Reducing Truth-telling Online Mechanisms to Online Optimization

Abstract: "We describe a general technique for converting an online algorithm [beta] to a truthtelling mechanism. We require that the original online competitive algorithm has certain 'niceness' properties in that actions on future requests are independent of the actual value of requests which were accepted (though these actions will of course depend upon the set of accepted requests). Under these conditions, we are able to give an online truth telling mechanism (where the values of requests are given by bids which may not accurately represent the valuation of the requesters) such that our total profit is within O([rho] + log [mu]) of the optimum offline profit obtained by an omniscient algorithm (one which knows the true valuations of the users). Here [rho] is the competitive ratio of [beta] for the optimization version of the problem, and [mu] is the ratio of the maximum to minimum valuation for a request. In general there is an [omega](log [mu]) lower bound on the ratio of worst-case profit for a truth telling mechanism when compared to the profit obtained by an omniscient algorithm, so this result is in some sense best possible. In addition, we prove that our construction is resilient against many forms of 'cheating' attempts, such as forming coalitions. We demonstrate applications of this result to several problems. We develop online truthtelling mechanisms for online routing and admission control of path or multicast requests, assuming large network capacities. Assuming the existance [sic] of an algorithm [beta] for the optimization version of the problem, our techniques provide truthtelling mechanisms for general combinatorial auctions. However, designing optimization algorithms may be difficult in general because of online or approximation lower bounds. For the cases described above, we are able to design optimization algorithms [beta] by amortizing the lost benefit from online computation (and from approximation hardness in the case of multicast) against the benefit obtained from accepted requests. We comment that our upper bounds on profit competitiveness imply, as an obvious corollary, similar bound on global efficiency, namely overall well-being of all the users. This contrasts with most other work on truthtelling mechanisms for general online resource allocation, where only efficiency is maximized, and competitiveness can be arbitrarily poor."