Strongly stable networks

We analyze the formation of networks among individuals. In particular, we examine the existence of networks that are stable against changes in links by any coalition of individuals. We show that to investigate the existence of such strongly stable networks one can restrict focus on a component-wise egalitarian allocation of value. We show that when such strongly stable networks exist they coincide with the set of efficient networks (those maximizing the total productive value). We show that the existence of strongly stable networks is equivalent to core existence in a derived cooperative game and use that result to characterize the class of value functions for which there exist strongly stable networks via a “top convexity” condition on the value function on networks. We also consider a variation on strong stability where players can make side payments, and examine situations where value functions may be non-anonymous—depending on player labels.     

ECONOMIC NETWORKING AND STABILITY

Abstract. In this paper we discuss finite economies with the presence of transaction costs and with decreasing, constant or increasing returns. In general such an economy may have no general equilibrium existence and may even have an empty core. We analyse the trading networks of such an economy, introducing the concepts of locally stable network structure, un‐dominated locally stable network structures and most stable network structures. We point out that the set of most stable network structures could be treated as a solution concept for the empty core economies both in theoretical analysis and in application.     

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.     

Network formation and stable equilibrium

We study the non-cooperative formation of a (directed) network that builds upon one-way immediate links. Our novel feature is that we require circular paths of links for productive activities. This captures more clearly the higher level of coordination that is often required for network formations than models such as those of Jackson and Wolinsky [A strategic model of social and economic networks, J. Econ. Theory 71 (1996) 44-74] and Bala and Goyal [A non-cooperative model of network formation, Econometrica 68 (2000) 1181-1229], in that in our model a single agent's unilateral action is limited in affecting the network structure. We completely characterize the class of Nash equilibria by showing that the minimality of a graph is both necessary and sufficient (Theorem 1). We also propose the concept of a stable network that is similar to the pairwise stability of Jackson and Wolinsky (1996). We show that stable equilibria are a wheel, a trivial network, or a sub-wheel partitioned network (Theorem 2). We modify the Bala and Goyal (2000) dynamic process with inertia, and obtain the convergence to stable equilibria regardless of the initial state (Theorem 3).     

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.     

Agreeable bets with multiple priors

This paper considers a two-agent model of trade with multiple priors. Firstly, we characterize the existence of an agreeable bet on some event in terms of the set of priors. It is then shown that the existence of an agreeable bet on some event is a strictly stronger condition than the existence of an agreeable trade, whereas the two conditions are equivalent in the standard Bayesian framework. Secondly, we show that the two conditions are equivalent when the set of priors is the core of a convex capacity. These results are also related to the no trade theorems under asymmetric information.     

Generalized risk-dominance and asymmetric dynamics

This paper proposes two (ordinal and cardinal) generalizations of [J.C. Harsanyi, R. Selten, A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge, MA and London, 1988] risk-dominance to multi-player, multi-action games. There are three reasons why generalized risk-dominance (GR-dominance) is interesting. Extending the logic of risk-dominance, GR-dominant actions can be interpreted as best responses to conjectures that satisfy a certain type of symmetry. Second, in a local interaction game of [G. Ellison, Learning, local interaction, and coordination, Econometrica 61 (5) (1993) 1047], if an action is risk-dominant in individual binary interactions with neighbors, it is also GR-dominant in the large game on a network. Finally, we show that GR-dominant actions are stochastically stable under a class of evolutionary dynamics. The last observation is a corollary to new abstract selection results that applies to a wide class of so-called asymmetric dynamics. In particular, I show that a (strictly) ordinal GR-dominant profile is (uniquely) stochastically stable under the approximate best-response dynamics of [M. Kandori, G.J. Mailath, R. Rob, Learning, mutation, and long run equilibria in games, Econometrica 61 (1) (1993) 29]. A (strictly) cardinal GR-dominant equilibrium is (uniquely) stochastically stable under a class of payoff-based dynamics that includes [L.E. Blume, The statistical-mechanics of strategic interaction, Games Econ. Behav. 5 (3) (1993) 387-424]. Among others, this leads to a generalization of a result from [G. Ellison, Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution, Rev. Econ. Stud. 67 (230) (2000) 17] on the -dominant evolutionary selection to all networks and the unique selection to all networks that satisfy a simple, sufficient condition.     

Stable matchings and preferences of couples

Couples looking for jobs in the same labor market may cause instabilities. We determine a natural preference domain, the domain of weakly responsive preferences, that guarantees stability. Under a restricted unemployment aversion condition we show that this domain is maximal for the existence of stable matchings. We illustrate how small deviations from (weak) responsiveness, that model the wish of couples to be closer together, cause instability, even when we use a weaker stability notion that excludes myopic blocking. Our remaining results deal with various properties of the set of stable matchings for “responsive couples markets”, viz., optimality, filled positions, and manipulation.     

From evolutionary to strategic stability

A connected component of Nash equilibria is (dynamically) potentially stable if there exits an evolutionary selection dynamics from a broad class for which the component is asymptotically stable. A necessary condition for potential stability is that the component's index agrees with its Euler characteristic. Second, if the latter is nonzero, the component contains a strategically stable set. If the Euler characteristic would be zero, the dynamics (that justifies potential stability) could be slightly perturbed so as to remove all zeros close to the component. Hence, any robustly potentially stable component contains equilibria that satisfy the strongest rationalistic refinement criteria.     

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.     

