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Register a new userStrength in Numbers: Robust Mechanisms for Public Goods with Many Agents
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This study examines the mechanism design problem for public-good provision in a large economy with $n$ independent agents. We propose a class of dominant-strategy incentive compatible (DSIC) and ex post individual rational (EPIR) mechanisms which we call the adjusted mean-thresholding (AMT) mechanisms. We show that when the cost of provision grows slower than the $sqrt{n}$ rate, the AMT mechanisms are both asymptotically ex ante budget balanced (AEABB) and asymptotically efficient (AE). When the cost grows faster than the $sqrt{n}$ rate, in contrast, we show that any DSIC, EPIR, and AEABB mechanism must have provision probability converging to zero and hence cannot be AE. Lastly, the AMT mechanisms are more informationally robust when compared to, for example, the second-best mechanism. This is because the construction of AMT mechanisms depends only on the first moments of the valuation distributions.
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This paper considers incentives to provide goods that are partially excludable along social links. Individuals face a capacity constraint in that, conditional upon providing, they may nominate only a subset of neighbours as co-beneficiaries. Our model has two typically incompatible ingredients: (i) a graphical game (individuals decide how much of the good to provide), and (ii) graph formation (individuals decide which subset of neighbours to nominate as co-beneficiaries). For any capacity constraints and any graph, we show the existence of specialised pure strategy Nash equilibria - those in which some individuals (the Drivers, D) contribute while the remaining individuals (the Passengers, P) free ride. The proof is constructive and corresponds to showing, for a given capacity, the existence of a new kind of spanning bipartite subgraph, a DP-subgraph, with partite sets D and P. We consider how the number of Drivers in equilibrium changes as the capacity constraints are relaxed and show a weak monotonicity result. Finally, we introduce dynamics and show that only specialised equilibria are stable against individuals unilaterally changing their provision level.
We study the design of revenue-maximizing bilateral trade mechanisms in the correlated private value environment. We assume the designer only knows the expectations of the agents values, but knows neither the marginal distribution nor the correlation structure. The performance of a mechanism is evaluated in the worst-case over the uncertainty of joint distributions that are consistent with the known expectations. Among all dominant-strategy incentive compatible and ex-post individually rational mechanisms, we provide a complete characterization of the maxmin trade mechanisms and the worst-case joint distributions.
In this Brief Report we study the evolutionary dynamics of the Public Goods Game in a population of mobile agents embedded in a 2-dimensional space. In this framework, the backbone of interactions between agents changes in time, allowing us to study the impact that mobility has on the emergence of cooperation in structured populations. We compare our results with a static case in which agents interact on top of a Random Geometric Graph. Our results point out that a low degree of mobility enhances the onset of cooperation in the system while a moderate velocity favors the fixation of the full-cooperative state.
Public goods games in undirected networks are generally known to have pure Nash equilibria, which are easy to find. In contrast, we prove that, in directed networks, a broad range of public goods games have intractable equilibrium problems: The existence of pure Nash equilibria is NP-hard to decide, and mixed Nash equilibria are PPAD-hard to find. We define general utility public goods games, and prove a complexity dichotomy result for finding pure equilibria, and a PPAD-completeness proof for mixed Nash equilibria. Even in the divisible goods variant of the problem, where existence is easy to prove, finding the equilibrium is PPAD-complete. Finally, when the treewidth of the directed network is appropriately bounded, we prove that polynomial-time algorithms are possible.
We consider agents with non-linear preferences given by private values and private budgets. We quantify the extent to which posted pricing approximately optimizes welfare and revenue for a single agent. We give a reduction framework that extends the approximation of multi-agent pricing-based mechanisms from linear utility to nonlinear utility. This reduction framework is broadly applicable as Alaei et al. (2012) have shown that mechanisms for linear agents can generally be interpreted as pricing-based mechanisms. We give example applications of the framework to oblivious posted pricing (e.g., Chawla et al., 2010), sequential posted pricing (e.g., Yan, 2011), and virtual surplus maximization (Myerson, 1981).
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