Natural models for many economic issues are games of incomplete information, where each player’s payoff depends on his or her actions, and those of others, as well as on some unknown economic fundamentals. Examples of currency attacks, bank runs, and liquidity crises include many that emphasise the importance of individuals’.
uncertainty about the actions of other players As a result of the actions of other players, The decision-maker must take into account the beliefs of those involved in the situation.
of the other players’ beliefs In light of the venerable contribution, we can that rational behaviour in such environments not only follows Harsanyi’s (1967–1968)
economic fundamentals, but also on the beliefs of economic agents depend on higher-order beliefs, such as players’ beliefs about what other players believe.
player perceptions of what other players perceive of their perceptions of what other players perceive well as other things. It has been demonstrated by Mertens and Zamir (1985) that
the description of a player’s “type” in an incomplete informational context full belief hierarchy in all its levels, including the game. Analyzing optimal strategic behaviour in the context of the given situation is a good starting point.
even though there are an infinite number of belief systems, such an analysis is extremely valuable. an intractable problem for both players and analysts alike
in general. As a result, identifying strategic environments with gaps is an important consideration. a level of detail sufficient to capture the importance of higher-order functions
beliefs in economic settings that are simple enough to be analysed. Carlsson and van Damme (1993a) introduced the concept of “global games” to the academic community.
one of these environments The following three words sum up the current state of the economy: a small signal of the state is observed by each player with their small-signal
the volume of sound. If noise technology is common knowledge, then we can assume each player’s signal generates beliefs about the fundamentals among the players.
beliefs about other players’ fundamental beliefs, and so on. Our goal is to serve the community. model-based reasoning and global game theory will be explained in this paper
on economic issues and how it relates to other areas of study and strategic analysis of higher-order beliefs in general.
A recurring theme is that players don’t need to use extremely sophisticated reasoning to take higher-order beliefs seriously. For binary action continuum player games with strategic complementarities, in which each player has the same payoff function, we present our benchmark result in Section 2.
Assuming that each player has the same belief about the proportion of his opponents who will take a particular action, there exists an optimal equilibrium in global games.
Because of this, each player is advised to hypothesise that other players will choose a particular action based on a random variable distributed uniformly over the unit interval when confronted with some information about the underlying state of the world. According to Laplace’s (1824) suggestion that one should apply a uniform before unknown events from “the principle of insufficient reason,” we call such beliefs (and the actions that they elicit) Laplacian.
This conclusion has the striking feature of reconciling Harsanyi’s fully rational view of optimal behaviour in incomplete information settings with the dissenting view of Kadane and Larkey (1982) and others that rational behaviour in games should only imply that each player chooses an optimal action in light of his subjective beliefs about other players’ behaviour, without deducing his subjective beliefs as part of the theory.
This is a remarkable conclusion. There is no contradiction with Harsanyi’s view that players should deduce rational beliefs about others’ behaviour in incomplete information settings if we let those subjective beliefs be the agnostic Laplacian prior.
Such an analysis is important, but it fails to do justice to the logic inherent in Harsanyi’s programme because it fails to capture the subtle reasoning of the players. As a result, we now have a heuristic device that allows economists to determine the actual outcomes of games like these, and this opens up the door to a more systematic analysis of economic problems that might otherwise seem intractable.
The debate over self-fulfilling beliefs and multiple equilibria is an example of this. There is an apparent indeterminacy if one set of beliefs motivates actions that produce the state of affairs predicted by those beliefs, while another set of self-fulfilling beliefs produces quite different outcomes.
Both sets of beliefs are supported by subsequent events and follow a logical path consistent with the known features of the economy. Without knowing how the initial beliefs are formed, it’s impossible to predict what will happen.
According to Morris and Shin, 2000, the apparent indeterminacy of beliefs can be seen as a result of two modelling assumptions introduced to simplify the theory in models with multiple equilibria. To begin with, the economic fundamentals are assumed to be widely known.
Second, in a state of equilibrium, economic agents are assumed to be confident in the behaviour of their counterparts. To be comprehensible, both assumptions are made, but they accomplish far more than that when agents’ actions and beliefs are in perfect sync, multiple equilibrium states can emerge.
Global games, on the other hand, allow theorists to more realistically model information and thus escape this shackle. More importantly, global games enable modellers to determine which set of self-fulfilling beliefs will prevail in equilibrium through the heuristic device of Laplacian actions.
There are more important issues at stake than just the satisfaction of finding a unique result in a game. Economic agents may be persuaded to take certain actions because they believe others are doing so, thanks to global games.
As a result, external circumstances may compel agents to take inefficient actions, even if doing so would benefit everyone. Examples include bank runs and financial crises We can make a crucial distinction between whether equilibrium outcomes can be inefficient and whether there is a single equilibrium outcome.
Therefore, global games are more than just theoretically interesting. Encouraging debate on important economic issues is possible because of them. Applications that use global games to model economic problems are discussed in Section 2.3.
New research directions are opened up as a result of global competition.
Public information is critical in situations where there is a degree of cooperation between the players. Numerous anecdotes show that public information has a greater impact than private information in a variety of contexts. Even when central bankers simply state the obvious or reaffirm well-known policy stances, the financial markets seem to “overreact.
” With the help of global games, the mystery of these cases becomes less baffling after a closer examination. Market participants may be more interested in how other market participants will react to the news if they are worried about how it will be received by the rest of the market.
For strategic reasons, it provides useful information about what other market participants are thinking.
An overreaction, in this case, would be completely rational and determined by the equilibrium logic inherent in a game with incomplete information. Section 3 goes into greater depth on each of these concerns.
One way to think of global games is as a special case of equilibrium selection by perturbations in action. Higher-order beliefs can be constructed using a wide range of perturbations, making the set particularly rich. In Section 4, we go a little deeper into the properties of general global games, rather than just those with binary action sets.
How global games relate to other concepts of equilibrium refinement and what kind of perturbation is implicit in global games are topics of discussion here. It is possible to separate two properties of global games using the general framework. The first characteristic is that the game has a unique outcome.
The second, more subtle, the question is how the underlying information structure and the noise in the players’ signals influence the unique outcome.
Some outcomes are indeed influenced by specific information structures, but this is not always the case. players’ signal noise is selected and where this outcome can withstand this form of noise.
The “robustness to incomplete information” theory developed by Kajii and Morris (1997) is the key to this property. Higher-order beliefs and global games are also discussed in the larger theoretical literature.