Farsightedly stable networks

A set of networks G is pairwise farsightedly stable (i) if all possible farsighted pairwise deviations from any network g G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). A non-empty pairwise farsightedly stable set always exists. We provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominant network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest pairwise consistent set and the von Neumann–Morgenstern pairwise farsightedly stable set.     

FARSIGHTED COALITIONAL STABILITY OF A PRICE LEADERSHIP CARTEL

This paper analyzes the farsighted behaviour of firms that form a dominant price leadership cartel. We consider stability concepts such as the farsighted core, the farsighted stable sets, and the largest consistent set. We show that: (i) the farsighted core is either an empty set or a singleton set of the grand cartel; (ii) any Pareto efficient cartel is itself a farsighted stable set; and (iii) the set of cartels in which fringe firms enjoy higher profits than the firms in the minimal Pareto efficient cartel is the largest consistent set.     

Toward Farsightedly Stable International Environmental Agreements

The stability of International Environmental Agreements (IEA) is analyzed by using game theory. The integrated assessment model FUND provides the cost-benefit payoff functions of pollution abatement for sixteen different world regions. The farsighted stability concept of Chwe (1994) is used and solved by combinatorial algorithms. Farsighted stability assumes perfect foresight of the players and predicts which coalitions can be formed when players are farsighted. All farsightedly stable coalitions are found, and their improvement to environment and welfare is considerable. The farsightedly stable coalitions are refined further to preferred farsightedly stable coalitions, which are coalitions where the majority of coalition members reach higher profits in comparison with any other farsightedly stable coalitions. Farsightedly stable coalitions contribute more to the improvement of environment and welfare in comparison to D'Aspremont et al.'s (1983) stable ones. Considering multiple farsighted stable coalitions, participation in coalitions for environmental protection is significantly increased, which is an optimistic result of our game theoretical model.     

Market structure and matching with contracts

Ostrovsky (2008) [9] develops a theory of stability for a model of matching in exogenously given networks. For this model a generalization of pairwise stability, chain stability, can always be satisfied as long as agents' preferences satisfy same side substitutability and cross side complementarity. Given this preference domain I analyze the interplay between properties of the network structure and (cooperative) solution concepts. The main structural condition is an acyclicity notion that rules out the implementation of trading cycles. It is shown that this condition and the restriction that no pair of agents can sign more than one contract with each other are jointly necessary and sufficient for (i) the equivalence of group and chain stability, (ii) the core stability of chain stable networks, (iii) the efficiency of chain stable networks, (iv) the existence of a group stable network, and (v) the existence of an efficient and individually stable network. These equivalences also provide a rationale for chain stability in the unrestricted model. The (more restrictive) conditions under which chain stability coincides with the core are also characterized.     

Networks and farsighted stability

We provide a new framework for the analysis of network formation and demonstrate the existence of farsightedly consistent directed networks. Our framework extends the standard notion of a network and also introduces the notion of a supernetwork. A supernetwork is made up of a collection of directed networks (the nodes) and represents (via the arcs connecting the nodes) preferences and rules governing network formation. By extending Chwe's 1994 result on the nonemptiness of farsightedly consistent sets, we show that for any supernetwork there exists a nonempty subset of farsightedly consistent directed networks.     

Networks of Free Trade Agreements among Heterogeneous Countries

The paper examines the formation of free trade agreements as a network formation game. We consider an n‐country model in which international trade occurs between economies with imperfectly competitive product markets. In each country, the labor market is either unionized or non‐unionized. We show that, if all countries are non‐unionized, the global free trade network is both the unique pairwise stable network and the unique efficient network. If all countries are unionized, the global free trade network is pairwise stable and the unique efficient network among the class of symmetric networks. If some countries are unionized while others are non‐unionized, other networks apart from the global free trade network may be pairwise stable. However, the efficient network is still the global free trade network. Thus, a conflict between stability and efficiency may occur. Moreover, starting from the network in which no country has signed a free trade agreement, all sequences of networks due to continuously profitable deviations do not lead (in most cases) to the global free trade network, even when global free trade is stable.     

