International Game Theory Review

An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive Cournot fixed point.

We consider a standard sequential decision to adopt/buy a good in a herding environment. The setup is same as in Sgroi (2002). Contrary to the basic herding case we introduce a cost that the agents have to pay for the information about their predecessors' actions. All agents receive informative signals as in the standard herding models but do not view the actions taken by their predecessors unless they pay the observation costs. In this set up the first and the second agents rely on their own signals when they make the decision to adopt/buy the good. Only the third agent is willing to buy the information on all of the preceding agents' actions. All agents following the third agent buy information on only one agent's action and decide to adopt/buy the good after updating their beliefs. What follows is that the two first agents' actions determine whether the rest of the agents will adopt/buy the good or not when information about the predecessors' actions is cheap enough. If the cost of the information about the predecessors' actions is very expensive then all the agents will act according to their own signals. If observing is free one gets the standard results. In essence we identify a discontinuity in the basic herding model since the herding arises deterministically when a small observation cost is introduced.

The aim of this paper is to discuss a new concept of well-posedness for non cooperative games. Starting from the definition of (∊,k) equilibrium as the point where every player either guarantees at least k or he (she) does not lose more than ∊, we introduce an original definition of well-posedness. We study characterizations of this well-posedness and its relations with the more known Tikhonov well-posedness. We prove that this well-posedness is an ordinal property if the payoff functions are bounded from below.

We present a generalized model of myopic best response adaptation in large populations. In asymmetric conflicts, individuals can be in the role of the row player or the column player. The idea that an individual's role need not be fixed is introduced explicitly in our model by a process of role switching. The best response dynamics, the symmetrized best response dynamics, and the continuous time fictitious play process are included as special cases. We show that the set of Nash equilibria is attracting for zero-sum games. Moreover, for any base game, convergence to a Nash equilibrium implies convergence to a Nash equilibrium on the Wright manifold in the role game.

Focusing on signaling games, I illustrate the relevance of the rationalizability approach for the analysis multistage games with incomplete information. I define a class of iterative solution procedures, featuring a notion of "forward induction": the Receiver tries to explain the Sender's message in a way which is consistent with the Sender's strategic sophistication and certain given restrictions on beliefs. The approach is applied to some numerical examples and economic models. In a standard model with verifiable messages a full disclosure result is obtained. In a model of job market signaling the best separating equilibrium emerges as the unique rationalizable outcome only when the high and low types are sufficiently different. Otherwise, rationalizability only puts bounds on the education choices of different types.

Core elements (a la Aubin) of a fuzzy game can be associated with additive separable supporting functions of fuzzy games. Generalized cores whose elements consist of more general separable supporting functions of the game are introduced and studied. While the Aubin core of unanimity games can be empty, the generalized core of unanimity games is nonempty. Properties of the generalized cores and their relations to stable sets are studied. For convex fuzzy games interesting properties are found such as the fact that the generalized core is a unique generalized stable set.

This paper establishes sufficient conditions for the existence of a stable coalition structure in the "coalition unanimity" game of coalition formation, first defined by Hart and Kurz (1983) and more recently studied by Yi (1997, 2003). Our conditions are defined on the strategic form game used to derive the payoffs of the game of coalition formation. We show that if no synergies are generated by the formation of coalitions, a stable coalition structure always exists provided that players are symmetric and either the game exhibits strategic complementarity or, if strategies are substitutes, the best reply functions are contractions.

We explore the relationship between proportionality and manipulation (via merging or splitting agents' claims) in bankruptcy problems. We provide an alternative proof to the well-known result that, in an unrestricted domain, immunity to manipulation is equivalent to requiring proportional division. We show that this result also holds for restricted (but sufficiently rich) domains, such as the domain of simple problems and the domain of zero-normalized problems. Finally, we characterize two adjustments of the proportional rule by combining non-manipulabilty on these domains and the usual axioms of independence of claims truncation and composition from minimal rights.

In this work we study situations in which communication among the players is not complete and it is represented by a family of subsets of the set of players. Although several models of partial cooperation have been proposed, we shall follow a model derived from the work of Faigle and Kern. We define the games on convex geometries and introduce marginal worth vectors and quasi-supermodular games. Furthermore, we analyze some properties of the marginal operators on the space of games on convex geometries.

Addressing the international threat of invasive species to biodiversity worldwide requires an international context due to the nature of the transboundary pollution. This paper presents a comparison of strategies to address the invasive species problem in noncooperative versus cooperative differential games. Asymmetry between the countries in terms of abatement costs and damages enables the investigation of sharing rules under cooperation. The empirical analysis includes data of maritime trade as a vector of invasive species pollution at ports along the Pacific coast of NAFTA countries. The Chander/Tulkens cost sharing rule induces countries to cooperate and achieve lower invasive species stock than under noncooperation.

The pre-nucleolus is a popular egalitarian solution concept for cost-sharing games. A drawback of this concept is that an associated cost allocation often cannot be calculated in polynomial time. Therefore, it would be convenient to know whether the pre-nucleolus of a particular game coincides with the outcome of a cost-allocation method which is computationally less demanding. We provide operational conditions for a coincidence of the pre-nucleolus (point) of a cost-sharing game and the center of the game's imputation set (CIS vector). These conditions can be checked with little computational effort as compared to the potential savings in terms of computation time of a general solution algorithm.