The Tragedy of the Commons from a Game-Theoretic Perspective

Plants appear to produce an excess of leaves, stems and roots beyond what would provide the most efficient harvest of available resources. One way to understand this overproduction of tissues is that excess tissue production provides a competitive advantage. Game theoretic models predict overproduction of all tissues compared with non-game theoretic models because they explicitly account for this indirect competitive benefit. Here, we present a simple game theoretic model of plants simultaneously competing to harvest carbon and nitrogen. In the model, a plant's fitness is influenced by its own leaf, stem and root production, and the tissue production of others, which produces a triple tragedy of the commons. Our model predicts (i) absolute net primary production when compared with two independent global datasets; (ii) the allocation relationships to leaf, stem and root tissues in one dataset; (iii) the global distribution of biome types and the plant functional types found within each biome; and (iv) ecosystem responses to nitrogen or carbon fertilization. Our game theoretic approach removes the need to define allocation or vegetation type a priori but instead lets these emerge from the model as evolutionarily stable strategies. We believe this to be the simplest possible model that can describe plant production.

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An oscillating tragedy of the commons in replicator dynamics with game-environment feedback

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1604096113 ◽

2016 ◽

Vol 113 (47) ◽

pp. E7518-E7525 ◽

Cited By ~ 54

Author(s):

Joshua S. Weitz ◽

Ceyhun Eksin ◽

Keith Paarporn ◽

Sam P. Brown ◽

William C. Ratcliff

Keyword(s):

Replicator Dynamics ◽

Evolutionary Game ◽

Tragedy Of The Commons ◽

Individual Behavior ◽

Global Maximum ◽

Rational Choices ◽

The Commons ◽

Game Theoretic ◽

Individual Actions ◽

Game Environment

A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of overgrazing of common pasture lands. In game-theoretic treatments of this example, there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments, respectively. Using this approach, we identify and characterize a class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing, we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state.

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Some plants dont play games: An ideal free distribution explains the root production of plants that do not engage in a tragedy of the commons game.

10.1101/004820 ◽

2014 ◽

Author(s):

Gordon McNickle ◽

Joel S Brown

Keyword(s):

Seed Yield ◽

Ideal Free Distribution ◽

Tragedy Of The Commons ◽

Stable Strategy ◽

Free Distribution ◽

Root Allocation ◽

The Commons ◽

Game Theoretic ◽

Soil Volume ◽

Ideal Free

1. Game theoretic models that seek to predict the most competitive strategy plants use for competition in soil are clear; they generally predict that over-proliferation of roots is the only evolutionarily stable strategy. However, empirical studies are equally clear that not all plants employ this strategy of over-proliferation of roots. Here, our goal was to develop and test an alternative non-game theoretic model that can be used to develop alternative hypotheses for plants that do not appear to play games. 2. The model is similar to previous models, but does not use a game theoretic optimization criterion. Instead, plants use only nutrient availability to select a root allocation strategy, ignoring neighbours. To test the model we compare root allocation and seed yield of plants grown either alone or with neighbours. 3. The model predicted plants that do not sense neighbours (or ignore neighbours) should allocate roots relative to resource availability following an ideal free distribution. This means that if a soil volume of quality R contains x roots, then a soil volume of quality R/n will contain x/n roots. The experimental data were consistent with this prediction. That is, plants grown with 1.2g of slow release fertilizer resources produced 0.043 g of roots, while plants grown with neighbours, or plants grown with half as much fertilizer produced half as much root mass (0.026g, and 0.24g respectively). Seed yield followed a similar pattern. 4. This model presents an alternative predictive framework for those plant species that do not seem to play a tragedy of the commons game for belowground competition. 5. Synthesis: It remains unclear why some plants do not engage in belowground games for competition. Models suggest over-proliferation is an unbeatable evolutionary stable strategy, yet plants that do not play the game apparently coexist with plants that do. We suggest that a greater understanding of trade-offs among traits that are important for other biotic interactions (above-ground competition, enemy defence, mutualisms) will lead to a greater understanding of why some species over-proliferate roots when in competition but other species do not.

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An oscillating tragedy of the commons in replicator dynamics with game-environment feedback

10.1101/043299 ◽

2016 ◽

Cited By ~ 2

Author(s):

Joshua S. Weitz ◽

Ceyhun Eksin ◽

Keith Paarporn ◽

Sam P. Brown ◽

William C. Ratcliff

Keyword(s):

Replicator Dynamics ◽

Evolutionary Game ◽

Tragedy Of The Commons ◽

Individual Behavior ◽

Global Maximum ◽

New Class ◽

Rational Choices ◽

The Commons ◽

Game Theoretic ◽

Game Environment

A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of over-grazing of common pasture lands. In game theoretic treatments of this example there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments respectively. Using this approach we identify and characterize a new class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose new directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state.

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The Tragedy of the Commons as a Prisoner’s Dilemma. Its Relevance for Sustainability Games

Sustainability ◽

10.3390/su13158125 ◽

2021 ◽

Vol 13 (15) ◽

pp. 8125

Author(s):

Alessio Carrozzo Magli ◽

Pompeo Della Posta ◽

Piero Manfredi

Keyword(s):

Prisoner's Dilemma ◽

Global Climate ◽

Prisoner’S Dilemma ◽

Tragedy Of The Commons ◽

Policy Interventions ◽

The Commons ◽

Game Theoretic ◽

Sustainability Policy ◽

Harmful Effects ◽

Ultimate Nature

In the current battle for sustainability and climate, understanding the nature of sustainability games is of paramount importance, especially to inform appropriate policy actions to contrast the harmful effects of global climate change. Relatedly, there is no consensus in the literature on the proper game-theoretic representation of the so-called Tragedy of the Commons. A number of contributions have questioned the prisoner’s dilemma as an appropriate framework. In this work, we provide a representation that reconciles these two positions, confirming the ultimate nature of the Tragedy as a prisoner’s dilemma, rather than a coordination issue, and discuss the ensuing implications for sustainability policy interventions.

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