Speaker:     Arkadii Slinko
Affiliation: The University of Auckland
Title:       Simple games: what are the questions?
Date:        Monday, 11 May 2009
Time:        3:00 pm
Location:    Room 401

A simple game consists of a finite set of objects (players) and some subsets (coalitions) are marked as winning and the rest are therefore losing. The monotonicity condition is imposed which says that a superset of a winning coalition is winning. Simple games are used to model the distribution of power in a body of agents, say which coalitions of countries can pass a motion in the UN Security Council. A simple game also may model the access structure of a secret-sharing scheme – in this case winning coalitions are those who authorised to know the secret.

In this talk I will introduce some basic concepts and formulate a number of open questions. Most are concerned either with finding conditions under which the power of a player can be expressed by a real number or conditions under which  all players can be ranked in accordance to their power.

The concept of a trading transform will be introduced and several numerical functions which characterise the game will be introduced too. The emphasis will be on games that have extremal values of those parameters. Gabelman games will be considered in particular.

The talk will not present anything new. A week later Tatyana Gvozdeva will discuss some new results.

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