Showing papers in "International Journal of Game Theory in 1998"

Dictator game giving: rules of fairness versus acts of kindness

Abstract: In both dictator and impunity games, one player, the dictator, divides a fixed amount of money between himself and one other, the recipient. Recent lab studies of these games have produced seemingly inconsistent results, re- porting substantially divergent amounts of dictator giving. Also, one prom- inent explanation for some of these dierences, the impact of experimenter observation, displayed weak explanatory power in a dierent but related lab game. Data from the new experiment reported here oers some explanations. We find that dictators determine how much they will give on the basis of the total money available for the entire experimental session, not on the basis of what is available per game. This explains the reported dierences between impunity and dictator studies. When distributing a gift among several recipi- ents, individual dictators show little tendency towards equal treatment. Also, we find no evidence for the experimenter observation eect. Comparison with earlier experiments suggests that dierences in the context of the game, aected by dierences in written directions and independent of experimenter obser- vation, account for dierences across dictator studies. We propose a hypo- thetical decision procedure, based on the notion that dictator giving originates with personal and social rules that eectively constrain self-interested behavior. The procedure provides a link between dictator behavior and a broader class of laboratory phenomena.

Population uncertainty and Poisson games

Abstract: A general class of models is developed for analyzing games with population uncertainty. Within this general class, a special class of Poisson games is defined. It is shown that Poisson games are uniquely characterized by properties of independent actions and environmental equivalence. The general definition of equilibrium for games with population uncertainty is formulated, and it is shown that the equilibria of Poisson games are invariant under payoff-irrelevant type splitting. An example of a large voting game is discussed, to illustrate the advantages of using a Poisson game model for large games.

Home-grown values and incentive compatible auction design

Abstract: The behavioral properties of several auctions designed to elicit individual valuations for an object are studied using controlled laboratory experiments. Our experiments lead us to conclude that there are some behavioral differences between alternative incentive-compatible institutions for eliciting home-grown values, contrary to the theoretical expectation that these institutions are isomorphic. These results are consistent with earlier experimental results using induced values. The most important finding is that English auctions appear to elicit lower bids than Vickrey auctions, after controlling for observable socio-economic characteristics. Moreover, English auction bids also exhibit significantly less residual variance and may be sensitive to the number of rival bidders. It appears that the real-time learning allowed in the English auction significantly affects subject behavior. We also find that values elicited with the Becker, DeGroot and Marshak institution differ from those in both English and Vickrey auctions.

Link formation in cooperative situations

Abstract: In this paper we study the endogenous formation of cooperation structures or communication graphs between players in a superadditive TU game. For each cooperation structure that is formed, the payoffs to the players are determined by an exogenously given solution. We model the process of cooperation structure formation as a game in strategic form. It is shown that several equilibrium refinements predict the formation of the complete cooperation structure or some structure which is payoff-equivalent to the complete structure. These results are obtained for a large class of solutions for cooperative games with cooperation structures.

Finitely additive stochastic games with Borel measurable payoffs

Abstract: We prove that a two-person, zero-sum stochastic game with arbitrary state and action spaces, a finitely additive law of motion and a bounded Borel measurable payoff has a value.

Computing the nucleolus of min-cost spanning tree games is NP -hard

Abstract: We prove that computing the nucleolus of minimum cost spanning tree games is in general NP-hard. The proof uses a reduction from minimum cover problems.

Strategy-proofness and “median voters”

Abstract: We consider the problem of choosing a level of the public good for an economy in which agents have continuous and single-peaked preferences (Black, 1948). We show that a solution satisfyingstrategy-proofness andcontinuity if and only if it is an augmented median-voter solution. Anaugmented median-voter solution is described in terms of 2n parameters (which satisfy an antimonotonicity condition) as follows:n+1 of them are selected according to an increasing order of the peaks; the outcome is the median of thesen+1 parameters and then peaks. This result establishes a formal connection between strategy-proofness and a generalized notion of median voter. (Similar median formulas were used by Moulin (1980) to describe smaller classes of solutions.) We provide an interpretation of these 2 n parameters in terms of the following properties:anonymity, voter sovereignty, unanimity, andPareto efficiency.

Multiple-issue bargaining and axiomatic solutions

Abstract: We study two-person, multiple-issue bargaining problems and identify four procedures by which the bargaining may take place. Drawing on some logic from non-cooperative game theory, we propose axioms which relate the outcomes of the procedures. We also promote a weak monotonicity axiom on solutions, called issue-by-issue monotonicity, which is geared toward multiple-issue bargaining. Our main result concerns the relationship between a sequential bargaining procedure — with the rule that agreements are implemented only after all issues are resolved — and global bargaining (in which all issues are negotiated simultaneously). If a bargaining solution predicts the same outcome with these two procedures, then we say that it satisfiesagenda independence. We prove that a solution satisfies axioms of efficiency, symmetry, scale invariance, issue-by-issue monotonicity, and agenda independence if and only if it is the Nash solution. This result provides new intuition for Nash's independence of irrelevant alternatives axiom. Among other results, we show that a solution is invariant to all four of the procedures and satisfies efficiency and symmetry if and only if it is the utilitarian solution with equal weights. We comment on the results of other authors who address multiple-issue bargaining.

