Social Reinforcement: Cascades, Entrapment and Tipping

There are many social situations in which the actions of different agents reinforce each other. These include network effects and the threshold models used by sociologists (Granovetter, Watts) as well as Leibenstein's "bandwagon effects." We model such situations as a game with increasing differences, and show that tipping of equilibria as discussed by Schelling, cascading and Dixit's results on clubs with entrapment are natural consequences of this mutual reinforcement. If there are several equilibria, one of which Pareto dominates, then we show that the inefficient equilibria can be tipped to the efficient one, a result of interest in the context of coordination problems.

Network formation and its Impact on Systemic Risk

In the aftermath of the financial crisis of 2008, many policy makers and researchers pointed to the interconnectedness of the financial system as one of the fundamental contributors to systemic risk. The argument is that the linkages between financial institutions served as an amplification mechanism: shocks to smaller parts of the system propagate through the system and result in broad damage to the financial system. In my dissertation, I explore the formation of networks when agents take into account systemic risk. The dissertation consists of three complementary papers on this topic. The first paper titled ``Network Formation and Systemic Risk\u27\u27, joint with Professor Rakesh Vohra. We set out the framework and construct a model of endogenous network formation and systemic risk. We find that fundamentally `safer\u27 economies with higher probability of getting good shocks generate higher interconnectedness, which leads to higher systemic risk. This provides network foundations for ``the volatility paradox\u27\u27 arguing that better fundamentals lead to worse outcomes due to excessive risk taking. Second, the network formed crucially depends on the correlation of shocks to the system. As a consequence, an observer, such as a regulator, facing an interconnected network who is mistaken about the correlation structure of shocks will underestimate the probability of system wide failure. This result relates to the ``dominoes vs. popcorn\u27\u27 discussion by Edward Lazear. He comments that a fundamental mistake in addressing the crisis was to think that it was ``dominoes\u27\u27 so that saving one firm would save many others in the line. He continues to argue that it was ``popcorn in a pan\u27\u27: all firms were exposed to same correlated risks and saving one would not save many others. We complement his discussion by arguing that the same mistake might have been the reason behind why sufficient regulatory precaution was not taken prior to the crisis. The third result is that the networks formed in the model are utilitarian efficient because the risk of contagion is high. This causes firms to minimize contagion by forming dense but isolated clusters that serve as firebreaks. This finding is suggestive that, the worse the contagion, the more the market takes care of it. In the second paper, titled ``Network Hazard and Bailouts\u27\u27, I ask how the anticipation of ex-post government bailouts affects network formation. I deploy a significant generalization of the model in the first paper and allow for time-consistent government transfers. I find that the presence of government bailouts introduces a novel channel for moral hazard via its effect on network architecture, which I call ``network hazard\u27\u27. In the absence of bailouts, firms form sparsely connected small clusters in order to eliminate second-order counterparty risk: expected losses due to defaulting counterparties that default because of their own defaulting counterparties. Bailouts, however, eliminate second-order counterparty risk already. Accordingly, when bailouts are anticipated, the networks formed become more interconnected, and exhibit a core-periphery structure (many firms connected to a smaller number of central firms, which is observed in practice). Interconnectedness within the periphery leads to higher extent of contagion with respect to the networks formed in the absence of intervention. Moreover, solvent core firms serve as a buffer against contagion by increasing the resilience of the many peripheral firms that are connected to the core. However, insolvent core firms serve as an amplifier of contagion since they make peripheral firms less resilient. This implies that in my model, ex-post time-consistent intervention by the government, while ex-ante welfare improving, increases systemic risk and volatility, solely through its effect on the network. A remark is that firms, in my model, do not make riskier individual choices regarding neither their choice of investment risk, nor the number of their counterparties they have. In this sense, network hazard is a genuine form of moral hazard solely through the formation of the detailed network. On another note, the model can also be viewed as a first attempt towards developing a theory of mechanism design with endogenously formed network externalities which might be useful in various other scenarios such as provision of local public goods. In the final paper, titled “Network Reactions to Banking Regulations”, joint with Professor Guilermo Ordonez, we consider the role of liquidity and capital requirements to alleviate network hazard and systemic risk. In the model, financial firms set up credit lines with each other in order to meet their funding needs on demand. Accordingly, higher liquidity requirements induce firms to form higher interconnectedness in order to be able to find deposits as needed. At a tipping point of liquidity requirements, the network discontinuously jumps in its interconnectedness, which contributes discontinuously to systemic risk. On the other hand, the reaction to capital requirements is smooth. Capital requirements indirectly work as an upper bound in the interconnectedness firms would form. This way, interconnectedness can be effectively reduced to a desired level via capital requirements. Yet capital requirements cannot be used to induce higher interconnectedness. Thusly, in times of credit freeze, capital requirements may not help promote circulation of credit. A conjunction of both liquidity and capital requirements is more effective in promoting desired circulation while reducing systemic risk. The work in this dissertation suggests that endogenous network architecture is an essential component of the study of financial markets. In particular, network hazard is a genuine form of moral hazard that will be overlooked unless network formation is taken into account, while it has implications about systemic risk. Moreover, this work illustrates how the reaction of networked financial markets to both fundamentals of the economy and to the policy can be non-trivial, featuring non-monotonicity and discontinuity

