Dynamic Matching,Two‐Sided Incomplete Information,and Participation Costs: Existence and Convergence to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length δ, and, each unit of time, continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and the winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady‐state equilibria that are perfect Bayesian. We show that, as δ converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show the existence of equilibria for δ sufficiently small, provided the discount rate is small relative to the participation costs.     

Computational risk management techniques for fixed charge network flow problems with uncertain arc failures

We consider a formulation for the fixed charge network flow (FCNF) problem subject to multiple uncertain arc failures, which aims to provide a robust optimal flow assignment in the sense of restricting potential losses using Conditional Value-at-Risk (CVaR). We show that a heuristic algorithm referred to as Adaptive Dynamic Cost Updating Procedure (ADCUP) previously developed for the deterministic FCNF problem can be extended to the considered problem under uncertainty and produce high-quality heuristic solutions for large problem instances. The reported computational experiments demonstrate that the described procedure can successfully tackle both the uncertainty considerations and the large size of the networks. High-quality heuristic solutions for problem instances with up to approximately 200,000 arcs have been identified in a reasonable time.     

Cheating in a contest with strategic inspection

We analyze a game between three players: two Athletes and an Inspector. Two athletes compete with each other and both may cheat to increase their chances of victory. The Inspector wishes to detect incidents of cheating, and performs tests on athletes to detect cheating. The test is costly for the Inspector. Both probability of cheating and that of testing decrease as cost of inspection diminishes.