Abstract
We analyze the space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal combinatorial auctions. We examine a model with multidimensional types, nonidentical items, private values and quasilinear preferences for the players with one relaxation; the players are subject to publicly-known budget constraints. We show that the space includes dictatorial mechanisms and that if dictatorial mechanisms are ruled out by a natural anonymity property, then an impossibility of design is revealed. The same impossibility naturally extends to other abstract mechanisms with an arbitrary outcome set if one maintains the original assumptions of players with quasilinear utilities, public budgets and nonnegative prices.
Highlights
We study the limitations of the possibility space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions in a model with twoGames 2013, 4 players and two nonidentical items
Our result shows that the basic design requirements of dominant strategy incentive compatibility (DSIC), individual rationality (IR), and Pareto optimality (PO) lead to the presence of dictatorial mechanisms and these mechanisms can exhibit zero prices
We show that there exists a deterministic dictatorial combinatorial auction mechanism with budget-constrained players that satisfies the properties of DSIC, IR, and PO
Summary
We study the limitations of the possibility space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions in a model with two. Our result shows that the basic design requirements of dominant strategy incentive compatibility (DSIC), individual rationality (IR), and Pareto optimality (PO) lead to the presence of dictatorial mechanisms and these mechanisms can exhibit zero prices This means a bandwidth auction can arise where one telecommunications company dictates its bandwidth allocation regardless of its competitors’. With such a requirement no single telecommunications company can dictate the auction’s allocation This motivates our discussion of how to go about designing a dominant-strategy incentive compatible combinatorial auction for allocating multiple nonidentical items in a Pareto-optimal manner when participants may be budget constrained and dictatorial design is ruled out. Our main result is an impossibility: in a model with multiple nonidentical items and nonarbitrary allocation of the all-item-bundle (a property we term nonarbitrary hoarding), there is no deterministic auction that is dominant-strategy incentive compatible, individually rational, and Pareto optimal. In budget-constrained mechanisms it is sufficient to require that either the price of the remaining items is at least his remaining budget (after paying his allocation) or at least his marginal value for those items
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