Von Neumann-Morgenstern stable sets in matching problems

The following properties of the core of a one-to-one matching problem are well-known: (i) the core is non-empty; (ii) the core is a distributive lattice; and (iii) the set of unmatched agents is the same for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (Von Neumann-Morgenstern) stable sets in one-to-one matching problems. We show that a set V of matchings is a stable set of a one-to-one matching problem only if V is a maximal set satisfying the following properties: (a) the core is a subset of V; (b) V is a distributive lattice; and (c) the set of unmatched agents is the same for all matchings belonging to V. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b), and (c).     

Stochastic stability for roommate markets

We show that for any roommate market the set of stochastically stable matchings coincides with the set of absorbing matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts have been proposed to extend the core to all roommate markets (including those with an empty core). An important implication of our results is that the set of absorbing matchings is the only solution concept that is core consistent and shares the stochastic stability characteristic with the core.     

Von Neumann-Morgenstern stable sets, discounting, and Nash bargaining

We establish a link between von Neumann-Morgenstern stable set and the Nash solution in a general n-player utility set. The stable set-solution is defined with respect to a dominance relation: payoff vector u dominates v if one player prefers u even with one period delay. We show that a stable set exists and, if the utility set has a smooth surface, any stable set converges to the Nash bargaining solution when the length of the period goes to zero.     

Inequality and network structure

We explore the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members, based on the following considerations: (i) any distribution of value must be stable with respect to coalitional deviations, and (ii) the network structure itself determines the coalitions that may form. We show that if players can jointly deviate only if they form a clique in the network, then the degree of inequality that can be sustained depends on the cardinality of the maximum independent set. For bipartite networks, the size of the maximum independent set fully characterizes the degree of inequality that can be sustained. This result extends partially to general networks and to the case in which a group of players can deviate jointly if they are all sufficiently close to each other in the network.     

On Forward Induction and Evolutionary and Strategic Stability

We analyze which normal form solution concepts capture the notion of forward induction, as defined by E. van Damme (1989, J. Econ. Theory48, 476-496) in the class of generic two player normal form games preceded by an outside option. We find that none of the known strategic stability concepts (including Mertens stable sets and hyperstable sets) capture this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (J. Swinkels, 1992, J. Econ. Theory57, 306-332) is always consistent with forward induction. Journal of Economic Literature Classification Number: C72.     

Networks of knowledge among unionized firms

Abstract.  We develop a model of strategic networks in order to analyze how trade unions will affect the stability of R&D networks through which knowledge is transmitted in an oligopolistic industry. Whenever firms settle wages, the partially connected network is likely to emerge in the long run if and only if knowledge spillovers are large enough. However, when unions settle wages, the complete network is the unique stable network. In other words, the stronger the union bargaining power is, the more symmetric stable R&D networks will be. In terms of network efficiency, the partially connected network (when firms settle wages) does not Pareto dominate the complete network (when unions settle wages) and vice versa.     

p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics

This paper studies equilibrium selection based on a class of perfect foresight dynamics and relates it to the notion of p-dominance. A continuum of rational players is repeatedly and randomly matched to play a symmetric n×n game. There are frictions: opportunities to revise actions follow independent Poisson processes. The dynamics has stationary states, each of which corresponds to a Nash equilibrium of the static game. A strict Nash equilibrium is linearly stable under the perfect foresight dynamics if, independent of the current action distribution, there exists a consistent belief that any player necessarily plays the Nash equilibrium action at every revision opportunity. It is shown that a strict Nash equilibrium is linearly stable under the perfect foresight dynamics with a small degree of friction if and only if it is the p-dominant equilibrium with p<1/2. It is also shown that if a strict Nash equilibrium is the p-dominant equilibrium with p<1/2, then it is uniquely absorbing (and globally accessible) for a small friction (but not vice versa). Set-valued stability concepts are introduced and their existence is shown. Journal of Economic Literature Classification Numbers: C72, C73.     

