the commons

28 thank you