Muhamet Yildiz | Massachusetts Institute of Technology (MIT) (original) (raw)

Papers by Muhamet Yildiz

Research Papers in Economics, Aug 11, 2004

In some games, the impact of higher-order uncertainty is very large, implying that present econom... more In some games, the impact of higher-order uncertainty is very large, implying that present economic theories may be misleading as these theories assume common knowledge of the type structure after specifying the first or the second orders of beliefs. Focusing on normal-form games in which the players' strategy spaces are compact metric spaces, we show that our key condition, called "global stability under uncertainty," implies a variety of results to the effect that the impact of higher-order uncertainty is small. Our central result states that, under global stability, the maximum change in equilibrium strategies due to changes in players' beliefs at orders higher than k is exponentially decreasing in k. Therefore, given any need for precision, we can approximate equilibrium strategies by specifying only finitely many orders of beliefs.

This paper develops and tests a model of how recall of information from past decisions affects su... more 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.

It is a common fear in many countries that ideological parties will come to power through electio... more It is a common fear in many countries that ideological parties will come to power through elections but will implement extreme policies or even end the democratic regime. Many countries cope with this problem by overriding the election results when such parties are elected. In a two-period model, we demonstrate that the alternative approach of containing these parties within the democratic system is more effective. In equilibrium, if an ideological party (IP) comes to power in the first period, depending on its type (i.e., its extremity), it either reveals its type or chooses a moderate policy in order to be elected again. We show that, as the probability of state's intervention in the next elections increases, IP's policy becomes more extreme: fewer types choose to moderate and, and when they do, they moderate less. This hurts the median voter. It also remains true when the probability of intervention depends on IP's policy. We further show that from the median voter...

Abstract. We show that in any game that is continuous at in…nity, if a plan of action ai is ratio... more Abstract. We show that in any game that is continuous at in…nity, if a plan of action ai is rationalizable for a type ti, then there are perturbations of ti for which following ai for an arbitrarily long future is the only rationalizable plan. One can pick the perturbation from a nite type space with common prior. As an application we prove an unusual folk theorem: Any individually rational and feasible payo ¤ is the unique rationalizable payo ¤ vector for some perturbed type pro…le. JEL Numbers: C72, C73. 1.

Abstract. Towards developing a theory of systematic biases about strate-gies, I analyze strategic... more Abstract. Towards developing a theory of systematic biases about strate-gies, I analyze strategic implications of a particular bias: wishful thinking about the strategies. Considering canonical state spaces for strategic uncer-tainty, I identify a player as a wishful thinker at a state if she hopes to enjoy the highest payoff that is consistent with her information about the others' strategies at that state. I develop a straightforward elimination process that characterizes the strategy profiles that are consistent with wishful thinking, mutual knowledge of wishful thinking, and so on. Every pure-strategy Nash equilibrium is consistent with common knowledge of wishful thinking. For generic two-person games, I further show that the pure Nash equilibrium strategies are the only strategies that are consistent with common knowl-edge of wishful thinking, providing an unusual epistemic characterization for equilibrium strategies. 1.

Members of different social groups often hold widely divergent public beliefs regarding the natur... more Members of different social groups often hold widely divergent public beliefs regarding the nature of the world in which they live. We develop a model that can accommodate such public disagreement, and use it to explore questions concerning the aggregation of distributed information and the consequences of social integration. The model involves heterogeneous priors, private information, and repeated communication until beliefs become public information. We show that when priors are correlated, all private information is eventually aggregated and public beliefs are identical to those arising under observable priors. When priors are independently distributed, however, some private information is never revealed and the expected value of public disagreement is greater when priors are unobservable than when they are observable. If the number of individuals is large, communication breaks down entirely in the sense that disagreement in public beliefs is approximately equal to disagreement ...

Given any two-person economy, we consider a simple alternating-offer bargaining game with complet... more Given any two-person economy, we consider a simple alternating-offer bargaining game with complete information where the agents offer prices. We provide conditions under which the outcomes of all stationary subgame-perfect equilibria converge to the Walrasian equilibrium (the price and the allocation) as the agents become infinitely patient. Therefore, price-taking behavior can be achieved with only two agents.

Econometrica, 2016

Consider a group of individuals with unobservable perspectives (subjective prior beliefs) about a... more 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 target's 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 target's 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.

In the reputation literature, players have commitment types which represent the possibility that ... more In the reputation literature, players have commitment types which represent the possibility that they do not have standard payos but instead are constrained to follow a particular plan. In this paper, we show that arbitrary commitment types can emerge from incomplete information about the stage payos. In particular, any …nitely repeated game with commitment types is strategically equivalent to a standard …nitely repeated game with incomplete information about the stage payos, such that the types with identical solutions have almost identical prior probability in two games. Then, classic reputation results can be achieved with uncertainty concerning only the stage payos.

