# Essays on information economics and game theory

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This dissertation consists of four chapters on the topic of information economics and game theory. I investigate Bayesian inference and persuasion restricted by a bureaucratic norm, strategic experimentation amidst private information, multiple-buyer bargaining influenced by concave utility, and cheap talk in contexts involving naïve players. By leveraging rigorous theoretical models, I aim to uncover the underlying mechanics of strategic interactions and the pivotal role of information dissemination in diverse economic contexts. Chapter 1 looks at an information design problem. In this model, a developer seeks to persuade a welfare-maximizing bureaucrat to award a contract to her. The official has a short tenure, and his successor's decisions are subject to a bureaucratic norm: an official's decision must be based on evidence that is either recorded by his predecessor or presented to him. Thus, Bayesian inference is restricted when the first official fails to record evidence. The first official can exploit this and induce the developer to conduct more informative experiments. I focus on parameter values where the static values of persuasion are zero to the bureaucracy and strictly positive for the developer. I show that there are two possibilities in the dynamic game. Either the developer conducts a more informative experiment and the official decides immediately, so that social welfare is greater. Or there is delay, where the cost of delay to the bureaucracy offsets the benefits of a more informed decision. In either case, the developer is worse off compared to static persuasion. With unrestricted inference, there exists an intuitive PBE that replicates the static outcome, so that the bureaucratic norm may increase social welfare and never reduces it. Chapter 2 studies a symmetric two-player game of strategic experimentation where both players have private information. I find that two-sided private information improves welfare, both at the ex ante and interim stages, by mitigating the free-rider problem. Furthermore, in some states of the world, there may be over-experimentation, i.e., players may experiment more than the social planner would under complete information. Chapter 3 is joint work with David Sibley. This chapter looks at a situation where s seller bargains with two buyers to make a deal with each of them, using an alternating-offer protocol (“AO”). The bargaining begins with one buyer, with the second entering at a future date. The seller has a concave utility function defined over total payments from buyers, so the two bargains affect each other. When the seller’s utility function exhibits decreasing absolute risk aversion, a higher price in the first bargain increases the price in the subsequent bargain. Even if two players are identical except for the arrival date, they will make different payments to the seller. The shape of the utility function and the arrival date determine whether there is a first or second-mover advantage. Although agreements in our model are reached on different dates, the usual limit payoffs for AO do not approach those of the sequential Nash bargaining solution. Finally, we extend the model to a vertical market, in which an upstream seller supplies downstream buyers with critical input. These buyers compete with each other in the downstream market. We find that, even if the buyers are symmetric Cournot competitors, the equilibrium of the model is asymmetric, with one buyer paying more than the other. With some utility functions of the seller, prior to entry by the second firm, the price set by the incumbent can decrease with the increased expected entry dates. Standard vertical models would not predict this. Chapter 4 endogenizes the probability of the receiver blindly believing in the sender by allowing the sender to increase this naivety probability at a cost, based on the cheap talk model with naive receivers who take the message at face value in Ottaviani and Squintani (2006). When the probability chosen is observed by receivers, receivers can benefit from this ability of the sender, and a fully revealing equilibrium is possible. But this ability of the sender damages information transmission and removes the fully revealing equilibrium if the probability is not observable. These results can explain how information is conveyed in advertising when the advertiser can design the content of advertising as well as use extra expenditure to affect the consumers' gullibility.