Simple Randomized Mechanism Research Articles

Optimal Budget-Feasible Mechanisms for Additive Valuations

In this article, we show a tight approximation guarantee for budget-feasible mechanisms with an additive buyer. We propose a new simple randomized mechanism with approximation ratio of 2, improving the previous best known result of 3. Our bound is tight with respect to either the optimal offline benchmark or its fractional relaxation. We also present a simple deterministic mechanism with the tight approximation guarantee of 3 against the fractional optimum, improving the best known result of (2+ √ 2) for the weaker integral benchmark.

Efficiency and budget balance in general quasi-linear domains

We consider efficiency and budget balance in general quasi-linear domains. Green and Laffont (1979) proved that one cannot generically achieve both. We consider strategyproof budget-balanced mechanisms with bounded valuations that are approximately efficient. We show that a deterministic, strategyproof, and budget-balanced mechanism must have a sink whose valuation is ignored in the decision, and is compensated with all the leftover money. We find a tight lower bound on the inefficiencies of strategyproof, budget-balanced mechanisms using this result. The bound shows that the inefficiency asymptotically disappears when the number of agents is large—we provide worst-case bounds and the best possible rate of convergence.We provide results for convex combination of inefficiency and budget imbalance and for randomized mechanisms. Experiments with real data from two applications show that the inefficiency for a simple randomized mechanism is 5–100 times smaller than the worst case.

Automatically inferring loop invariants via algorithmic learning

By combining algorithmic learning, decision procedures, predicate abstraction and simple templates for quantified formulae, we present an automated technique for finding loop invariants. Theoretically, this technique can find arbitrary first-order invariants (modulo a fixed set of atomic propositions and an underlying satisfiability modulo theories solver) in the form of the given template and exploit the flexibility in invariants by a simple randomized mechanism. In our study, the proposed technique was able to find quantified invariants for loops from the Linux source and other realistic programs. Our contribution is a simpler technique than the previous works yet with a reasonable derivation power.

Patterns of apparent co-operativity in a simple random non-equilibrium enzyme–substrate–modifier mechanism. Comparison with equilibrium allosteric models

It has often been claimed that random non-equilibrium mechanisms can result in apparent homotropic and heterotropic effects in steady-state kinetics of the kind more usually attributed to intersubunit allosteric interactions. However, it has never been shown whether any simple random mechanism could in fact give patterns of apparent interaction similar to those predicted by the well-known allosteric models. The patterns of apparent substrate co-operativity and affinity given by the steady-state of a standard simple random substrate-modifier mechanism in which catalytic velocity is proportional to substrate binding have been analysed mathematically and numerically. All patterns possible with this model are described. Some of them rather resemble those possible with standard allosteric models, in that there is a high-affinity and a low-affinity form at zero and infinite modifier concentrations (or vice versa) which show Michaelian behaviour, apparent co-operativity passing through a maximum or minimum at intermediate affinities. Unlike the allosteric models the family of curves is in principle not symmetrical. The random model can also give behaviour not possible with the standard allosteric models, such as higher substrate affinity at intermediate modifier concentrations than at either zero or infinite modifier, with concomitant negative apparent substrate co-operativity, or a single change of sign of apparent substrate co-operativity. The analysis uses recently discovered simplified forms of steady-state equations for random models.