The RAND Journal of Economics

SSRN Electronic Journal, 2000

A coordination game with incomplete information is played through time. In each period, payoffs d... more A coordination game with incomplete information is played through time. In each period, payoffs depend on a fundamental state and an additional idiosyncratic shock. Fundamentals evolve according to a random walk where the changes in fundamentals (namely common shocks) have a fat tailed distribution. We show that majority play shifts either if fundamentals reach a critical threshold or if there are large common shocks, even before the threshold is reached. The fat tails assumption matters because it implies that large shocks make players more unsure about whether their payoffs are higher than others. This feature is necessary for large shocks to matter.

It is a common fear in many countries that ideological parties will come to power through electio... more It is a common fear in many countries that ideological parties will come to power through elections but will implement extreme policies or even end the democratic regime. Many countries cope with this problem by overriding the election results when such parties are elected. In a two-period model, we demonstrate that the alternative approach of containing these parties within the democratic system is more effective. In equilibrium, if an ideological party (IP) comes to power in the first period, depending on its type (i.e., its extremity), it either reveals its type or chooses a moderate policy in order to be elected again. We show that, as the probability of state's intervention in the next elections increases, IP's policy becomes more extreme: fewer types choose to moderate and, and when they do, they moderate less. This hurts the median voter. It also remains true when the probability of intervention depends on IP's policy. We further show that from the median voter's perspective, the optimal intervention scheme can be implemented by committing not to intervene and adjusting election times appropriately. That is, elections are a better incentive mechanism than the threat of a coup. Our results are extended to a model in which IP can try a coup.

These notes are somewhat incomplete-they do not include some of the topics covered in the class. ... more These notes are somewhat incomplete-they do not include some of the topics covered in the class. I will add the notes for these topics soon. † Some parts of these notes are based on the notes by Professor Daron Acemoglu, who taught this course before.

One of the most robust empirical regularities in bargaining is the phenomenon called the deadline... more One of the most robust empirical regularities in bargaining is the phenomenon called the deadline e¤ ect: the agreement is delayed until the very last minute before the deadline. In this paper we show that optimism about future bargaining power naturally generates a deadline e¤ect. Optimism before elections generates a similar delay, which we refer to as the election e¤ ect. We further show that deadline and election e¤ects are special cases of a more general phenomenon, the durability e¤ ect, which applies when the discipline on players'beliefs about bargaining prospects dramatically increases over a short period of time.

We consider a general class of games that have been used to model many economic problems where pl... more We consider a general class of games that have been used to model many economic problems where players' sentiments are believed to play an important role. Dropping the common-prior assumption, we identify the relevant notion of sentiments for strategic behavior in these games. This notion is tied to how likely a player thinks that some other player has a more

Research Papers in Economics, Aug 11, 2004

In some games, the impact of higher-order uncertainty is very large, implying that present econom... more In some games, the impact of higher-order uncertainty is very large, implying that present economic theories may be misleading as these theories assume common knowledge of the type structure after specifying the first or the second orders of beliefs. Focusing on normal-form games in which the players' strategy spaces are compact metric spaces, we show that our key condition, called "global stability under uncertainty," implies a variety of results to the effect that the impact of higher-order uncertainty is small. Our central result states that, under global stability, the maximum change in equilibrium strategies due to changes in players' beliefs at orders higher than k is exponentially decreasing in k. Therefore, given any need for precision, we can approximate equilibrium strategies by specifying only finitely many orders of beliefs.

This paper develops and tests a model of how recall of information from past decisions affects su... more 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.

It is a common fear in many countries that ideological parties will come to power through electio... more It is a common fear in many countries that ideological parties will come to power through elections but will implement extreme policies or even end the democratic regime. Many countries cope with this problem by overriding the election results when such parties are elected. In a two-period model, we demonstrate that the alternative approach of containing these parties within the democratic system is more effective. In equilibrium, if an ideological party (IP) comes to power in the first period, depending on its type (i.e., its extremity), it either reveals its type or chooses a moderate policy in order to be elected again. We show that, as the probability of state's intervention in the next elections increases, IP's policy becomes more extreme: fewer types choose to moderate and, and when they do, they moderate less. This hurts the median voter. It also remains true when the probability of intervention depends on IP's policy. We further show that from the median voter...

Abstract. We show that in any game that is continuous at in…nity, if a plan of action ai is ratio... more Abstract. We show that in any game that is continuous at in…nity, if a plan of action ai is rationalizable for a type ti, then there are perturbations of ti for which following ai for an arbitrarily long future is the only rationalizable plan. One can pick the perturbation from a nite type space with common prior. As an application we prove an unusual folk theorem: Any individually rational and feasible payo ¤ is the unique rationalizable payo ¤ vector for some perturbed type pro…le. JEL Numbers: C72, C73. 1.

