This thesis studies three game theoretic models of pricing, in which a seller is interested in optimally pricing and allocating her product or service to a market of agents, in order to maximize her revenue. These markets feature a large number of self-interested agents, who are generally heterogeneous with respect to some payoff relevant feature, e.g., willingness to pay when agents are consumers or private cost when agents are firms. Agents strategically interact with one another, and their actions affect other agents' payoffs, either directly through social influence or competition, or indirectly through a review system. The seller has demand uncertainty and strives to optimize expected discounted revenues. I use either a mean-field approximation or a continuum of agents assumption to reduce the complexity of the problems and provide crisp characterizations of system aggregates and equilibrium policies. Chapter 2 considers the problem of an information provider who sells information products, such as demand forecasts, to a market of firms that compete with one another in a downstream market. We propose a general model that subsumes both price and quantity competition as special cases. We characterize the optimal selling strategy and find that it depends on both mode and intensity of competition. Several important extensions to heterogeneous production costs, information quality discrimination, and information leakage through aggregate actions are studied. Chapter 3 considers the problem of optimally extracting a stream of revenues from a sequence of consumers, who have heterogeneous willingness to pay and uncertainty about the quality of the product being sold. Using an intuitive maximum likelihood procedure, we characterize the solution of consumers' quality estimation problem. Then, we use a mean-field approximation to characterize the transient dynamics of quality estimates and demand. These allow us to simplify and solve the monopolist's problem, and ultimately provide a characterization of her optimal pricing policy. Chapter 4 considers the problem of a seller who is interested in dynamically pricing her product when consumers' utility is influenced by the mass of consumers that have purchased in the past. Two scenarios are studied, one in which the monopolist has commitment power and one in which she does not. We characterize the optimal selling strategy under both scenarios and derive comparisons on equilibrium prices and demands. Our main result is a characterization of the value of price commitment as a function of the social influence level in the market.

A large literature has documented a pattern of stochastic, or random, choice in individual decision making. In games, in which payoffs depend on beliefs over opponents’ behavior, another potentially important source of stochasticity is in the beliefs themselves. Hence, there may be both “noisy actions” and “noisy beliefs”. This dissertation explores the equilibrium implications of both types of noise in normal form games. Theory is developed to understand the effects of noisy beliefs, and the model is compared to the canonical model of noisy actions. Predictions—and assumptions—are tested using existing and novel experimental data. Chapter 1 introduces noisy belief equilibrium (NBE) for normal form games, a model that injects “noisy beliefs” into an otherwise standard equilibrium framework. Axioms restrict the belief distributions to be unbiased with respect to and responsive to changes in the opponents’ behavior. We compare NBE to an axiomatic form of quantal response equilibrium (QRE) in which players have correct beliefs over their opponents’ behavior, but take “noisy actions”. We show that NBE generates similar predictions as QRE such as the “own-payoff effect”, and yet is more consistent with the empirically documented effects of changes in payoff magnitude. Unlike QRE, NBE is a refinement of rationalizability and invariant to affine transformations of payoffs. Chapter 2, joint with Jeremy Ward, studies an equilibrium model in which there is both “noisy actions” and “noisy beliefs”. The model primitives are an action-map, which determines a distribution of actions given beliefs, and a belief-map, which determines a distribution of beliefs given opponents’ behavior. These are restricted to satisfy the axioms of QRE and NBE, respectively, which are simply stochastic generalizations of “best response” and “correct beliefs”. In our laboratory experiment, we collect actions data and elicit beliefs for each game within a family of asymmetric 2-player games. These games have systematically varied payoffs, allowing us to “trace out” both the action- and belief-maps. We find that, while both sources of noise are important in explaining observed behaviors, there are systematic violations of the axioms. In particular, although all subjects observe and play the same games, subjects in different roles have qualitatively different belief biases. To explain this, we argue that the player role itself induces a higher degree of strategic sophistication in the player who faces more asymmetric payoffs. This is confirmed by structural estimates. Chapter 3 considers logit QRE (LQRE), the common parametric form of QRE; and we endogenize its precision parameter "lambda", which controls the degree of “noisy actions”. In the first stage of an endogenous quantal response equilibrium (EQRE), each player chooses her precision optimally subject to costs, taking as given other players’ (second-stage) behavior. In the second stage, the distribution of players’ actions is a heterogenous LQRE given the profile of first-stage precision choices. EQRE satisfies a modified version of the regularity axioms, nests LQRE as a limiting case for a sequence of cost functions, and admits analogues of classic results for LQRE such as those for equilibrium selection. We show how EQRE differs from LQRE using the family of generalized matching pennies games.

