Muhamet Yildiz

Waiting to Persuade

I analyze a sequential bargaining model in which players are optimistic about their bargaining power (measured as the probability of making offers), but learn as they play the game. I show that there exists a uniquely predetermined settlement date, such that in equilibrium the players always reach an agreement at that date, but never reach one before it. Given any discount rate, if the learning is sufficiently slow, the players agree immediately. I show that, for any speed of learning, the agreement is delayed arbitrarily long, provided that the players are sufficiently patient. Therefore, although excessive optimism alone cannot cause delay, it can cause long delays if the players are expected to learn.

Bargaining without a common prior-An immediate agreement theorem

In sequential bargaining models without outside options, each players bargaining power is ultimately determined by which player will make an offer and when. This paper analyzes a sequential bargaining model in which players may hold different beliefs about which player will make an offer and when. Excessive optimism about making offers in the future can cause delays in agreement. The main result states that, despite this, if players will remain sufficiently optimistic for a sufficiently long future, then in equilibrium they will agree immediately. This result is also extended to other canonical models of optimism.

Fragility of asymptotic agreement under Bayesian learning

Under the assumption that individuals know the conditional distributions of signals given the payoff-relevant parameters, existing results conclude that as individuals observe infinitely many signals, their beliefs about the parameters will eventually merge. We first show that these results are fragile when individuals are uncertain about the signal distributions: given any such model, vanishingly small individual uncertainty about the signal distributions can lead to substantial (non-vanishing) differences in asymptotic beliefs. Under a uniform convergence assumption, we then characterize the conditions under which a small amount of uncertainty leads to significant asymptotic disagreement.

Finite-Order Implications of any Equilibrium

Present economic theories make a common-knowledge assumption that implies that the first or the second-order beliefs determine all higher order beliefs. We analyze the role of such closing assumptions at finite orders by instead allowing higher orders to vary arbitrarily. Assuming that the space of underlying uncertainty is sufficiently rich, we show that the resulting set of possible outcomes, under an arbitrary fixed equilibrium, must include all outcomes that survive iterated elimination of strategies that are never a strict best reply. For many games, this implies that, unless the game is dominance solvable, every equilibrium will be highly sensitive to higher-order beliefs, and thus economic theories based on such equilibria may be misleading. Moreover, every equilibrium is discontinuous at each type for which two or more actions survive our elimination process.

The Impact of Prior Decisions on Subsequent Valuations in a Costly Contemplation Model

This paper develops and tests a model of how recall of information from past decisions affects subsequent related decisions. A boundedly rational individual has to determine her willingness to pay for a good that she previously considered purchasing at a given price, or provide valuations for a set of goods that she previously ranked in order of preference. The individual is ex ante uncertain about her utility from consumption of the goods and can exert costly cognitive effort to reduce this uncertainty. We show that incorporating information from a prior decision has three primary effects: (a) Valuations are expected to exhibit higher variance---in particular, the spread of valuations between the most and least preferred alternatives increases; (b) decision makers will, in expectation, exert more effort during the valuation phase; and (c) the relative impact of prior decisions on valuation spread increases, the more each attribute contributes to overall utility. The model predictions are then tested in a series of controlled lab experiments.

The Lindahl solution with changing population and resources1

Abstract Studying economies with a single private and a single normal public good, we show that, under Lindahl equilibrium, the adjunction of new agents is beneficial to incumbents if the newcomers bring positive initial endowments, but that otherwise no incumbent will benefit from their adjunction unless his own initial endowment is augmented at the same time. It follows also that manipulation of Lindahl equilibria via destruction or donation of endowment (to fellow incumbents or to newcomers) is ruled out when this equilibrium is single-valued. Normalcy of the public good is shown to be crucial for all these results.

Sequential Bargaining without a Common Prior on the Recognition Process

We analyze a sequential bargaining model, where players are allowed to hold different beliefs about which players will make an offer and when. Excessive optimism about making offers in the future can cause a delay in agreement. Despite this, the main result states that, if players will remain sufficiently optimistic for a sufficiently long future, then in equilibrium they will agree immediately.

Impossibility of a Walrasian Bargaining Solution

Is there a bargaining solution that pays out the Walrasian welfare for exchange economies? We show that there is none, for there are distinct exchange economies whose Walrasian equilibrium welfare payoffs disagree but which define the same bargaining problem and should have hence determined the same bargaining solution and its payoffs.

Communication with unknown perspectives

Consider a group of individuals with unobservable perspectives (subjective prior beliefs) about a sequence of states. In each period, each individual receives private information about the current state and forms an opinion (a posterior belief). She also chooses a target individual and observes the targets opinion. This choice involves a trade‐off between well‐informed targets, whose signals are precise, and well‐understood targets, whose perspectives are well known. Opinions are informative about the targets perspective, so observed individuals become better understood over time. We identify a simple condition under which long‐run behavior is history independent. When this fails, each individual restricts attention to a small set of experts and observes the most informed among these. A broad range of observational patterns can arise with positive probability, including opinion leadership and information segregation. In an application to areas of expertise, we show how these mechanisms generate own field bias and large field dominance.

Invariance to representation of information

Under weak assumptions on the solution concept, I construct an invariant selection across all finite type spaces, in which the types with identical information play the same action. Along the way, I establish an interesting lattice structure for finite type spaces and construct an equilibrium on the space of all finite types.