Search Results (5)

In symmetric games with externalities across coalitions, we investigate how three players form coalitions using two solutions: ${\mathbf{n}}^{\ast }$, which is a focal prediction of coalition structure in a class of noncooperative coalitional bargaining games, and equilibrium binding agreements, which represent the cooperative blocking approach. We find that the coarsest equilibrium coalition structure (based on the latter notion) is never finer than ${\mathbf{n}}^{\ast }$, and we provide a sufficient and necessary condition for these two solutions to generate the same coalition structure (i.e., the two solutions coincide if and only if the first coalition to form in ${\mathbf{n}}^{\ast }$ is not a two-player coalition or a particular condition about average coalitional worths is satisfied). In symmetric games with more than three players, we demonstrate through a series of examples that any relationship between these two solutions is possible. We also discuss symmetric games with positive externalities or equal division in which these two solutions coincide. Full article

The subject of this study is an oligopolistic market in which three firms operate in an environment of quantitative competition known as the Cournot oligopoly model. Firms and their production are differentiated, which brings the theoretical model closer to real market conditions. The main objective was to expand the Cournot duopoly and add another firm, resulting in an oligopolistic market structure assuming a partially differentiated production and coalition strategy between two firms. This article contains an oligopolistic model specifically designed for three different types of expectations, and has been applied to find and verify the stability of the net equilibrium of oligopolists. The market of telecommunication operators in Slovakia was selected as a real market case with accessible data on an oligopoly with three companies and partial differentiation. There are studies in which the authors limit their considerations to a certain number of repetitions of oligopolistic games. An infinite time interval is considered here. Three types of future expectations were considered: a simple dynamic model (or naïve expectations) in which the oligopolist assumes that its competitors will behave in the future based on their response functions, an adaptive expectations model in which the oligopolist considers a weighted average of the quantities offered by its competitors, and real expectations in which firms behave as rational players and do not have complete information about demand and offer output based on expected marginal profit. While the presented model proved to be stable under naïve and adaptive expectations, no stable equilibrium was found under real expectations and further results indicate a chaotic behavior. Full article

In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative games—namely, core partitions, the von Neumann–Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)—and in developing relationships between coalition structures that are stable under these different stability concepts. We first define two special classes of players for PMAS profit games—extreme and strong players—and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness. We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions. Full article

Coalition formation is often analysed in an almost non-cooperative way, as a two-stage game that consists of a first stage comprising membership actions and a second stage with physical actions, such as the provision of a public good. We formalised this widely used approach for the case where actions are simultaneous in each stage. Herein, we give special attention to the case of a symmetric physical game. Various theoretical results, in particular, for cartel games, are provided. As they are crucial, recent results on the uniqueness of coalitional equilibria of Cournot-like physical games are reconsidered. Various concrete examples are included. Finally, we discuss research strategies to obtain results about equilibrium coalition structures with abstract physical games in terms of qualitative properties of their primitives. Full article

We study the recursive core introduced in Huang and Sjöström [8]. In general partition function form games, the recursive core coalition structure may be either coarser or finer than the one that maximizes the social surplus. Moreover, the recursive core structure is typically different from the one predicted by the α-core. We fully implement the recursive core for general games, including non-superadditive games where the grand coalition does not form in equilibrium. We do not put any restrictions, such as stationarity, on strategies. Full article