An ordering on a lattice is quasisupermodular if and only if inserting it into any parametric optimization problem with the single crossing property cannot destroy the monotonicity of the set of optima. More detailed conditions for the monotonicity of the set of optima in a parameter influencing...

For a correspondence from a partially ordered set to a lattice, three sets of sufficient conditions for the existence of a monotone selection are obtained. (1) The correspondence is weakly ascending while each value is chain-complete. (2) The correspondence is ascending while the target is a...

Two new properties of a finite strategic game, strong and weak BR-dominance solvability, are introduced. The first property holds, e.g., if the game is strongly dominance solvable or if it is weakly dominance solvable and all best responses are unique. It ensures that every simultaneous best...

Game forms are studied where the acyclicity, in a stronger or weaker sense, of (coalition or individual) improvements is ensured in all derivative games. In every game form generated by an ``ordered voting'' procedure, individual improvements converge to Nash equilibria if the players restrict...

Let a preference ordering on a lattice be perturbed. As is well known, single crossing conditions are necessary and sufficient for a monotone reaction of the set of optimal choices from every chain. Actually, there are several interpretations of monotonicity and several corresponding single...

We consider strategic games where strategy sets are linearly ordered while the preferences of the players are described by binary relations. All restrictions imposed on the preferences are satisfied in the case of epsilon-optimization of a bounded-above utility function. A Nash equilibrium...

We study what topological assumptions should be added to the acyclicity of individual best response improvements in order to ensure the existence of a (pure strategy) Nash equilibrium as well as the possibility to reach a Nash equilibrium in the limit of a best response improvement path.

A rather general class of strategic games is described where the coalition improvements are acyclic and hence strong equilibria exist: The players derive their utilities from the use of certain "facilities"; all players using a facility extract the same amount of "local utility" therefrom, which...

The acyclicity of individual improvements in a generalized congestion game (where the sums of local utilities are replaced with arbitrary aggregation rules) can be established with a Rosenthal-style construction if aggregation rules of all players are "quasi-separable." Every universal separable...

We study what useful implications strategic complementarity or substitutability may have when the indifference relation(s) need not be transitive. Two results are obtained about the existence of a monotone selection from the best response correspondence when both strategies and parameters form...