We study extinction in a commons problem in which agents have access to capital markets. When the commons grows more quickly than the interest rate, multiple equilibria are found for intermediate commons endowments. In one of these, welfare decreases as the resource becomes more abundant, a `re-...

Jordan [2006] defined ‘pillage games’, a class of cooperative games whose dominance operator represents a ‘power function’ constrained by monotonicity axioms. In this environment, he proved that stable sets must be finite. We bound their cardinality above by a Ramsey number and show this...

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on...

We introduce 'formal methods' of mechanized reasoning from computer science to address two problems in auction design and practice: is a given auction design soundly specified, possessing its intended properties; and, is the design faithfully implemented when actually run? Failure on either...

Formal methods use computers to verify proofs or even discover new theorems. Interest in applying formal methods to problems in economics has increased in the past decade, but - to date - none of this work has been published in economics journals. This paper applies formal methods to a familiar...

We introduce efficient sets, a class of sets in Rp in which, in each set, no element is greater in all dimensions than any other. Neither differentiability nor continuity is required of such sets, which include: level sets of utility functions, quasi-indifference classes associated with a...

Pillage games (Jordan, 2006a) have two features that make them richer than cooperative games in either characteristic or partition function form: they allow power externalities between coalitions; they allow resources to contribute to coalitions’ power as well as to their utility. Extending...

Jordan [2006, “Pillage and property”, JET] characterises stable sets for three special cases of ‘pillage games’. For anonymous, three agent pillage games we show that: when the core is non-empty, it must take one of five forms; all such pillage games with an empty core represent the same...

Jordan [2006] defined ‘pillage games’, a class of cooperative games whose dominance operator is represented by a ‘power function’ satisfying coalitional and resource monotonicity axioms. In this environment, he proved that stable sets must be finite. We use graph theory to reinterpret...

This paper models aid agencies as financial intermediaries that do not make a financial return to depositors, whose concern is to transfer resources to investor-beneficiaries. This leads to a problem of verifying that the agency is using donations as intended. One solution to this problem is for...