Dynamics of a Threshold Public Goods Game in Ambiguity
Arnaud Dragicevic (CIRANO)
SER at GATE Lyon St Etienne. September, 2010.
Abstract
We propose a theoretical model of a threshold public goods game with ambiguous risk of the species survival and ambiguous expected losses from the extinction. As a collectivity, economic agents are faced with the option of privately funding the protection of biodiversity. The loss of species deprives of tools for biomedical research and precludes new medicines for currently untreatable human diseases, both common and rare. To avoid this loss, agents can jointly produce public goods when they attain the threshold level of cost of producing the public goods. Specifically, public goods are provided if joint fair-share contributions equal or exceed the required threshold level of provisions;
otherwise, no public good is provided. Rational agents have an incentive to avoid contributing and to free-ride on others’ provisions, as contributors always benefit others at a cost to their wealth. This rationale leads to social dilemmas and the abandonment of the public goods. We are interested in the capacity of agents to cooperate and to produce the public goods when they are confronted by ambiguous risks and face ambiguous individual losses. We consider population dynamics represented by replicator equation with proportional fair-share contributors (given the distribution of disease in the population), who donate the minimum average amount, versus free-riders, who provide null contributions. We find that agents contribute only if they face ambiguous risks;
otherwise, they free-ride. In detail, agents will contribute if their proportional fair-share amounts less than their expected salvage of wealth. When the trade-off rule is verified, agents end up contributing and free-ride vice versa. While a common disease can induce social cooperation, a rare disease will provoke social free-riding.
