Payoff security combined with reciprocal upper semicontinuity is sufficient for better-reply security, and consequently for the existence of a pure strategy Nash equilibrium in compact, quasiconcave games by Reny's (1999) theorem. Analogously, diagonal payoff security combined with upper...

The Riemann Hypothesis (RH) is one of the major unsolved problems in pure mathematics. In this note, a parameterized family of non-cooperative games is constructed with the property that, if RH holds true, then any game in this family admits a unique Nash equilibrium. We argue that this result...

The n-player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can that model be solved more generally? In this paper, we show that key characteristics of the...

Optimal rank-order tournaments have traditionally been studied using a first-order approach. The present analysis relies instead on the construction of an "upper envelope" over all incentive compatibility conditions. It turns out that the first-order approach is not innocuous. For example, in...