James Schummer

Algorithmic Game Theory: Mechanism Design without Money

Despite impossibility results on general domains, there are some classes of situations in which there exist interesting dominant-strategy mechanisms. While some of these situations (and the resulting mechanisms) involve the transfer of money, we examine some that do not. Specifically, we analyze problems where agents have single-peaked preferences over a one-dimensional “public” policy space; and problems where agents must match with each other.

Eliciting Preferences to Assign Positions and Compensation

Abstract We describe strategy-proof rules for economies where an agent is assigned a position (e.g., a job) plus some of a divisible good. For the 2-agent–2-position case we derive a robust characterization. For the multi-agent–position case, many “arbitrary” such rules exist, so we consider additional requirements. By also requiring coalitional strategy-proofness or nonbossiness , the range of a solution is restricted to the point that such rules are not more complex than those for the Shapley–Scarf housing model (no divisible good). Third, we show that essentially only constant solutions are immune to manipulations involving “bribes.” Finally, we demonstrate a conflict between efficiency and strategy-proofness . The results extend to models (without externalities) in which agents share positions. Journal of Economic Literature Classification Numbers: C72, D70.

Two derivations of the uniform rule and an application to bankruptcy

We consider the problem of allocating a single infinitely divisible commodity to agents with single-peaked preferences, and establish two properties of the rule that has played the central role in the analysis of this problem, the uniform role. Among the efficient allocations, it selects (1) the one at which the difference between the largest amount received by any agent and the smallest sush amount is minimal, and (2) the one at which the variance of the amounts received by the agents is minimal.

Bribing and signaling in second price auctions

Abstract We examine whether a two-bidder, second-price auction for a single good (with private, independent values) is immune to a simple form of collusion, where one bidder may bribe the other to commit to stay away from the auction (i.e. submit a bid of zero). In either of two cases—where the potential bribe is fixed or allowed to vary—the only robust equilibria involve bribing. In the fixed-bribe case, there is a unique such equilibrium. In the variable bribes case, all robust equilibria involve low briber-types revealing themselves through the amount they offer, while all high types offer the same bribe; only one such equilibrium is continuous. Bribing in all cases causes inefficiency.

Auctions for Procuring Options

We examine the mechanism-design problem for a single buyer to procure purchase options for a homogeneous good when that buyer is required to satisfy an unknown future demand. Suppliers have two-dimensional types in the form of commitment costs and production costs. The efficient schedule of options depends on the distribution of demand. To implement an efficient outcome, we introduce a class of mechanisms which are essentially pivotal mechanisms (Vickrey-Clarke-Groves) with respect to the expected costs of the suppliers. We show that the computational task of running such mechanisms is not burdensome. Our discussion uses electricity markets as an example.

Almost-dominant strategy implementation: exchange economies

Abstract We relax strategy-proofness (a form of dominant strategy implementation) by allowing “small” gains from manipulation. In 2-agent exchange economies, this relaxation is shown to have a discontinuous effect on the range of efficient rules, demonstrating a type of non-robustness in previous impossibility results. When gains are measured with respect to a single good and preferences are linear, we characterize a particular rule as being the most equitable among all efficient rules satisfying the relaxation.

Credible deviations from signaling equilibria

In games with costly signaling, some equilibria are vulnerable to deviations which could be “unambiguously” interpreted as coming from a unique set of Sender-types. This occurs when these types are precisely the ones who gain from deviating for any beliefs the Receiver could form over that set. We show that this idea characterizes a unique equilibrium outcome in two classes of games. First, in monotonic signaling games, only the Riley outcome is immune to this sort of deviation. Our result therefore provides a plausible story behind the selection made by Cho and Kreps’s (Q J Econ 102:179–221, 1987) D1 criterion on this class of games. Second, we examine a version of Crawford and Sobel (Econometrica 50:1431–1451, 1982) model with costly signaling, where standard refinements have no effect. We show that only a Riley-like separating equilibrium is immune to these deviations.