On the number of blocks required to access the core

The following review has been written for Mathematical Reviews on the paper written by +Sylvain Béal, Eric Rémila, and Philippe Solal.

On the accessibility of the core (Review)

This paper by Yang (2010) belongs to a recent wave of literature that study the core of a cooperative game as a dynamic concept. Sengupta and Sengupta (1996) have shown that from any imputation the core can be accessed by a finite number of blocks. Kóczy (2006) provided an alternative blocking sequence and showed that the number of blocks required is bounded. The present paper relies on the proof of Sengupta and Sengupta by using z-dominance and provides an explicit bound on the length of z-dominance paths: the number of active coalitions, that is, coalitions with a payoff higher than the sum of their members' individual payoffs.

Finessing a point: augmenting the core (Review)

The competition between two election candidates is modelled in a policy space, where the voters are represented by their ideal points and the candidates by their position on the policy. A voter will support the candidate whose programme is closer to his ideal point, using Euclidean distance. The candidate supported by at least q voters, where q is the quota, is elected. For simple majority q is simply the smallest integer that is at least half of the number of voters.

Cooperation to save species

In a recent paper Frank and Sarkar apply game theory to enhance conservation efforts. Their examples include the wild dogs in South Africa, red grouse and raptors in Britain and the conservation of coral reefs near the Philippenes. I find the application thrilling, though the game theory is not completely correct.