On the impact of an event

Abstract: Given an information structure a function that measures how the inferences made by the agents spread among the states is defined; it specifies for each event its impact at each state, for each agent Several properties are established

A note on the inclusion of the kernal in the core of the bilateral assignment game

Abstract: In this note we prove that the kernel of a bilateral assignment game is always included in the core. This solves an outstanding open problem for bilateral assignment games.

On implementation via demand commitment games

Abstract: A simple version of the Demand Commitment Game is shown to implement the Shapley value as the unique subgame perfect equilibrium outcome for any n-person characteristic function game. This improves upon previous models devoted to this implementation problem in terms of one or more of the following: a) the range of characteristic function games addressed, b) the simplicity of the underlying noncooperative game (it is a finite horizon game where individuals make demands and form coalitions rather than make comprehensive allocation proposals and c) the general acceptability of the noncooperative equilibrium concept. A complete characterization of an equilibrium strategy generating the Shapley value outcomes is provided. Furthermore, for 3 player games, it is shown that the Demand Commitment Game can implement the core for games which need not be convex but have cores with nonempty interiors.

Characterization sets for the nucleolus

Abstract: . We introduce the concept of a characterization set for the nucleolus of a cooperative game and develop sufficient conditions for a collection of coalitions to form a characterization set thereof. Further, we formalize Kopelowitz's method for computing the nucleolus through the notion of a sequential LP process, and derive a general relationship between the size of a characterization set and the complexity of computing the nucleolus.

On the core of a collection of coalitions

Abstract: For a collection Ω of subsets of a finite set N we define its core to be equal to the polyhedral cone {x∈IR N : ∑ i∈N x i =0 and ∑ i∈S x i ≥0 for all S∈Ω} This note describes several applications of this concept in the field of cooperative game theory Especially collections Ω are considered with core equal to {0} This property of a one-point core is proved to be equivalent to the non-degeneracy and balancedness of Ω Further, the notion of exact cover is discussed and used in a second characterization of collections Ω with core equal to {0}

Equilibria in repeated games of incomplete information: the general symmetric case

Abstract: Every two person repeated game of symmetric incomplete information, in which the signals sent at each stage to both players are identical and generated by a state and moves dependent probability distribution on a given finite alphabet, has an equilibrium payoff.

Pure equilibria of repeated games with public observation

Abstract: The set of payoffs associated to pure uniform equilibria of a repeated game with public observation is characterized in terms of the one shot-game. The key of the result is first, a study of the effect of undetectable deviations and second, the definition of new types of punishments using approachability techniques.

Satisficing leads to cooperation in mutual interests games

Abstract: We study the play of mutual interests games by satisficing decision makers. We show that, for a high enough initial aspiration level, and under certain assumptions of “tremble”, there is a high probability (close to unity) of convergence to the Pareto dominant cooperative outcome. Simulations indicate that the theoretical result is robust with respect to the “trembling” mechanism.

Dominance or maximin: how to solve an English auction

Abstract: It is widely believed that the English auction is solved after the dominated strategies are eliminated. This paper demonstrates that the dominance criterion is not very effective in many English auction models. To bid more than the true willingness to pay is dominated but a stronger solution concept is needed to deduce that the buyers increase the price in small steps up to their valuation. An iterated application of the dominance criterion does not solve the problem, but if it is assumed that the buyers use their maximin strategies the usual argument holds.

On the cores of cooperative games and the stability of the Weber set

Abstract: In this paper conditions are given guaranteeing that the Core equals the D-core (the set of unDominated imputations). Under these conditions, we prove the non-emptiness of the intersection of the Weber set with the imputation set. This intersection has a special stability property: it is externally stable. As a consequence we can give a new characterization (th. 3.2) for the convexity of a cooperative game in terms of its stability (von Neumann-Morgenstern solutions) using the Weber set.

The speed of convergence in repeated games with incomplete information on one side

Abstract: In a repeated two-person zero-sum game with incomplete information on one side, the values upsilon(n) of the n-stage games converge to the value upsilon(infinity) of the infinite game with worst case error similar to (ln n/n)(1/3)

On the incentive properties of multi-item auctions

Abstract: In a market of indivisible objects where a buyer consumes at most one object, the buyer-optimal auction is a multi-item generalization of Vickrey's second-price auction. If the optimal auction is formulated as a strategic game, it is well-known that it satisfies good incentive properties, i.e., the honest strategy profile is a Nash equilibrium, a unique perfect equilibrium and a dominant strategy equilibrium. For each of the three incentive properties, it is shown that the optimal auction is aunique auction satisfying the property. The uniqueness results are derived in a general setting with budget constraints and non-linear utilities.

Values and potential of games with cooperation structure

Abstract: Games with cooperation structure are cooperative games with a family offeasible coalitions, that describes which coalitions can negotiate in the game. We study a model ofcooperation structure and the corresponding restricted game, in which the feasible coalitions are those belonging to apartition system. First, we study a recursive procedure for computing the Hart and Mas-Colell potential of these games and we develop the relation between the dividends of Harsanyi in the restricted game and the worths in the original game. The properties ofpartition convex geometries are used to obtain formulas for theShapley andBanzhaf values of the players in the restricted game υℒ in terms of the original gamev. Finally, we consider the Owen multilinear extension for the restricted game.

