Abstract
Voluntary contribution games are a classic social dilemma in which the individually dominant strategies result in a poor performance of the population. However, the negative zero-contribution predictions from these types of social dilemma situations give way to more positive (near-)efficient ones when assortativity, instead of random mixing, governs the matching process in the population. Under assortative matching, agents contribute more than what would otherwise be strategically rational in order to be matched with others doing likewise. An open question has been the robustness of such predictions when heterogeneity in budgets amongst individuals is allowed. Here, we show analytically that the consequences of permitting heterogeneity depend crucially on the exact nature of the underlying public-good provision efficacy, but generally are rather devastating. Using computational methods, we quantify the loss resulting from heterogeneity vis-a-vis the homogeneous case as a function of (i) the public-good provision efficacy and (ii) the population inequality.
Highlights
Suppose a population of agents faces the collective action (Olson 1965) challenge to provide public goods by means of simultaneous, separate voluntary contributions games (Isaac et al 1985)
New equilibria emerge through assortative matching that are as good as near-efficient (Gunnthorsdottir et al 2010a; Nax et al 2014)
The above game exhibits different Nash equilibria depending on the value of γ and on the players having different or the same initial endowments
Summary
Suppose a population of agents faces the collective action (Olson 1965) challenge to provide public goods by means of simultaneous, separate voluntary contributions games (Isaac et al 1985). Predictions may change dramatically, when agents are matched ‘assortatively’ instead, that is, based on their pre-committed choice on how much to contribute so that high (low) contributors are matched with other high (low) contributors Such mechanisms have been coined ‘meritocratic group-based matching’ (Gunnthorsdottir et al 2010a), short ‘meritocratic matching’ (Nax et al 2014).. Equilibrium or new, previously impossible, complex mixed-strategy Nash equilibria emerge In the latter case, the expected level of resulting public-good provision depends crucially on (i) the public-good provision efficacy and (ii) the population inequality. The expected level of resulting public-good provision depends crucially on (i) the public-good provision efficacy and (ii) the population inequality These mixed equilibria are virtually impossible to characterize and to evaluate analytically for general cases.
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