Hannu Vartiainen

Von Neumann-Morgenstern stable sets, discounting, and Nash bargaining

We establish a link between von Neumann–Morgenstern stable set and the Nash solution in a general n-player utility set. The stable set-solution is defined with respect to a dominance relation: payoff vector u dominates v if one player prefers u even with one period delay. We show that a stable set exists and, if the utility set has a smooth surface, any stable set converges to the Nash bargaining solution when the length of the period goes to zero.

Subgame perfect implementation: A full characterization

Abstract Moore and Repullo [Subgame perfect implementation, Econometrica 56 (1988) 1191–1220], and Abreu and Sen [Subgame perfect implementation: a necessary and almost sufficient condition, J. Econ. Theory 50 (1990) 285–299] introduce distinct necessary and sufficient conditions for SPE implementation, when the number of players is at least three. This paper closes the gap between the conditions—a complete characterization of the SPE implementable choice rules is provided. The characterization consists of α * , which strengthens α of Abreu–Sen by adding it a restricted veto-power condition, and the unanimity condition. Under strict preferences α * is equal to α .

Collective choice with endogenous reference outcome

A collective choice problem—essentially a bargaining problem without disagreement outcome—is studied. An extended solution, which determines a solution and a reference point simultaneously, is characterized. The unique extended solution that meets the extended versions of Pareto-optimality, independence of irrelevant alternatives, symmetry, and scale invariance maximizes the Nash product with respect to both the solution and the reference point.

Nash implementation and the bargaining problem

We study Nash implementation of the bargaining solutions in a cake sharing set up. We argue that the minimal Pareto optimal, symmetric and Nash implementable SBS is the one inducing all Pareto optimal and midpoint-dominating utility vectors in each state.

Subgame perfect implementation of voting rules via randomized mechanisms

We characterize completely ordinal and onto choice rules that are subgame perfect of Nash equilibrium (SPE) implementable via randomized mechanisms under strict preferences. The characterization is very operationalizable, and allows us to analyse SPE implementability of voting rules. We show that no scoring rule is SPE implementable. However, the top-cycle and the uncovered correspondences as well as plurality with runoff and any strongly Condorcet consistent voting rule can be SPE implemented. Therefore our results are favourable to majority based voting rules over scoring rules. Nevertheless, we show that many interesting Condorcet consistent but not strongly Condorcet consistent rules, such as the Copeland rule, the Kramer rule and the Simpson rule, cannot be SPE implemented.