We define the class of two-player zero-sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For games in this class we establish sufficient conditions for existence of a value of the game and minimax or Nash equilibrium strategies...

We apply three axioms adapted from decision theory to refinements of the Nash equilibria of games with perfect recall that select connected closed sub- sets called solutions. No player uses a weakly dominated strategy in an equilibrium in a solution. Each solution contains a quasi-perfect...

Three axioms from decision theory are applied to refinements that select connected subsets of the Nash equilibria of games with perfect recall. The first axiom requires all equilibria in a selected subset to be admissible, i.e. each player's strategy is an admissible optimal reply to other...

For an all-pay sealed-bid auction of an item for which each bidder's realized value can depend on every bidder's privately observed signal, existence of equilibria in behavioral strategies is established using only the assumption that bidders' value functions and the density function of signals...

A first-price sealed-bid auction of an item for which bidders are risk-neutral and have privately known values is shown to have an equilibrium in mixed behavioral strategies if the joint distribution of bidders' values has a continuous density on a cubical support. Such an equilibrium has...

If a connected component of perfect equilibria of a two-player game contains a stable set as defined by Mertens, then the component is itself stable. Thus the stable sets maximal under inclusion are connected components of perfect equilibria.

We define the class of two‐player zero‐sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For such games, we establish sufficient conditions for existence of a value of the game, maximin and minimax strategies for the players,...