Credible Equilibria in Games with Utility Changing during the Play

Publicado por Tilburg Center Economic Research 1992Whenever one deals with an interactive decision situation of long duration, one has to take into account that priorities of the participants may change during the conflicto In this paper we propose an extensiveform game model to handle such situations and suggest and study a solution concept, called credible equilibrium, which generalizes the concept of Nash equilibrium. We also discuss possible variants to this concept and applications of the model to other types of games

Credible Equilibria in Games with Utility Changing during the Play

Whenever one deals with an interactive decision situation of long duration, one has to take into account that priorities of the participants may change during the conflict. In this paper we propose an extensive-form game model to handle such situations and suggest and study a solution concept, called credible equilibrium, which generalizes the concept of Nash equilibrium. We also discuss possible variants to this concept and applications of the model to other types of games.Publicad

Preplanned Esthetics in Prosthodontics - A Controlled Approach

The benefits of preplanned oral rehabilitation procedures are: high quality dentistry, better patient-dentist communication, increased efficiency, and reduced stress throughout treatment. The preplanned esthetic approach is a controlled, staged procedure in which every stage is a copy of the previous one, allowing for improvement where necessary. The final result fulfills the patient’s expectations, agreed upon and documented at the outset. The procedure follows these three steps: 1. Imaging. Imaging is based on esthetic evaluation and diagnosis of the patient. Composite resin and a black marker are commonly used to add or reduce tooth structure in this process. Documentation by photography and stone casts are used for reference and duplication. The proposed result should be approved by the patient. 2. Provisional restorations. The teeth are waxed according to the imaging models and then duplicated in acrylic resin. On delivery, the provisional restorations are evaluated functionally and esthetically and improved upon if necessary. The result is confirmed and agreed upon and documented again by photography and stone casts. 3. Final restoration. The final restoration is a duplicate of the provisional restoration. A technique of cross mounting is used to mount the provisional casts and the working cast on the same articulator. Silicone keys guide the dental technician in constructing the metal framework and the porcelain buildup. This systematic approach can be applied in every dental procedure that involves changes in the esthetic zone. It ensures a better match between the patients expectations and the final result and promotes higher quality dentistry

Dominance-solvable lattice games

This paper derives sufficient and necessary conditions for dominance-solvability of so-called lattice games whose strategy sets have a lattice structure while they simultaneously belong to some metric space. The argument combines and extends Moulin's (1984) approach for nice games and Milgrom and Roberts' (1990) approach for supermodular games. The analysis covers - but is not restricted to - the case of actions being strategic complements as well as the case of actions being strategic substitutes. Applications are given for n-firm Cournot oligopolies, auctions with bidders who are optimistic - respectively pessimistic - with respect to an imperfectly known allocation rule, and Two-player Bayesian models of bank runs

Settling Some Open Problems on 2-Player Symmetric Nash Equilibria

Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the following; it was stated by Papadimitriou in 2007: find a non-symmetric Nash equilibrium (NE) in a symmetric game. We show that this problem is NP-complete and the problem of counting the number of non-symmetric NE in a symmetric game is #P-complete. In 2005, Kannan and Theobald defined the "rank of a bimatrix game" represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be computed in rank 1 games in polynomial time. Observe that the rank 0 case is precisely the zero sum case, for which a polynomial time algorithm follows from von Neumann's reduction of such games to linear programming. In 2011, Adsul et. al. obtained an algorithm for rank 1 games; however, it does not solve the case of symmetric rank 1 games. We resolve this problem

Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior