Comparative accuracy of value solutions in non-sidepayment games with empty core

This article reports a test of the predictive accuracy of solution concepts in cooperative non-sidepayment n-person games with empty core. Six solutions were tested. Three of these were value solutions (i.e., -transfer value, -transfer nucleolus, and -transfer disruption value) and three were equilibrium solutions (deterrence set, stable set, and imputation set). The test was based on a laboratory experiment utilizing 5-person, 2-choice normal form games with empty core; other related data sets were also analyzed. Goodness-of-fit results based on discrepancy scores show that the three value solutions are about equally accurate in predicting outcomes, and that all three are substantially more accurate than the other solutions tested.     

Dynamic focal points in N-person coordination games

To understand how groups coordinate, we study infinitely repeated N-player coordination games in the context of strategic uncertainty. In a situation where players share no common language or culture, ambiguity is always present. However, finding an adequate principle for a common language is not easy: a tradeoff between simplicity and efficiency has to be made. All these points are illustrated on repeated N-player coordination games on m loci. In particular, we demonstrate how a common principle can accelerate coordination. We present very simple rules that are optimal in the space of all languages for m (number of coordination loci) from 2 to 5 and for all N, the number of players. We also show that when more memory is used in the language (strategies), players may not coordinate, whereas this is never the case when players remember only the previous period.     

Communication and its cost in graph-restricted games

We consider cooperative games which are modified by subordination to communication networks. Two players i and j will be able to cooperate only if they pay for the cost w _ij of their communication link (i,j). Coalitions of players are treated similarly and a new characteristic function form game is developed thus. We also examine incentive for players to cooperate in such situations as well as a related index of a player's communicative strength.     

A μ-σ-Risk Aversion Paradox and Wealth Dependent Utility

We report a surprising property of --preferences: the assumption of nonincreasing relative risk aversion implies the optimal portfolio being riskless. We discuss a solution of that paradox using wealth dependent utility functions in detail. Using the revealed preference theory we show that (general, i.e. not necessary -) wealth dependent utility functions can be characterized by Wald's axiom.     

Expected utility, μ-σ preferences,and linear distribution classes: A further result

This article is an extension of Meyer and Sinn's results on the representation of arbitrary von Neumann-Morgenstern functions in - space when the probability distributions to be compared belong to a linear distribution class. It shows that, when absolute risk aversion decreases, stays constant, or increases not too fast, an increase in , given , increases the indifference curve slope: increased riskiness increases the required marginal compensation for risk when risk is measured by the standard deviation of wealth or income.I gratefully acknowledge useful comments by Wolfgang Buchholz, Kai Konrad, Jack Meyer, Hans Schneeweiß, Dominique Thon, and Bengt Arne Wickström.     

Simultaneous moves multi-person continuous time concession game

The alternating offers strategic bargaining approach (Rubinstein, 1982) suggest a unique perfect equilibrium. In this equilibrium the bargaining ends immediately and the outcome is Pareto optimal. In this paper we consider a bargaining game in which players move simultaneously. Since we allow players only to lower their demands over time we denote this game as a concession game. We demonstrate that in this game there is a perfect equilibrium in which the bargaining lasts long enough so that the pie shrinks to zero. We show that we can generalize this game to a multi-player concession game in a straightforward manner and so avoiding the difficulties of generalizing the alternating offers game to the multi-player case.     

A theory of forward induction in finitely repeated games

A forward induction solution for finitely repeated games with complete information is developed. This notion is motivated in terms of its implications on the way deviations affect the opponents' expectations about the future behavior of the deviating player. We argue that the inability of the notion of perfect equilibrium to take account of forward induction is a key factor responsible for a number of difficulties encountered in the use of perfect equilibria in repeated games. It is then shown that the solution proposed in this paper remedies some of these problems in the study of three important classes of repeated games: (i) finitely repeated coordination games; (ii) repeated games where one long-term player plays a sequence of short-term players; (iii) repeated battle of the sexes games.     

Any complete preference structure without circuit admits an interval representation

This article proves that all complete preference structures where the strict preference relation (P) has no circuit admit a representation by intervals of the real line; the rule for deciding whether an interval is indifferent or preferred to another is less straightforward than for interval orders: strict preference is indeed compatible with a certain degree of overlapping of intervals, the allowed degree being specified by means of a so-called tolerance function.     

Communication Protocols with Belief Messages

This paper presents a communication protocol to reach consensus. In our setting, every player has asymmetric information and evaluates a fixed event on his information. According to the protocol, the sender sends non-partitional messages that he believes the event with a probability of at least his evaluation. We show that the posteriors for the event must be equal among the players after the communication. Journal of Economic Literature Classification: C62, C78.     

Pascal’s and Tabarrok’s Wagers

In a recent paper A. Tabarrok [Believe in Pascal’s Wager? Have I Got a Deal for You!, Theory and Decision 48, 123--128, 2000] argued that a believer who accepts Pascal’s Wager should in addition accept payment of any given fee in return for a given increase in the probability of reaching God. However the conclusion is obtained from manipulations of infinities which are not valid in an expected utility model. In this note, an alternative model is formulated in which Tabarrok’s conclusion can be obtained.     

A Paretian liberal dilemma without collective rationality

This note proposes a principle of liberalism which is a simple and plausible variant of Sen's principle of minimal liberalism. The former principle is shown to be incompatible with the weak Pareto principle; and this impossibility result is not dependent on the preference-aggregating rule being restricted by any collective rationality condition.     

A paradox in decision theory and some experimental results: The relative nature of decisions

A simple two-choice single outcome valued decision under risk is presented which should show up the limitations in the classical approach of von Neumann, its extensions and its alternatives. An empirical testing of this hypothesis strongly supports this criticism. A rationale for explaining the apparent irrational decision is put forward and the case is made for understanding the relative nature of decision choices especially when multi-criteria are involved.     

Gender,risk and stereotypes

This paper reports results from an economic experiment where respondents are asked to make choices between risky outcomes for themselves and others. We investigate whether subjects’ own risk preferences and gender stereotypes are reflected in the predictions they make for the risk preferences of others and the way this occurs. When predicting other people’s risk preferences, the respondents tend to use a combination of their own risk preferences and stereotypes. Moreover, when making risky choices for others, the respondents generally use a combination of their own risk preferences and their average predicted risk preference of the targeted group.

Another impossibility result for normal form games

It is shown that the axioms Cubitt and Sugden (1994; Economic J. 104: 798) impose on a theory of rationally justifiable play (TRJP) do not prevent the possibility that two players necessarily disagree concerning the probability they ascribe to the choice of a third player. This appears to indicate that those axioms are not sufficient for defining a `reasonable' TRJP. In addition, for the case in which a player's beliefs are statistically independent, conditions for a TRJP are suggested under which the existence of a quasi-strict equilibrium is sufficient, but the existence of a consistent n-pair is not, for defining a TRJP meeting those requirements.     

Far-sighted equilibria in 2 × 2, non-cooperative,repeated games

Consider a two-person simultaneous-move game in strategic form. Suppose this game is played over and over at discrete points in time. Suppose, furthermore, that communication is not possible, but nevertheless we observe some regularity in the sequence of outcomes. The aim of this paper is to provide an explanation for the question why such regularity might persist for many (i.e., infinite) periods.Each player, when contemplating a deviation, considers a sequential-move game, roughly speaking of the following form: if I change my strategy this period, then in the next my opponent will take his strategy b and afterwards I can switch to my strategy a, but then I am worse off since at that outcome my opponent has no incentive to change anymore, whatever I do. Theoretically, however, there is no end to such reaction chains. In case that deviating by some player gives him less utility in the long run than before deviation, we say that the original regular sequence of outcomes is far-sighted stable for that player. It is a far-sighted equilibrium if it is far-sighted stable for both players.     

The Right to Remain Silent

The paper points out that in dynamic games a player may be better-off if other players do not know his choice of strategy. That is, a player may benefit by not revealing (or not pre-determining) the choice of his action in an information set he (thereby) hopes will not be reached. He would be better-off by exercising his ``right to remain silent' if he believes –- as the empirical evidence shows –- that players display aversion to ``Knightian uncertainty'. In this case, a player who behaves strategically, may wish to avoid revealing his strategy. This is true under various interpretations of the notion of ``strategy profiles'.     

Bargaining and Strategic Demand Commitment

On occasion, in multilateral negotiations, interested parties make unilateral demands. Certain agreements need unanimity. However, a lesser degree of consensus may be feasible. In this paper, an alternating demand bargaining game among n players is proposed, which envisages varying consensus requirements and commitment, both crucial in generating a unique and efficient outcome of the bargaining process.     

LEXICOGRAPHIC ADDITIVITY FOR MULTI-ATTRIBUTE PREFERENCES ON FINITE SETS

Payoff dominance, a criterion for choosing between equilibrium points in games, is intuitively compelling, especially in matching games and other games of common interests, but it has not been justified from standard game-theoretic rationality assumptions. A psychological explanation of it is offered in terms of a form of reasoning that we call the Stackelberg heuristic in which players assume that their strategic thinking will be anticipated by their co-player(s). Two-person games are called Stackelberg-soluble if the players' strategies that maximize against their co-players' best replies intersect in a Nash equilibrium. Proofs are given that every game of common interests is Stackelberg-soluble, that a Stackelberg solution is always a payoff-dominant outcome, and that in every game with multiple Nash equilibria a Stackelberg solution is a payoff-dominant equilibrium point. It is argued that the Stackelberg heuristic may be justified by evidentialist reasoning.     

A Comparison of Some Distance-Based Choice Rules in Ranking Environments

We discuss the relationships between positional rules (such as plurality and approval voting as well as the Borda count), Dodgsons, Kemenys and Litvaks methods of reaching consensus. The discrepancies between methods are seen as results of different intuitive conceptions of consensus goal states and ways of measuring distances therefrom. Saaris geometric methodology is resorted to in the analysis of the consensus reaching methods.     

Ordinal equivalence of power notions in voting games

In this paper, we are concerned with the preorderings (SS) and (BC) induced in the set of players of a simple game by the Shapley–Shubik and the Banzhaf–Coleman's indices, respectively. Our main result is a generalization of Tomiyama's 1987 result on ordinal power equivalence in simple games; more precisely, we obtain a characterization of the simple games for which the (SS) and the (BC) preorderings coincide with the desirability preordering (T), a concept introduced by Isbell (1958), and recently reconsidered by Taylor (1995): this happens if and only if the game is swap robust, a concept introduced by Taylor and Zwicker (1993). Since any weighted majority game is swap robust, our result is therefore a generalization of Tomiyama's. Other results obtained in this paper say that the desirability relation keeps itself in all the veto-holder extensions of any simple game, and so does the (SS) preordering in all the veto-holder extensions of any swap robust simple game.