Nash equilibrium and the law of large numbers

Abstract: Pascoa (1993a) showed that the failure of the law of large numbers for a continuum of independent randomizations implies that Schmeidler's (1973) concept of a measure-valued profile function in equilibrium might not coincide with the concept of mixed strategies equilibrium of a nonatomic game. The latter should be defined as a probability measure on pure strategies profiles which is induced by the product measure of players' mixed strategies. This paper addresses existence and approximate purification of the latter and presents an assumption on continuity of payoffs that guarantees the equivalence between the two equilibrium concepts.

The MC-value for monotonic NTU-games

Abstract: The MC-value is introduced as a new single-valued solution concept for monotonic NTU-games. The MC-value is based on marginal vectors, which are extensions of the well-known marginal vectors for TU-games and hyperplane games. As a result of the definition it follows that the MC-value coincides with the Shapley value for TU-games and with the consistent Shapley value for hyperplane games. It is shown that on the class of bargaining games the MC-value coincides with the Raiffa-Kalai-Smorodinsky solution. Furthermore, two characterizations of the MC-value are provided on subclasses of NTU-games which need not be convex valued. This allows for a comparison between the MC-value and the egalitarian solution introduced by Kalai and Samet (1985).

Multi-level evolution in population games

Abstract: In this paper, we analyze a generalization of the evolutionary model of Kandori, Mailath, & Rob (1993) where the population is partitioned into groups and evolution takes place “in parallel” at the following two levels: (i) within groups, at the lower level; among groups, at the higher one. Unlike in their context, efficiency considerations always overcome those of risk-dominance in the process of selecting the long-run equilibrium. This provides an explicitly dynamic basis for a conclusion reminiscent of those put forward in the biological literature by the so-called theories group selection. From a normative viewpoint, it suggests the potential importance of “decentralization”, here understood as local and independent interaction.

Paths leading to the Nash set for nonsmooth games

Abstract: Maschler, Owen and Peleg (1988) constructed a dynamic system for modelling a possible negotiation process for players facing a smooth n-person pure bargaining game, and showed that all paths of this system lead to the Nash point. They also considered the non-convex case, and found in this case that the limiting points of solutions of the dynamic system belong to the Nash set. Here we extend the model to i) general convex pure bargaining games, and to ii) games generated by “divide the cake” problems. In each of these cases we construct a dynamic system consisting of a differential inclusion (generalizing the Maschler-Owen-Peleg system of differential equations), prove existence of solutions, and show that the solutions converge to the Nash point (or Nash set). The main technical point is proving existence, as the system is neither convex valued nor continuous. The intuition underlying the dynamics is the same as (in the convex case) or analogous to (in the division game) that of Maschler, Owen, and Peleg.

e-consistent equilibrium in repeated games

Abstract: We introduce the concept of ɛ-consistent equilibrium where each player plays a ɛ-best response after every history reached with positive probability. In particular, an ɛ-consistent equilibrium induces an ɛ-equilibrium in any subgame reached along the play path. The existence of ɛ-consistent equilibrium is examined in various repeated games. The main result is the existence in stochastic games with absorbing states.

Strong equilibria in claim games corresponding convex games

Abstract: This paper deals with a specific aspect of the problem of coalition formation in a situation described by a TU-game. First, we define a very simple normal form game which models the process of coalition formation. To define the payoff functions of the players we use an allocation rule for TU-games. The main objective of this paper is ascertain what conditions of the allocation rule lead to the grand coalition being a strong equilibrium of the normal form game, when the original TU-game is convex.

Perfect folk theorems. Does public randomization matter

Abstract: I consider two player games, where player 1 can use only pure strategies, and player 2 can use mixed strategies. I indicate a class of such games with the property that under public randomization both the discounted and the undiscounted finitely repeated perfect folk theorems do hold, but the discounted theorem does not without public randomization. Further, I show that the class contains games such that without public randomization the un-discounted theorem does not hold, as well as games such that without public randomization the undiscounted theorem does hold.

Rationality and the definition of consistent pairs

Abstract: A consistent pair specifies a set of “rational” strategies for both players such that a strategy is rational if and only if it is a best reply to a Bayesian belief that gives positive probability to every rational strategy of the opponent and probability zero otherwise. Although the idea underlying consistent pairs is quite intuitive, the original definition suffers from non-existence problems. In this article, we propose an alternative formalization of consistent pairs. According to our definition, a strategy is “rational” if and only if it is a best reply to some lexicographic probability system that satisfies certain consistency conditions. These conditions imply in particular that a player's probability system gives infinitely more weight to rational strategies than to other strategies. We show that modified consistent pairs exist for every game.

On consistent solutions for strategic games

Abstract: Nash equilibria for strategic games were characterized by Peleg and Tijs (1996) as those solutions satisfying the properties of consistency, converse consistency and one-person rationality.