Abstract. Towards developing a theory of systematic biases about strate-gies, I analyze strategic... more Abstract. Towards developing a theory of systematic biases about strate-gies, I analyze strategic implications of a particular bias: wishful thinking about the strategies. Considering canonical state spaces for strategic uncer-tainty, I identify a player as a wishful thinker at a state if she hopes to enjoy the highest payoff that is consistent with her information about the others' strategies at that state. I develop a straightforward elimination process that characterizes the strategy profiles that are consistent with wishful thinking, mutual knowledge of wishful thinking, and so on. Every pure-strategy Nash equilibrium is consistent with common knowledge of wishful thinking. For generic two-person games, I further show that the pure Nash equilibrium strategies are the only strategies that are consistent with common knowl-edge of wishful thinking, providing an unusual epistemic characterization for equilibrium strategies. 1.

Members of different social groups often hold widely divergent public beliefs regarding the natur... more Members of different social groups often hold widely divergent public beliefs regarding the nature of the world in which they live. We develop a model that can accommodate such public disagreement, and use it to explore questions concerning the aggregation of distributed information and the consequences of social integration. The model involves heterogeneous priors, private information, and repeated communication until beliefs become public information. We show that when priors are correlated, all private information is eventually aggregated and public beliefs are identical to those arising under observable priors. When priors are independently distributed, however, some private information is never revealed and the expected value of public disagreement is greater when priors are unobservable than when they are observable. If the number of individuals is large, communication breaks down entirely in the sense that disagreement in public beliefs is approximately equal to disagreement ...

Given any two-person economy, we consider a simple alternating-offer bargaining game with complet... more Given any two-person economy, we consider a simple alternating-offer bargaining game with complete information where the agents offer prices. We provide conditions under which the outcomes of all stationary subgame-perfect equilibria converge to the Walrasian equilibrium (the price and the allocation) as the agents become infinitely patient. Therefore, price-taking behavior can be achieved with only two agents.

Econometrica, 2016

Consider a group of individuals with unobservable perspectives (subjective prior beliefs) about a... more 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 target's 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 target's 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.

In the reputation literature, players have commitment types which represent the possibility that ... more In the reputation literature, players have commitment types which represent the possibility that they do not have standard payos but instead are constrained to follow a particular plan. In this paper, we show that arbitrary commitment types can emerge from incomplete information about the stage payos. In particular, any …nitely repeated game with commitment types is strategically equivalent to a standard …nitely repeated game with incomplete information about the stage payos, such that the types with identical solutions have almost identical prior probability in two games. Then, classic reputation results can be achieved with uncertainty concerning only the stage payos.

The RAND Journal of Economics

SSRN Electronic Journal, 2000

A coordination game with incomplete information is played through time. In each period, payoffs d... more A coordination game with incomplete information is played through time. In each period, payoffs depend on a fundamental state and an additional idiosyncratic shock. Fundamentals evolve according to a random walk where the changes in fundamentals (namely common shocks) have a fat tailed distribution. We show that majority play shifts either if fundamentals reach a critical threshold or if there are large common shocks, even before the threshold is reached. The fat tails assumption matters because it implies that large shocks make players more unsure about whether their payoffs are higher than others. This feature is necessary for large shocks to matter.

It is a common fear in many countries that ideological parties will come to power through electio... more It is a common fear in many countries that ideological parties will come to power through elections but will implement extreme policies or even end the democratic regime. Many countries cope with this problem by overriding the election results when such parties are elected. In a two-period model, we demonstrate that the alternative approach of containing these parties within the democratic system is more effective. In equilibrium, if an ideological party (IP) comes to power in the first period, depending on its type (i.e., its extremity), it either reveals its type or chooses a moderate policy in order to be elected again. We show that, as the probability of state's intervention in the next elections increases, IP's policy becomes more extreme: fewer types choose to moderate and, and when they do, they moderate less. This hurts the median voter. It also remains true when the probability of intervention depends on IP's policy. We further show that from the median voter's perspective, the optimal intervention scheme can be implemented by committing not to intervene and adjusting election times appropriately. That is, elections are a better incentive mechanism than the threat of a coup. Our results are extended to a model in which IP can try a coup.

These notes are somewhat incomplete-they do not include some of the topics covered in the class. ... more These notes are somewhat incomplete-they do not include some of the topics covered in the class. I will add the notes for these topics soon. † Some parts of these notes are based on the notes by Professor Daron Acemoglu, who taught this course before.

One of the most robust empirical regularities in bargaining is the phenomenon called the deadline... more One of the most robust empirical regularities in bargaining is the phenomenon called the deadline e¤ ect: the agreement is delayed until the very last minute before the deadline. In this paper we show that optimism about future bargaining power naturally generates a deadline e¤ect. Optimism before elections generates a similar delay, which we refer to as the election e¤ ect. We further show that deadline and election e¤ects are special cases of a more general phenomenon, the durability e¤ ect, which applies when the discipline on players'beliefs about bargaining prospects dramatically increases over a short period of time.

We consider a general class of games that have been used to model many economic problems where pl... more We consider a general class of games that have been used to model many economic problems where players' sentiments are believed to play an important role. Dropping the common-prior assumption, we identify the relevant notion of sentiments for strategic behavior in these games. This notion is tied to how likely a player thinks that some other player has a more