This paper identifies a central role of the topological separation axiom T1 in the definition of mixed strategies in noncooperative games with arbitrary pure strategy spaces. Our main result says that a pure strategy space is topologically T1 if and only if (i) all singleton strategy sets are...

In a canonical model of military conflict, victory and defeat depend stochastically on the difference of resources deployed by the conflict parties. The present paper offers a comprehensive analysis of that model. The unique Nash equilibrium reflects either (i) peace, (ii) submission, (iii)...

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...

This paper studies the dynamic construction of a blockchain by competitive miners. In contrast to the literature, we assume a finite time horizon. It is shown that popular mining strategies such as adherence to conservative mining or to the longest-chain rule constitute pure-strategy Nash...

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...

While smooth exact potential games are easily characterized in terms of the cross-derivatives of players' payoff functions, an analogous differentiable characterization of ordinal or generalized ordinal potential games has been elusive for a long time. In this paper, it is shown that the...