On the Complexity of Tipping in Super-Modular Games

The problem of finding the minimum tipping set in a super modular game is known to be NP-hard. Here, I derive an approximation algorithm to find a small tipping set in such a game. In the special case of the uniform game, the approximation provides the exact minimum tipping set. Interdependent security is a growing field. One model used for interdependent security is the airline security model. This model is used as an example for the approximation methods, and was the working model for many of the proofs and strategies developed to find tipping sets and their approximations. This algebraic approach, which makes use of group theory, is then evaluated for accuracy, It is then applied to a dynamic approach, using a simple learning function without the complete information often assumed. This method links the non-greedy approximation to a version of SAT, and a type of influence graphs and the covering problem. The approximation fared well when finding the key players in a game, but struggled with cascades

Team Formation And Incentives

This dissertation analyzes the incentives of workers in organizations that utilize teams. In Chapter 1, I study a moral hazard in teams model in which a principal knows that the agents she compensates are identical and independent, but does not know all of the actions they can take. In the face of this uncertainty, the principal chooses a symmetric contract that yields her the highest worst-case expected profit. I show that, counterintuitively, any such contract exhibits joint performance evaluation — each agent\u27s pay is increasing in the performance of the other — and is nonlinear in team output. In Chapter 2, Carlos Segura-Rodriguez and I study profit-maximizing matching in the presence of adverse selection and moral hazard. We show that when productive complementarities between workers are weak and effort costs are high, expected wage payments increase in the assortativity of the matching the manager implements. Hence, either random or negative assortative matching can be profit-maximizing, even when positive assortative matching is efficient. Finally, in Chapter 3, Carlos Segura-Rodriguez, Peng Shao, and I study the efficiency of decentralized team formation inside research organizations through the lens of a one-sided matching model with non-cooperative after-match information production. Our equilibrium analysis identifies two inefficiencies observed inside of non-hierarchical organizations. First, productive teams composed of workers producing complementary information may form at the expense of excluded workers who must form relatively unproductive teams consisting of workers producing substitutable information. Second, even when productive teams are efficient, they need not form; a worker in such a team may prefer to join a less productive team if she can exert less effort in this deviating team

Energy transition under scenario uncertainty: a mean-field game approach

We study the impact of transition scenario uncertainty, and in particular, the uncertainty about future carbon price and electricity demand, on the pace of decarbonization of the electricity industry. To this end, we build a discrete time mean-field game model for the long-term dynamics of the electricity market subject to common random shocks affecting the carbon price and the electricity demand. These shocks depend on a macroeconomic scenario, which is not observed by the agents, but can be partially deduced from the frequency of the shocks. Due to this partial observation feature, the common noise is non-Markovian. We consider two classes of agents: conventional producers and renewable producers. The former choose an optimal moment to exit the market and the latter choose an optimal moment to enter the market by investing into renewable generation. The agents interact through the market price determined by a merit order mechanism with an exogenous stochastic demand. We prove the existence of Nash equilibria in the resulting mean-field game of optimal stopping with common noise, developing a novel linear programming approach for these problems. We illustrate our model by an example inspired by the UK electricity market, and show that scenario uncertainty leads to significant changes in the speed of replacement of conventional generators by renewable production.Comment: 41 pages, 3 figure

Monopoly Pricing of Social Goods

We analyse the roles of social network topology and size on the monopoly pricing of network goods in a market, where consumers interact with each other and are characterised by their social relations. The size effect is the well-known network externalities phenomenon, while the topological effect has not been previously studied in this context. The topological effect works against, and dominates, the size effect in monopoly pricing by reducing the monopoly's capacity to extract consumer surplus. Under asymmetric information about consumer types, the monopoly prefers symmetric network topologies, but the social optimum is an asymmetric network

On Influence, Stable Behavior, and the Most Influential Individuals in Networks: A Game-Theoretic Approach

We introduce a new approach to the study of influence in strategic settings where the action of an individual depends on that of others in a network-structured way. We propose \emph{influence games} as a \emph{game-theoretic} model of the behavior of a large but finite networked population. Influence games allow \emph{both} positive and negative \emph{influence factors}, permitting reversals in behavioral choices. We embrace \emph{pure-strategy Nash equilibrium (PSNE)}, an important solution concept in non-cooperative game theory, to formally define the \emph{stable outcomes} of an influence game and to predict potential outcomes without explicitly considering intricate dynamics. We address an important problem in network influence, the identification of the \emph{most influential individuals}, and approach it algorithmically using PSNE computation. \emph{Computationally}, we provide (a) complexity characterizations of various problems on influence games; (b) efficient algorithms for several special cases and heuristics for hard cases; and (c) approximation algorithms, with provable guarantees, for the problem of identifying the most influential individuals. \emph{Experimentally}, we evaluate our approach using both synthetic influence games as well as several real-world settings of general interest, each corresponding to a separate branch of the U.S. Government. \emph{Mathematically,} we connect influence games to important game-theoretic models: \emph{potential and polymatrix games}.Comment: Accepted to AI Journal, subject to addressing the reviewers' points (which are addressed in this version). An earlier version of the article appeared in AAAI-1