Difference-form persuasion contests

We explore the equilibrium properties of two types of "difference-form" persuasion contest functions derived in Skaperdas and Vaidya in which contestants spend resources to persuade an audience. We find that both types of functions generate interior pure strategy Nash equilibria unlike Baik and Che and Gale with characteristics different to existing literature. For one type of function, we find that the reaction function of each player is "flat" and nonresponsive to the level of resources devoted by the rival so that the "preemption effect" as defined by Che and Gale is absent. Further, the equilibrium is invariant to the sequencing of moves. For the second type of function, which applies when there is asymmetry among contestants with regard to the quality of evidence, we find that the reaction functions of the stronger and weaker players have gradients with opposite signs relative to Dixit and therefore their incentive to precommit expenditures in a sequential move game is also different. For both types of functions, the extent of rent dissipation is partial. From the equilibrium analysis, we are also able to establish the potential effects of some specific factors affecting persuasion such as evidence potency, the degree of truth, and bias on aggregate resource expenditures and welfare.

Pareto Dominance of Deferred Acceptance through Early Decision

An early decision market is governed by rules that allow each student to apply to (at most) one college and require the student to attend this college if admitted. This market is ubiquitous in college admissions in the United States. We model this market as an extensive-form game of perfect information and study a refinement of subgame perfect equilibrium (SPE) that induces undominated Nash equilibria in every subgame (SPUE). Our main result shows that this game can be used to define a decentralized matching mechanism that weakly Pareto dominates student-proposing deferred acceptance.