What is a core allocation?

● The core of an exchange economy is the set of feasible allocations which cannot be improved upon (or blocked) by any coalition of agents. ● For 2 agent-exchange economies core allocations are those satisfying individual rationality and Pareto efficiency.

How do I know my core allocation?

Quote: So nevertheless we can use margin rate of substitution a equals marginal rate of substitution b to find uh pretty optimal allocations uh because uh i mean you'll see.

What is the core allocation in general equilibrium?

The core in general equilibrium theory



Graphically, and in a two-agent economy (see Edgeworth Box), the core is the set of points on the contract curve (the set of Pareto optimal allocations) lying between each of the agents’ indifference curves defined at the initial endowments.

Where is the core in Edgeworth box?

Quote:
Quote: So the total number of units of good-y Alice has 4 units and Kevin has six. So we have 10 units of good-y. And that will describe the width of the Edgeworth box.

How do you find the core of a game?

Quote:
Quote: Putting these two things together it's possible to show that in a simple game the core is empty. Exactly when there is no veto player.

What are cores in economics?

The core of an economy consists of those states of the economy that no group of agents can improve upon. A group of agents can improve upon a state of the economy if the group, by using the means available to it, can make each member of that group better off, regardless of the actions of the agents outside that group.

What is the core of a cooperative game?

1 Introduction. The core is the most widely used solution concept in cooperative game theory. It is the set of all allocations of the worth of the grand coalition that prevent any other coalition from forming and standing alone.

Is competitive equilibrium in the core?

That competitive equilibrium is in the core occurs also in private-goods- exchange economies. However, in exchange economies with perfectly divisible goods and convex preferences, a core state of the economy may not be an equilibrium, unlike club economies, where every core state of the economy is an equilibrium.

What is a convex game?

In game theory, a convex game is one in which the incentives for joining a coalition increase as the coalition grows. This paper shows that the core of such a game — the set of outcomes that cannot be improved on by any coalition of players — is quite large and has an especially regular structure.

Does the Shapley value lie in the core?

Every convex game has a nonempty core. In every convex game, the Shapley value is in the core.

How is Shapley value calculated?

The solution, known as the Shapley value, has a nice interpretation in terms of expected marginal contribution. It is calculated by considering all the possible orders of arrival of the players into a room and giving each player his marginal contribution.

How do you read Shapley values?

The interpretation of the Shapley value is: Given the current set of feature values, the contribution of a feature value to the difference between the actual prediction and the mean prediction is the estimated Shapley value.

What are Shap values?

SHAP values (SHapley Additive exPlanations) is a method based on cooperative game theory and used to increase transparency and interpretability of machine learning models.

What is Shapley regression?

Shapley Value regression is a technique for working out the relative importance of predictor variables in linear regression. Its principal application is to resolve a weakness of linear regression, which is that it is not reliable when predicted variables are moderately to highly correlated.

What is Python Shap?

SHAP is a Python library that uses Shapley values to explain the output of any machine learning model.

What is Shap and lime?

LIME and SHAP are two popular model-agnostic, local explanation approaches designed to explain any given black-box classifier. These methods explain individual predictions of any classifier in an interpretable and faithful manner, by learning an interpretable model (e.g., linear model) locally around each prediction.

Which is better lime or Shap?

I use LIME to get a better grasp of a single prediction. On the other hand, I use SHAP mostly for summary plots and dependence plots. Maybe using both will help you to squeeze out some additional information.

Is Shap deterministic?

Non-deterministic – KernelExplainer’s SHAP values are estimated, with variance introduced both by the coalition sampling method and the background dataset selection.

Can lime be used for regression?

There exist a method called LIME, a novel explanation technique that explains the predictions of any classifier or regression problem in an interpretable and faithful manner, by learning an interpretable model locally around the prediction.

What is intercept in lime?

At the top, the intercept of the linear model created by LIME is presented, followed by the local prediction generated by the linear model, and the actual prediction from our model (this is the result of setting verbose in the explainer to True).

Why is lime unstable?

Why does LIME suffer from Instability? Because of the Generation Step. Remember that LIME generates x values all over the ℝᵖ space of the X variables of the dataset (explained here). The points are generated at random, so each call to LIME creates a different dataset.

How does lime library work?

LIME takes an individual sample and generates fake dataset based on it. It then permutes the fake dataset. It then calculates distance metrics (or similarity metric) between permuted fake data and original observations. This helps to understand how similar permuted fake data is compared to original data.

What is Python lime?

What is LIME? The acronym LIME stands for Local Interpretable Model-agnostic Explanations. The project is about explaining what machine learning models are doing (source). LIME supports explanations for tabular models, text classifiers, and image classifiers (currently).

Why should I trust you explaining Thepredictions of any classifier?

Although an explanation of a single prediction provides some understanding into the reliability of the classifier to the user, it is not sufficient to evaluate and assess trust in the model as a whole. We propose to give a global understanding of the model by explaining a set of individual instances.