Working Paper
1. The Economics of Linguistic Diversity: Theory and Experiment (JMP; with Leanna Mitchell)
In the first part of the paper, we propose a theory that relates linguistic diversity (i.e. the number of languages within a region) to cooperative and competitive incentives in a game theoretic framework. In our model, autonomous groups interact periodically in games that represent either cooperation, competition, or no interaction. Language matters in these interactions because language common to a pair of groups facilitates cooperation; whereas language unique to one group affords that group an advantage in competitions against other groups. The relative frequency of cooperation and conflict in a region provide incentives for each group to modify their own language, and therefore leads to changes in linguistic diversity over time. Hence, a main contribution of our paper is to model strategic incentives as a cause of linguistic divergence. Our model predicts that higher frequency of cooperative interactions relative to competitive ones reduces a region's linguistic diversity. In the second part of the paper, we test our theory in a laboratory environment. Pairs of subjects endowed with a set of vocabulary interact repeatedly in a series of underlying games where they use the words in their vocabulary to signal their intended action in the game. The games are either coordination or zero-sum. As the subjects are allowed to modify their vocabulary by learning and creating new words, we observe that, over time, vocabularies in coordination games tend to converge, while in zero-sum games, the vocabularies experience constant pressure to diverge.
2. The Evolutionary Foundation of the Preference for Surprise
This paper uses a principal-agent model to provide an evolutionary explanation of the preference for surprise, where surprise is measured by the Kullback-Leibler divergence between the prior and posterior. The principal in our model is interpreted as the blind force of evolution, who tries to maximize the fitness of the agent—generations of human beings—whose objective is to maximize a utility function designed by the principal. In a typical period, the agent first decides how many signals about the state to purchase, and then he chooses an action that, together with the state, determines his fitness. The variance of the signal distribution changes across time, but the agent is predisposed to believe that it is the same as the one in the previous period. I show that if the variance of the signal distribution decreases at a sufficiently fast rate over time, it is evolutionarily optimal for the utility function to include a component that rewards surprises.
Work in Progress
1. Efficient Vocabulary with Homonyms in a Sender-Receiver Game
Homonymy is the phenomenon that one word is associated with more than one meaning. This paper examines the efficiency of a vocabulary that embodies homonyms. Specifically, I consider a sender-receiver game in which the two players' interests are aligned; the sender needs to communicate a privately observed object to the receiver using a commonly understood vocabulary; the receiver then makes a decision that determines the utility of both. The efficiency of a vocabulary is measured by its ability to maximize the agents' ex ante expected utility. I show that, when the object space is one-dimensional, an efficient vocabulary must be such that words refer to connected, non-overlapping intervals of objects. The condition characterizing the optimal length of the intervals is also derived.
2. Public Protection of Privacy: An Economic Perspective
This paper is interested in the question: When, if at all, should the protection of privacy be publicly provided? To answer the question, this paper focuses on the public goods nature of information, and the interactions between the efforts to gather and to conceal private information. Specifically, a model is proposed in which a privately informed individual interacts with a firm that tries to gather and use that private information. The key feature of the model is a measure of externality that enters positively into the firm's preference and negatively into the individual's. The externality measure, a function of how much private information is revealed, represents the firm's gain from being better informed. For example, this could be its gain from a more effective price discriminating strategy, or from the resale of the private information to some other company. The firm gains at the expense of the individual, who bears the external cost of the firm. Preliminary analysis suggests that the optimal privacy policy depends largely on the relative magnitudes between the individual's marginal gain from trade and the marginal externality imposed by the firm's use of her private information.