On Multicriteria Games with Uncountable Sets of Equilibria

The famous Harsanyi's (1973) Theorem states that generically a finite game has an odd number of Nash equilibria in mixed strategies. In this paper, we show that for finite multicriteria games (games with vector-valued payoffs) this kind of result does not hold. In particular, we show, by examples, that it is possible to find balls in the space of games such that every game in this set has uncountably many equilibria so that uncountable sets of equilibria are not nongeneric in multicriteria games. Moreover, we point out that, surprisingly, all the equilibria of the games cor- responding to the center of these balls are essential, that is, they are stable with respect to every possible perturbation on the data of the game. However, if we consider the scalarization stable equilibrium concept (introduced in De Marco and Morgan (2007) and which is based on the scalarization technique for multicriteria games), then we show that it provides an effective selection device for the equilibria of the games corresponding to the centers of the balls. This means that the scalarization stable equilibrium concept can provide a sharper selection device with respect to the other classical refinement concepts in multicriteria games.

Kalai-Smorodinsky Bargaining Solution Equilibria

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don't have an a-priori opinion on the rel- ative importance of all these criteria. Roemer (2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution. We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered in Roemer (2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations such as the the extension to multicriteria games of the Selten's (1975) trembling hand perfect equilibrium concept.

Bargaining and Distribution of Power in the EU's Conciliation Committee

The European Union (EU) has moved towards bicameralism, making the codecision procedure its most important mechanism for decision making. To gauge if European Parliament (EP) and Council of Ministers (CM) are equally powerful ‘codecision makers’, understanding of the final stage of the procedure – bargaining in the Conciliation Committee – is crucial. Here, EP and CM are assumed to have spatial preferences determined by their respective internal decision mechanisms. Applying bargaining theory to predict inter-institutional agreements in the Conciliation Committee, it turns out that although institutionally the Council and the Parliament are seemingly in a symmetric position, CM has significantly greater influence on EU legislation.European Union codecision procedure, Conciliation Committee, bargaining, spatial voting, decision procedures

Bargaining and the theory of cooperative games: John Nash and beyond

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution

Trade openness and the settlement of domestic disputes in the shadow of the future

© 2015 University of Venice. We explore the severity of an ongoing dispute over a productive resource within a country that participates in world trade. In addition to arming, the contending groups in our setting choose either to engage in destructive conflict or to settle their dispute peacefully. Our central objective is to characterize the conditions under which the dispute might be resolved peacefully instead of violently. The analysis underscores the intuitive roles played by the destructiveness of open conflict and the salience of the future that have been identified in the previous literature, but it also provides some novel insights into how world prices and trade openness matter. Among other things, we find that, given conflict's destructive effects and time preferences, settlement is most likely to be supported as a stable equilibrium when the "traditional" gains from trade are largest. However, there also exist circumstances under which increased trade openness can induce destructive conflict

Nash Networks with Heterogeneous Agents

A non-cooperative model of network formation is developed. Agents form links with others based on the cost of the link and its assessed benefit. Link formation is one-sided, i.e., agents can initiate links with other agents with- out their consent, provided the agent forming the link makes the appropriate investment. Information flw is two-way. The model builds on the work of Bala and Goyal, but allows for agent heterogeneity. Whereas they permit links to fail with a certain common probability, in our model the probability of failure can be different for different links. We investigate Nash networks that exhibit connectedness and super-connectedness. We provide an explicit characterization of certain star networks. Efficiency and Pareto-optimality issues are discussed through examples. We explore alternative model specifications to address potential shortcomings.

Multiple Criteria Games Theory and Applications

After a review of basic concepts in multiple criteria optimization, the paper presents a characterization of noncooperative equilibria in multiple criteria games in normal form either by weighted sums or by order-consistent achievement scalarizing functions, for convex and nonconvex cases. Possible applications of multiple criteria games and such characterizations of their equilibria are indicated. The analysis of multiple criteria games night be especially useful when studying reasons of possible conflict escalation processes and ways of preventing them