In the first chapter, I measure the effects of street-level political advertising on voting behavior. I use a novel dataset on ad location in a major Spanish city during elections for the national parliament as well as granular socio-economic and voting data. This set-up, where more than two parties are running for office and elections are very competitive, allows me to explore the heterogeneous effects of ads across parties as well as how parties' ads affect other parties' vote shares. To identify the effects of parties' ads, I exploit a legally mandated randomized assignment of ad location to parties across multiple years. I find that a party's own ads have a positive effect on its vote share, although the effects are heterogeneous across parties. A one standard deviation increase in the number of ads increases a party's vote share by 0.79 percentage points on average. Ads of parties with ideologically distant platforms consistently have a negative effect on a party's vote share. In contrast, ads of parties that are close competitors may act either as complements or substitutes in different years. The second chapter analyses the effects of an economic shock on the emergence of new parties and other changes in voting parties by using regional variation in the exposure to the shock. I find that a worsening of economic conditions as measured by unemployment rate leads to an increase in electoral competition and volatility. In particular, the deeper the effects of the recession in a area, the larger the number of new parties emerge and become more successful and there is an increase in the changes in vote shares. On the other hand, the vote share of parties previously in government decreases and a decrease in vote share concentration. The third chapter is a co-authored works where we present experimental evidence establishing that the level of incentives affects both gameplay and beliefs. Holding fixed the actions of the other player, we find that, in the context of dominance-solvable games, higher incentives make subjects more likely to best-respond to their beliefs. Moreover, higher incentives result in more responsive beliefs but not necessarily less biased. We provide evidence that incentives affect effort and that it is effort, and not incentives directly, that accounts for the changes in belief formation. The results support models where, in addition to choice mistakes, players exhibit costly attention.

This dissertation studies econometric analysis of game-theoretic models. I develop novel empirical models and methodologies to facilitate robust and computationally tractable econometric analysis. In Chapter 1, I develop an empirical model for analyzing stable outcomes in the presence of incomplete information. Empirically, many strategic settings are characterized by stable outcomes in which players’ decisions are publicly observed, yet no player takes the opportunity to deviate. To analyze such situations, I build an empirical framework by introducing a novel solution concept that I call Bayes stable equilibrium. The framework allows the researcher to be agnostic about players’ information and the equilibrium selection rule. Furthermore, I show that the Bayes stable equilibrium identified set is always weakly tighter than the Bayes correlated equilibrium identified set; numerical examples show that the shrinkage can be substantial. I propose computationally tractable approaches for estimation and inference and apply the framework to study the strategic entry decisions of McDonald’s and Burger King in the US. In Chapter 2, I study identification and estimation of a class of dynamic games when the underlying information structure is unknown to the researcher. I introduce Markov correlated equilibrium, a dynamic analog of Bayes correlated equilibrium studied in Bergemann and Morris (2016), and show that the set of Markov correlated equilibrium predictions coincides with the set of Markov perfect equilibrium predictions that can arise when the players might observe more signals than assumed by the analyst. I propose an econometric approach for estimating dynamic games with weak assumption on players’ information using Markov correlated equilibrium. I also propose multiple computational strategies to deal with the non-convexities that arise in dynamic environments. In Chapter 3, I propose an extremely fast and simple approach to estimating static discrete games of complete information under pure strategy Nash equilibrium and no assumptions on the equilibrium selection rule. I characterize an identified set of parameters using a set of inequalities that are expressed in terms of closed-form multinomial logit probabilities. The key simplifications arise from using a subset of all identifying restrictions that are particularly easy to handle. Under standard assumptions, the identified set is convex and its projections can be obtained via convex programs. Numerical examples show that the identified set is quite tight. I also propose a simple approach to construct confidence sets whose projections can be obtained via convex programs. I demonstrate the usefulness of the approach using real-world data.

This dissertation is concerned with international financial crisis response and the role that formal and informal international institutions play in this process. It is about understanding the potential of and limits to international crisis governance. It tries to answer three interrelated questions. First, what are the mechanics of international crisis lending? Second, what role can international institutions play in effectively distributing information so that policy responses can be optimized? Finally, what crisis governance structures are best suited to economic and political circumstances of the global financial system? In order to address these questions this dissertation uses a combination of formal (game theory) and informal theory building. It then examines these theoretical arguments using an empirical analysis based on historical survey of crisis response since the late nineteenth century and a comparative case study of crisis management during the Great Depression (1930-31) and the Asian Financial Crisis (1997-98). With regard to the first question, it argues that crisis lending is not simply shaped by the interaction of crisis lenders and borrowers. Ultimately, the terms of a crisis loan are negotiated in a space whose limits are determined by two additional actors: international investors/speculators and domestic political opposition. With regard to the second, it argues that both formal and informal international institutions play an important role in disseminating information and thus policy adaptation and change. However, there are clear limits to what institutions can do. In practice, this means that the goal of creating a crisis-free system is impossible. Finally, with regard to the broad question of crisis governance, it argues that the most effective financial governance system is one build around a partnership between a concert of key financial powers and an international financial institution dedicated to maintaining stability in the financial system.