International Environmental Agreements—The Role of Foresight

The present paper attempts to bridge the gap between the cooperative and the non-cooperative approach employed to examine the size of stable coalitions, formed to address global environmental problems. We do so by endowing countries with foresightedness, that is, by endogenizing the reaction of the coalition’s members to a deviation by one member. We assume that when a country contemplates withdrawing or joining an agreement, it takes into account the reactions of other countries ignited by its own actions. We identify conditions under which there always exists a unique set of farsighted stable IEAs. The new farsighted IEAs can be much larger than those some of the previous models supported but are not always Pareto efficient.     

Resource availability in the social cloud: An economics perspective

Social cloud has emerged as a case of sharing economy, where socially connected agents share their computing resources within the community. This paper considers the social cloud as an endogenous resource-sharing network, where agents are involved in closeness-based conditional resource sharing. This study focuses on (1) the impact of agents' decisions of link addition and deletion on their own local and global resource availability as well as on others' global resource availability (as spillover effects), (2) the role of agents' closeness in determining spillover effects, (3) agents' link addition behavior, and (4) stability and efficiency of the social cloud. The findings include the following: (i) Agents' decision of link addition (deletion) increases (decreases) their local resource availability. However, these observations do not hold in the case of global resource availability. (ii) In a connected network, agents experience either a positive or a negative spillover effect and there is no case with no spillover effects. Agents observe no spillover effects if and only if the network is disconnected with three or more components. Furthermore, an agent experiences negative spillover if there is no change in its closeness. Although an increase in the closeness of agents is necessary to experience positive spillover effects, the condition is not sufficient. (iii) We study the relation between agents' distance from each other, and their local as well as global resource availabilities. We prove that the local resource availability of an agent from another agent increases with decrease in the distance between them and that maximum local resource availability is obtained from the agent with the least closeness. Using these results, we discuss which agent to add a link to, so as to maximize the local resource availability. We discuss why such results are difficult to establish for global resource availability. However, in a two-diameter network, we show that for an agent, link formation always increases the global resource availability. (iv) We also study resource-sharing network formation and its efficiency in a strategic setting. We prove the existence of a pairwise stable network. Furthermore, we provide a set of conditions for a few prominent network structures (star, complete, wheel, and bipartite networks) to be pairwise stable. We show that the “connected in pairs, otherwise disconnected” network is better than a connected network, in terms of social welfare.     

Networks and clubs

We formulate a club model where players’ have identical single-peaked preferences over club sizes as a network formation game. For situations with “many” clubs, we provide necessary and sufficient for non-emptiness of the farsighted core and the direct (or myopic) core. With “too few” clubs, if players are farsighted then the farsighted core is empty. In this same case, if players are myopic then the direct core is always nonempty and, for any club network in the direct core, clubs are of nearly equal size (i.e., clubs differ in size by at most one member).     

Essential equilibria in normal-form games

A Nash equilibrium x of a normal-form game G is essential if any perturbation of G has an equilibrium close to x. Using payoff perturbations, we show that for games that are generic in the set of compact, quasiconcave, and generalized payoff secure games with upper semicontinuous sum of payoffs, all equilibria are essential. Some variants of this result are also established.     

Increasing Nth degree risk

Generalizing the Rothschild-Stiglitz increasing risk and the Menezes et al. increasing downside risk concepts, it still holds that G has more nth degree risk than F if and only if every nth degree risk averter prefers F to G.     

Unmediated communication in games with complete and incomplete information

We study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^U(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^U(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e., all profiles of types have positive probability), then S^U(G) is equal to the set of communication equilibria of G.     

Robust equilibria under non-common priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.