An Entropy-Based Information Sharing Rule for Asymmetric Information Economies
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Claudia Meo
Abstract
The possibility to compare information partitions is investigated for economies with asymmetric information. First, we focus on two potentially suitable instruments, the Boylan distance and the entropy, and show that the former does not fit the purpose. Then, we use the entropy associated with the information partition of each trader to construct a partially endogenous rule which regulates the information sharing process among traders. Finally, we apply this rule to some examples and analyze its impact on two cooperative solutions: the core and the coalition structure value.
We collect here some calculations relative to Example 2 provided in Section 2.
Let us consider the set S = {s 1, s 2, s 3} formed by three states of nature s 1, s 2, and s 3 that occur with probabilities q 1, q 2, q 3, respectively, with q 1 + q 2 + q 3 = 1 and q 1 > q 2 > q 3.
The initial information of each trader is displayed below:
Let first compute and compare among themselves the Boylan distances
The algebras generated by these partitions are given by:
It holds that:
Since q
1 > q
2 > q
3, it cannot be the case that
On the other side, we have:
In all cases, it is true that
Let us compare now
It holds that:
Hence,
Consider now the entropies associated with partitions P 1, P 2, and P 3.
It holds that:
We want to prove that the following implication is true:
Consider the function
For the case
If
Finally, since
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Articles in the same Issue
- Frontmatter
- Research Articles
- On the Choice of Liability Rules
- Social Image Concern and Reference Point Formation
- Extreme Parties and Political Rents
- On the Observational Implications of Knightian Uncertainty
- Functions with Linear Price Elasticity for Forecasting Demand and Supply
- Foreign Direct Investment and Crime Linkage: Drug Traffic and Kidnapping
- Absence of Envy among “Neighbors” Can Be Enough
- Financial Integration, Savings Gluts, and Asset Price Booms
- Social Coordination and Network Formation in Bipartite Networks
- A Choice Model of University Endowments Governance
- Envy Manipulation at Work
- An Entropy-Based Information Sharing Rule for Asymmetric Information Economies
- Notes
- A Comment on Arrow’s Impossibility Theorem
Articles in the same Issue
- Frontmatter
- Research Articles
- On the Choice of Liability Rules
- Social Image Concern and Reference Point Formation
- Extreme Parties and Political Rents
- On the Observational Implications of Knightian Uncertainty
- Functions with Linear Price Elasticity for Forecasting Demand and Supply
- Foreign Direct Investment and Crime Linkage: Drug Traffic and Kidnapping
- Absence of Envy among “Neighbors” Can Be Enough
- Financial Integration, Savings Gluts, and Asset Price Booms
- Social Coordination and Network Formation in Bipartite Networks
- A Choice Model of University Endowments Governance
- Envy Manipulation at Work
- An Entropy-Based Information Sharing Rule for Asymmetric Information Economies
- Notes
- A Comment on Arrow’s Impossibility Theorem
