Εφαρμογές της θεωρίας παιγνίων στον αναλογισμό
Applications of game theory in actuarial science
Λάμα, Αικατερίνη Δ.
The present MSc thesis deals with the presentation of basic concepts and techniques of Game Theory and especially with their application in problem solving related to Actuarial Science and more specifically to Insurance. Every problem is represented by a game where the players either have a conflict of interest (zero-sum games) or by a cooperation where players share common interest (cooperative games). The players choose from the available strategies, the one that will maximize the payoff function when negotiating profit or respectively minimizing the loss in the case of dealing with losses. As far as zero sum games are concerned, the profit of the one player is considered equal to the loss for the other. Therefore, the sum of these two payoffs equals zero. The name of this family of games is due to the aforementioned fact. In zero-sum games an extremely important property, is that if a solution yields for a player its best payoff given his opponent’s choice, it is characterized as Nash equilibrium. In the present thesis, several methods are presented and clarifying examples are given. The study of cooperative games shows that players participate in a cooperation with the motive of gaining better payoffs than the ones gained when they stand alone. In this category of games what really matters is the allocation of the total payoff so that the individual payoff gained by each player is proportional to the participation cost he paid (since in these games, someone can invest more or less money than somebody else).