GAMES · Game theory and cooperation from economics to evolutionary biology
FP7 — People (Marie Curie Actions)
- Duration
- 2010-09-01 → 2012-08-31
- EU contribution
- €241,482
- Participants
- 1
- Scheme
- MC-IIF
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Results in brief
Game theory and cooperation from economics to evolutionary biology
The objectives of the project were to study the origin and stability of cooperation, still one of the major unsolved questions in evolutionary biology and in the social sciences. The study of cooperation among multiple individuals is essentially the study of public goods games (PGGs), which has a long tradition in economics. It has long been argued that rational, self-interested behaviour leads to the inefficient provision of public goods or the overexploitation of common resources (the 'tragedy of the commons') because of the incentive to free-ride on the contribution of other group members. Evolutionary game theory has also, more recently, focused on PGGs in order to understand, for example, the production of diffusible molecules in microbes. Variations of the simplest PGG, the n-person prisoner's dilemma (NPD), are well known. In the NPD the benefit of the public good is a linear function of the number of contributors. While linearity makes the NPD analytically tractable, it is also an unrealistic assumption. No examples of linear public goods in nature have been reported, whereas non-linear (sigmoid) benefits have been described for cooperative behaviour in animals and for the production of diffusible molecules in microbes. This is likely to be a common feature of public goods in biology, as the effect of enzyme production is generally a sigmoid, saturating function of its concentration. General non-linear public goods have been so far beyond analytical tractability. During the course of the project we used economic game theory to understand the evolution of cooperation in multi-player social dilemmas. We have completed the analysis of the comparative statics of threshold public goods games (the volunteer's dilemma) showing that the contribution to public goods decreases with group size. We have then gone further to analyse more general non-linear games using a new approach based on Bernstein polynomials, a rather neglected piece of mathematics, that allows to analyse all N-player 2-strategies PGGs, including non-linear games that are impossible to analyse using the standard approach of evolutionary game theory. Moreover, this approach establishes an equivalence between two-strategy games and more realistic games with continuous strategies. Analysing the Bernstein coefficient of the gradient of selection of the replicator dynamics, we can now characterize analytically the dynamics of any non-linear game, and compute the equilibria for complex social dilemmas that have been so far beyond the reach of evolutionary game theory. This has implications for social dilemmas such as the contribution to measures against global warming. We can show that, counterintuitively, the amount of cooperation in public goods games is maximised at intermediate levels of threshold uncertainty. We find that the optimal uncertainty level is a function of group size, the cost of cooperation and a constant. This suggests a practical way for improving efficiency in the solution of social dilemmas by increasing uncertainty rather than using incentives for contributors or sanctions against free-riders.
Data: CORDIS, © European Union
Project objective
I will use game theory to study how ideas initially developed in economics can be applied to the problem of the evolution of cooperation in biology. Cooperation is usually explained by evolutionary theory by invoking iterations, which allow reciprocation, punishment or reputation effects; the prisoner’s dilemma has become the standard model to analyse these problems. However, there are other possible explanations and different, more appropriate theoretical models that can shed light on the problem. First, in a bilateral relationship in which one individual contracts another to carry out an action, setting the right costs and rewards of the interaction may lead the possible partners to screen themselves according to their own interest. Moreover, by making the reward conditional on the outcome of the effort, an individual can give an incentive to the partner to cooperate even in the absence of iterations. These two ideas are known in microeconomics as adverse selection and moral hazard. In the first part of my research I will develop similar models for evolutionary biology, analyse the differences of the assumptions and extend the models to cases of biological interest. Second, social dilemmas arising in N-person games can often be more properly described as a volunteer’s dilemma, in which if volunteering is costly, but so is failure to produce the public good, cheaters can invade and form a stable mixed equilibrium with cooperators. The dilemma is that the benefit for the group decreases with group size because the larger the group is, the less likely it is that someone volunteers. I will analyse this problem for cases in which individuals are related, more than one volunteer is needed and other specific assumptions. This will provide predictions that will be tested with behavioural experiments and will ultimately provide practical solution for the production of collective goods.
Original text from CORDIS.
Participants
- UNIVERSITAT BASEL · BaselCoordinatorSwitzerland
Links
Data: CORDIS, © European Union