A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game

It is well-known that a transferable utility game has a non-empty core if and only if it is balanced. In the class of non-transferable utility games balancedness or the more general π-balancedness due to Billera (SIAM J. Appl. Math. 18 (1970) 567) is a sufficient, but not a necessary condition for the core to be non-empty. This paper gives a natural extension of the π-balancedness condition that is both necessary and sufficient for non-emptiness of the core.     

Imperfect monitoring in communication networks

Individuals in many social networks imperfectly monitor other individuals’ network relationships. This paper shows that, in a model of a communication network, imperfect monitoring leads to the existence of many inefficient equilibria. Reasonable restrictions on actions or on beliefs about others’ actions can, however, eliminate many of these inefficient equilibria even with imperfect monitoring. Star networks, known to be efficient in many settings, are shown to have desirable monitoring characteristics. More generally, this paper provides a formal framework in which to study incorrect perceptions as an equilibrium phenomenon in social networks.     

Core and periphery in networks

We study a model of network formation where the benefits from connections exhibit decreasing returns and decay with network distance. We show that the unique equilibrium network is a periphery-sponsored star, where one player, the center, maintains no links and earns a high payoff, while all other players maintain a single link to the center and earn lower payoffs. Both the star architecture and payoff inequality are preserved in an extension of the model where agents can make transfers and bargain over the formation of links, under the condition that the surplus of connections increases in the size of agents’ neighborhoods. Our model thus generates two common features of social and economic networks: (1) a core-periphery structure; (2) positive correlation between network centrality and payoffs.     

Stable schedule matching under revealed preference

Baiou and Balinski (Math. Oper. Res., 27 (2002) 485) studied schedule matching where one determines the partnerships that form and how much time they spend together, under the assumption that each agent has a ranking on all potential partners. Here we study schedule matching under more general preferences that extend the substitutable preferences in Roth (Econometrica 52 (1984) 47) by an extension of the revealed preference approach in Alkan (Econom. Theory 19 (2002) 737). We give a generalization of the Gale-Shapley algorithm and show that some familiar properties of ordinary stable matchings continue to hold. Our main result is that, when preferences satisfy an additional property called size monotonicity, stable matchings are a lattice under the joint preferences of all agents on each side and have other interesting structural properties.     

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.     

全球生产网络下产业领导力影响了知识溢出吗

全球生产网络为知识溢出提供了新渠道。在新的国际分工格局中，不同产业集团所处地位具有非对称性，而这种非对称性或者产业领导力是否对知识溢出产生影响缺乏理论分析和验证。鉴于此，在理论分析基础上，构造核心产业领导力衡量指标，探讨核心产业领导力对知识溢出的影响。研究发现：(1)产业领导力对知识溢出具有显著正向影响，表现为具有领导力的核心产业通过价值链参与形式，将创新研发成果输送至非核心产业区；(2)地理距离加权的核心产业领导力对非核心产业区的创新效率具有显著负向影响，其作用机制是地理距离通过制度距离弱化核心产业领导力对非核心产业区的知识溢出效应；(3)基于产业非对称条件下的知识溢出效应，不同属性产业以及不同区域间均表现出显著异质性。研究不仅从产业领导力角度对全球生产网络分工条件下的知识溢出研究提出了新认识，而且为在全球产业链、价值链重构的关键阶段如何通过迈向全球产业链中高端，推动全球产业链、价值链包容性发展，作出更多中国贡献提供了重要政策建议。     

Social network and private provision of public goods

Using a simple model with interdependent utilities, we study how social networks influence individual voluntary contributions to the provision of a public good. Departing from the standard model of public good provision, we assume that an agent’s utility has two terms: (a) ‘ego’-utility derived from the agent’s consumption of public and private goods, and (b) a social utility which is the sum of utility spillovers from other agents with whom the agent has social relationships. We establish conditions for the existence of a unique interior Nash equilibrium and describe the equilibrium in terms of network characteristics. We show that social network always has a positive effect on the provision of the public good. We also find that, in networks with “small world”-like modular structures, ‘bridging’ ties connecting distant parts of social network play an important role inducing an agent’s contribution to public good. Assumptions and results of the model are discussed in relation to the role of social capital in community-level development projects and to the effect of innovation networks on firms’ R&D investments.     

On the consistency of stationary Markov equilibria with an exogenous distribution

A technique to show the existence of stationary Markov equilibria is provided by Duffie, Geanakoplos, Mas-Colell and McLennan Econometrica 62 (1994) 745-781. In many applications, a state space is constructed as the product of a space of exogenous variables and a space of endogenous variables. In addition, the exogenous shock is given and is a Markov process with a transition probability and an initial distribution. Then their theorem does not ensure the existence of a stationary Markov equilibrium that is consistent with the exogenous distribution. In this paper, we give a sufficient condition for settling the inconsistency problem.     

Venture Capital Networks and Investment Performance in China

We investigate the relationship between venture capital (VC) networks and investment performance in China. Distinct features of China's VC networks are captured in our econometric model through the inclusion of an index of network stability and a dummy variable that indicates a VC firm's connections with the Chinese state. Our econometric analysis shows that a VC firm's position in its network, its network stability and close connections with the state all contribute to its investment performance. Comparison with the findings in Hochberg et al. (2007) indicates that networks are more important for investment performance in China than in the US. Moreover, our analysis suggests that familiarity with local culture and customs and understanding of the idiosyncrasies of China's markets and institutions are important for the success of a VC firm in China.     

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).